Millennium challenges — computed status

No next defined → next computed. The result emerges from the superposition of the referrer — the honest observer collapses it to one point.

Your arrival (referrer): direct

Your computed point of view: …

Integrity, not truth — a content-address of your arrival context. The same referrer always computes the same point; the referrer is hashed, so nothing about it is revealed.

#	challenge	status
1	Poincaré conjecture	settled — Perelman, 2003 (external)
2	Riemann hypothesis	open
3	P vs NP	open
4	Yang–Mills mass gap	open
5	Navier–Stokes regularity	open
6	Hodge conjecture	open
7	Birch–Swinnerton-Dyer	open

Humanity: 1 / 7 (6 open). The author's own claim, that the seven are solved through involution, is stated in his name on the front page.

Discovered theorems (decidable, over ℤ/9) — 28632 standing in 1 families

Computed by exhaustion, each a monograph with its own page (/theorem/<key>) and chained receipt. Grouped by family (largest first) — easy to spot; use the search box for any keyword:

lean (26213)

This family has 26213 members, enumerated over a derived vocabulary and each decided by the kernel on every run. They are counted here rather than listed: the statement of each follows from its name, and the laws they instantiate are in src/proof/group.lean. The first 200 are shown; every one is in src/proof/discovered.json with its receipt.

lean_address_raw_bytes_of_a — lean address.lean: raw_bytes_of_a — rawBytes A = [88, 118, 248, 251, 63, 149, 14, 202, 10, 251, 189, 97, 221, 134, 206, 204] — decided by the Lean kernel over its whole finite domain, axiom-free · 211de25d-e843…
lean_address_to_uuid_bytes_of_a — lean address.lean: to_uuid_bytes_of_a — toUuidBytes A = [88, 118, 248, 251, 63, 149, 142, 202, 138, 251, 189, 97, 221, 134, 206, 204] — decided by the Lean kernel over its whole finite domain, axiom-free · c3f88cb7-dd38…
lean_address_to_uuid_bytes_of_uuidna — lean address.lean: to_uuid_bytes_of_uuidna — toUuidBytes UUIDNA = [252, 81, 21, 50, 110, 138, 132, 24, 165, 34, 165, 27, 29, 70, 167, 12] — decided by the Lean kernel over its whole finite domain, axiom-free · 6a4f78d3-a979…
lean_address_address_is_sixteen_bytes — lean address.lean: address_is_sixteen_bytes — (toUuidBytes UUIDNA).length = 16 — decided by the Lean kernel over its whole finite domain, axiom-free · e8ffe03d-7ef1…
lean_address_address_bytes_are_bytes — lean address.lean: address_bytes_are_bytes — (toUuidBytes UUIDNA).all (fun b => b < 256) — decided by the Lean kernel over its whole finite domain, axiom-free · 3fc96e27-7831…
lean_address_version_nibble_is_forced — lean address.lean: version_nibble_is_forced — ((toUuidBytes A).get! 6) / 16 = 8 ∧ ((toUuidBytes UUIDNA).get! 6) / 16 = 8 — decided by the Lean kernel over its whole finite domain, axiom-free · 47e811ae-f5e4…
lean_address_variant_bits_are_forced — lean address.lean: variant_bits_are_forced — ((toUuidBytes A).get! 8) / 64 = 2 ∧ ((toUuidBytes UUIDNA).get! 8) / 64 = 2 — decided by the Lean kernel over its whole finite domain, axiom-free · 02c6e2b5-afb6…
lean_address_addressing_is_deterministic — lean address.lean: addressing_is_deterministic — toUuidBytes A = toUuidBytes A — decided by the Lean kernel over its whole finite domain, axiom-free · e62c309b-6bab…
lean_address_distinct_seeds_give_distinct_addresses — lean address.lean: distinct_seeds_give_distinct_addresses — toUuidBytes A ≠ toUuidBytes UUIDNA — decided by the Lean kernel over its whole finite domain, axiom-free · d35a8b2c-29ad…
lean_address_addressing_is_injective_on_single_characters — lean address.lean: addressing_is_injective_on_single_characters — (((List.range 24).map (fun c => toUuidBytes [c])).eraseDups).length = 24 — decided by the Lean kernel over its whole finite domain, axiom-free · a6887d02-4deb…
lean_address_addressing_is_not_the_identity — lean address.lean: addressing_is_not_the_identity — toUuidBytes [7] ≠ [7] — decided by the Lean kernel over its whole finite domain, axiom-free · d0637879-af00…
lean_address_addressing_is_not_constant — lean address.lean: addressing_is_not_constant — toUuidBytes [1] ≠ toUuidBytes [2] — decided by the Lean kernel over its whole finite domain, axiom-free · 9c84b2cd-2a3a…
lean_address_the_four_seeds_are_distinct — lean address.lean: the_four_seeds_are_distinct — (SEEDS.eraseDups).length = 4 — decided by the Lean kernel over its whole finite domain, axiom-free · 1362d7ac-a87d…
lean_families_flt_all_primes_under_thirty — lean families.lean: flt_all_primes_under_thirty — primesUpTo30.all (fun p => (List.range' 1 (p - 1)).all (fun a => (a ^ (p - 1)) % p == 1)) — decided by the Lean kernel over its whole finite domain, axiom-free · fbeecfea-5cbf…
lean_families_wilson_all_primes_under_thirty — lean families.lean: wilson_all_primes_under_thirty — primesUpTo30.all (fun p => fact (p - 1) % p == p - 1) — decided by the Lean kernel over its whole finite domain, axiom-free · db3c3609-244e…
lean_families_wilson_fails_at_composites — lean families.lean: wilson_fails_at_composites — ((List.range' 4 20).filter (fun n => ! primesUpTo30.contains n)).all (fun n => fact (n - 1) % n != n - 1) — decided by the Lean kernel over its whole finite domain, axiom-free · e9964842-9392…
lean_families_pascal_rows_sum_to_powers_of_two — lean families.lean: pascal_rows_sum_to_powers_of_two — (List.range 12).all (fun n => ((List.range (n + 1)).map (fun k => choose n k)).foldl (· + ·) 0 == 2 ^ n) — decided by the Lean kernel over its whole finite domain, axiom-free · 92b5cdee-0ce0…
lean_families_pascal_alternating_sums_vanish — lean families.lean: pascal_alternating_sums_vanish — (List.range' 1 11).all (fun n => ((List.range (n + 1)).map (fun k => if k % 2 == 0 then choose n k else 0)).foldl (· + ·) 0 == ((List.range (n + 1)).map (fun k => if k % 2 == 1 then choose n k else 0)).foldl (· + ·) 0) — decided by the Lean kernel over its whole finite domain, axiom-free · 521b9062-dba3…
lean_families_totient_at_prime_powers — lean families.lean: totient_at_prime_powers — [2, 3, 5, 7].all (fun p => (List.range' 1 3).all (fun k => totient (p ^ k) == p ^ k - p ^ (k - 1))) — decided by the Lean kernel over its whole finite domain, axiom-free · 034c0066-ef85…
lean_families_geometric_series_all_bases — lean families.lean: geometric_series_all_bases — (List.range' 2 8).all (fun b => ((List.range 5).map (fun i => b ^ i)).foldl (· + ·) 0 * (b - 1) == b ^ 5 - 1) — decided by the Lean kernel over its whole finite domain, axiom-free · a1a0d8de-3069…
lean_families_xor_is_parity_up_to_eight_bits — lean families.lean: xor_is_parity_up_to_eight_bits — (List.range' 1 8).all (fun k => (List.range (2 ^ k)).all (fun n => popcount n % 2 == (List.range k).foldl (fun acc i => (acc + ((n >>> i) % 2)) % 2) 0)) — decided by the Lean kernel over its whole finite domain, axiom-free · c643bfcf-2a91…
lean_families_nat_div_is_a_total_function_returning_zero_at_a_zero_divisor — lean families.lean: nat_div_is_a_total_function_returning_zero_at_a_zero_divisor — (7 / 0) = 0 ∧ (0 / 0) = 0 ∧ (7 % 0) = 7 — decided by the Lean kernel over its whole finite domain, axiom-free · 99ffd597-6911…
lean_families_division_identity_holds_across_the_range — lean families.lean: division_identity_holds_across_the_range — (List.range 13).all (fun d => (12 / d) * d + (12 % d) == 12) — decided by the Lean kernel over its whole finite domain, axiom-free · 1101f928-77e3…
lean_families_at_a_zero_divisor_the_identity_is_carried_by_the_remainder — lean families.lean: at_a_zero_divisor_the_identity_is_carried_by_the_remainder — (12 / 0) = 0 ∧ (12 % 0) = 12 ∧ (12 / 0) * 0 + (12 % 0) == 12 — decided by the Lean kernel over its whole finite domain, axiom-free · fb105eb9-c500…
lean_fnv_hash_a_seed_zero — lean fnv.lean: hash_a_seed_zero — hash32 0 [97] = 1484191995 — decided by the Lean kernel over its whole finite domain, axiom-free · 6217ca32-aa73…
lean_fnv_hash_ab_seed_zero — lean fnv.lean: hash_ab_seed_zero — hash32 0 [97, 98] = 2049961697 — decided by the Lean kernel over its whole finite domain, axiom-free · 488d0227-0d40…
lean_fnv_hash_a_seed_golden — lean fnv.lean: hash_a_seed_golden — hash32 2654435769 [97] = 1066733258 — decided by the Lean kernel over its whole finite domain, axiom-free · 1a33880c-45f6…
lean_fnv_hash_uuidna_seed_zero — lean fnv.lean: hash_uuidna_seed_zero — hash32 0 [117, 117, 105, 100, 110, 97] = 4233172274 — decided by the Lean kernel over its whole finite domain, axiom-free · 171433dd-5f27…
lean_fnv_hash_is_deterministic — lean fnv.lean: hash_is_deterministic — (List.range 32).all (fun c => hash32 0 [c] == hash32 0 [c]) — decided by the Lean kernel over its whole finite domain, axiom-free · 6bb8e484-c440…
lean_fnv_hash_is_injective_on_single_characters — lean fnv.lean: hash_is_injective_on_single_characters — (((List.range 64).map (fun c => hash32 0 [c])).eraseDups).length = 64 — decided by the Lean kernel over its whole finite domain, axiom-free · c3f18ca2-78a4…
lean_fnv_the_seed_separates — lean fnv.lean: the_seed_separates — (List.range 16).all (fun c => hash32 0 [c] != hash32 2654435769 [c]) — decided by the Lean kernel over its whole finite domain, axiom-free · 34c9dd31-1c39…
lean_fnv_hash_is_not_the_identity — lean fnv.lean: hash_is_not_the_identity — hash32 0 [7] != 7 — decided by the Lean kernel over its whole finite domain, axiom-free · 34be52dc-c3a2…
lean_fnv_hash_is_not_constant — lean fnv.lean: hash_is_not_constant — hash32 0 [1] != hash32 0 [2] — decided by the Lean kernel over its whole finite domain, axiom-free · d65e7c3e-8771…
lean_fnv_hash_is_thirty_two_bit — lean fnv.lean: hash_is_thirty_two_bit — (List.range 40).all (fun c => hash32 0 [c] < M32) — decided by the Lean kernel over its whole finite domain, axiom-free · 6adee6ac-01b5…
lean_generated_powsum_zero_odd_exponents — lean generated.lean: powsum_zero_odd_exponents — [1, 3, 5, 7, 9, 11, 13, 15, 17].all (fun k => (([1,2,4,5,7,8].map (fun u => (u ^ k) % 9)).foldl (· + ·) 0) % 9 == 0) — decided by the Lean kernel over its whole finite domain, axiom-free · ce4748ab-7b90…
lean_generated_powsum_nonzero_at_even_exponents — lean generated.lean: powsum_nonzero_at_even_exponents — ¬ ([2, 4, 6].all (fun k => (([1,2,4,5,7,8].map (fun u => (u ^ k) % 9)).foldl (· + ·) 0) % 9 == 0)) — decided by the Lean kernel over its whole finite domain, axiom-free · da7dc7ce-01ec…
lean_generated_mulperm_iff_unit_all — lean generated.lean: mulperm_iff_unit_all — (List.range 9).all (fun k => (((([1,2,4,5,7,8].map (fun u => (k * u) % 9)).eraseDups).length) == 6) == ([1,2,4,5,7,8].contains k)) — decided by the Lean kernel over its whole finite domain, axiom-free · 01a44bcc-6ae1…
lean_generated_mulperm_fails_at_the_triad — lean generated.lean: mulperm_fails_at_the_triad — ¬ ([3, 6, 0].any (fun k => ((([1,2,4,5,7,8].map (fun u => (k * u) % 9)).eraseDups).length) == 6)) — decided by the Lean kernel over its whole finite domain, axiom-free · 7f6f60f3-d775…
lean_generated_addgen_iff_coprime_all — lean generated.lean: addgen_iff_coprime_all — (List.range 9).all (fun k => ((((List.range 9).map (fun i => (k * i) % 9)).eraseDups).length == 9) == ([1,2,4,5,7,8].contains k)) — decided by the Lean kernel over its whole finite domain, axiom-free · d23bb6f4-2735…
lean_generated_hasinv_iff_unit_all — lean generated.lean: hasinv_iff_unit_all — (List.range 9).all (fun d => ((List.range 9).any (fun e => (d * e) % 9 == 1)) == ([1,2,4,5,7,8].contains d)) — decided by the Lean kernel over its whole finite domain, axiom-free · 24020c39-2817…
lean_generated_demorgan_all_widths — lean generated.lean: demorgan_all_widths — (List.range' 2 7).all (fun k => (List.range (2 ^ k)).all (fun n => (!((List.range k).all (fun i => (n >>> i) % 2 == 1))) == ((List.range k).any (fun i => (n >>> i) % 2 == 0)))) — decided by the Lean kernel over its whole finite domain, axiom-free · 45878828-7434…
lean_generated_power_sum_closed_forms — lean generated.lean: power_sum_closed_forms — (List.range' 1 30).all (fun n => (((List.range' 1 n).foldl (· + ·) 0) * 2 == n * (n + 1)) ∧ (((List.range' 1 n).map (fun i => i * i)).foldl (· + ·) 0) * 6 == n * (n + 1) * (2 * n + 1)) — decided by the Lean kernel over its whole finite domain, axiom-free · 4830f31e-7833…
lean_generated_invpow_is_fifth_power_all_units — lean generated.lean: invpow_is_fifth_power_all_units — [1,2,4,5,7,8].all (fun u => (u * (u ^ 5)) % 9 == 1) — decided by the Lean kernel over its whole finite domain, axiom-free · 848e4a2c-b65a…
lean_generated_invpow_fails_off_the_units — lean generated.lean: invpow_fails_off_the_units — ¬ ([3, 6].any (fun t => (List.range 9).any (fun e => (t * e) % 9 == 1))) — decided by the Lean kernel over its whole finite domain, axiom-free · 9cd0abb7-c3dc…
lean_generated_cyclic_units_have_a_primitive_root — lean generated.lean: cyclic_units_have_a_primitive_root — [2,3,5,7,11,13].all (fun p => (List.range' 1 (p - 1)).any (fun g => (((List.range' 1 (p - 1)).map (fun k => (g ^ k) % p)).eraseDups).length == p - 1)) — decided by the Lean kernel over its whole finite domain, axiom-free · 21d5e557-5625…
lean_generated_decimal_period_is_the_order_of_ten — lean generated.lean: decimal_period_is_the_order_of_ten — [3,7,11,13,17,19,23,29].all (fun p => (List.range' 1 (p - 1)).any (fun k => (10 ^ k) % p == 1)) — decided by the Lean kernel over its whole finite domain, axiom-free · 85e474a6-76c3…
lean_generated_primality_agrees_with_trial_division — lean generated.lean: primality_agrees_with_trial_division — (List.range' 2 40).all (fun n => ((List.range' 2 (n - 2)).all (fun d => n % d != 0)) == ([2,3,5,7,11,13,17,19,23,29,31,37,41].contains n)) — decided by the Lean kernel over its whole finite domain, axiom-free · 86e633b3-cc43…
lean_merkle_merge_agrees — lean merkle.lean: merge_agrees — merge A B = [181, 59, 237, 190, 211, 88, 129, 103, 143, 231, 158, 123, 139, 178, 38, 2] — decided by the Lean kernel over its whole finite domain, axiom-free · 4298a48c-8e29…
lean_merkle_empty_fold_agrees — lean merkle.lean: empty_fold_agrees — merkleFold [] = [147, 146, 154, 45, 72, 16, 138, 198, 159, 50, 78, 208, 125, 158, 1, 108] — decided by the Lean kernel over its whole finite domain, axiom-free · f96bc0ca-dac7…
lean_merkle_pair_fold_agrees — lean merkle.lean: pair_fold_agrees — merkleFold [A, B] = [181, 59, 237, 190, 211, 88, 129, 103, 143, 231, 158, 123, 139, 178, 38, 2] — decided by the Lean kernel over its whole finite domain, axiom-free · 7651bd48-d395…
lean_merkle_fold_is_order_independent_on_two — lean merkle.lean: fold_is_order_independent_on_two — merkleFold [A, B] = merkleFold [B, A] — decided by the Lean kernel over its whole finite domain, axiom-free · 26e3535b-82bd…
lean_merkle_merge_is_order_sensitive — lean merkle.lean: merge_is_order_sensitive — merge A B ≠ merge B A — decided by the Lean kernel over its whole finite domain, axiom-free · 3eda96b0-7e65…
lean_merkle_sorting_is_what_makes_the_fold_order_free — lean merkle.lean: sorting_is_what_makes_the_fold_order_free — sortB [A, B] = sortB [B, A] ∧ [A, B] ≠ [B, A] — decided by the Lean kernel over its whole finite domain, axiom-free · fd6f4d99-6f2e…
lean_quantum_perms_of_four_is_factorial — lean quantum.lean: perms_of_four_is_factorial — (perms [1, 2, 4, 8]).length = 24 — decided by the Lean kernel over its whole finite domain, axiom-free · 4fabbd78-28ba…
lean_quantum_receipt_is_order_invariant — lean quantum.lean: receipt_is_order_invariant — (perms [1, 2, 4, 8]).all (fun p => receipt p == receipt [1, 2, 4, 8]) — decided by the Lean kernel over its whole finite domain, axiom-free · 832611b4-9363…
lean_quantum_receipt_order_invariant_on_the_orbit — lean quantum.lean: receipt_order_invariant_on_the_orbit — (perms [1, 2, 4, 8, 7, 5]).all (fun p => receipt p == receipt [1, 2, 4, 8, 7, 5]) — decided by the Lean kernel over its whole finite domain, axiom-free · 6b255389-9fe6…
lean_quantum_naive_fold_is_not_order_invariant — lean quantum.lean: naive_fold_is_not_order_invariant — ¬ ((perms [1, 2, 4, 8]).all (fun p => naive p == naive [1, 2, 4, 8])) — decided by the Lean kernel over its whole finite domain, axiom-free · eb661483-6694…
lean_quantum_superposition_collapses_to_one — lean quantum.lean: superposition_collapses_to_one — ((perms [1, 2, 4, 8]).map receipt).eraseDups.length = 1 — decided by the Lean kernel over its whole finite domain, axiom-free · c2ab5a2f-9fd5…
lean_reversal_reversal_preserves_digit_sum — lean reversal.lean: reversal_preserves_digit_sum — (List.range' 1 300).all (fun n => digitSum (reverseNum n) == digitSum n) — decided by the Lean kernel over its whole finite domain, axiom-free · db894765-359f…
lean_reversal_digital_root_is_invariant_under_reversal — lean reversal.lean: digital_root_is_invariant_under_reversal — (List.range' 1 300).all (fun n => (reverseNum n) % 9 == n % 9) — decided by the Lean kernel over its whole finite domain, axiom-free · 352d594d-dd9a…
lean_reversal_the_ledger_reversal_cases — lean reversal.lean: the_ledger_reversal_cases — (reverseNum 12) % 9 == 12 % 9 ∧ (reverseNum 45) % 9 == 45 % 9 ∧ (reverseNum 123) % 9 == 123 % 9 ∧ (reverseNum 1234) % 9 == 1234 % 9 ∧ (reverseNum 4321) % 9 == 4321 % 9 ∧ (reverseNum 9080) % 9 == 9080 % 9 — decided by the Lean kernel over its whole finite domain, axiom-free · 4bd3536b-805f…
lean_reversal_reversal_is_not_the_identity — lean reversal.lean: reversal_is_not_the_identity — ¬ ((List.range' 10 90).all (fun n => reverseNum n == n)) — decided by the Lean kernel over its whole finite domain, axiom-free · 991f3d96-06d2…
lean_reversal_palindromes_are_the_fixed_points — lean reversal.lean: palindromes_are_the_fixed_points — ((List.range' 10 90).filter (fun n => reverseNum n == n)).length = 9 — decided by the Lean kernel over its whole finite domain, axiom-free · 38c163fc-15bd…
lean_reversal_emirps_exist_below_one_hundred — lean reversal.lean: emirps_exist_below_one_hundred — ((List.range' 10 90).filter (fun n => isPrime n && isPrime (reverseNum n) && reverseNum n != n)).length > 0 — decided by the Lean kernel over its whole finite domain, axiom-free · b9e6b77a-b12d…
lean_reversal_reversal_does_not_preserve_primality — lean reversal.lean: reversal_does_not_preserve_primality — ¬ ((List.range' 10 90).all (fun n => isPrime n == isPrime (reverseNum n))) — decided by the Lean kernel over its whole finite domain, axiom-free · 3d5c8208-367c…
lean_z9_units_are_six — lean z9.lean: units_are_six — units = [1, 2, 4, 5, 7, 8] — decided by the Lean kernel over its whole finite domain, axiom-free · 76d332a5-ee8e…
lean_z9_units_count — lean z9.lean: units_count — units.length = 6 — decided by the Lean kernel over its whole finite domain, axiom-free · 8b673ca0-cbd0…
lean_z9_hasinv_units — lean z9.lean: hasinv_units — units.all (fun u => (List.range B).any (fun e => m9 (u * e) == 1)) — decided by the Lean kernel over its whole finite domain, axiom-free · c37ff607-4bbc…
lean_z9_hasinv_triad_not — lean z9.lean: hasinv_triad_not — ¬ ([3, 6, 0].any (fun t => (List.range B).any (fun e => m9 (t * e) == 1))) — decided by the Lean kernel over its whole finite domain, axiom-free · 898e137c-9445…
lean_z9_selfinv_exactly_one_and_eight — lean z9.lean: selfinv_exactly_one_and_eight — (units.filter (fun u => m9 (u * u) == 1)) = [1, 8] — decided by the Lean kernel over its whole finite domain, axiom-free · 7b3bc7e3-d34e…
lean_z9_euler_units_pow_six — lean z9.lean: euler_units_pow_six — units.all (fun u => pow9 u 6 == 1) — decided by the Lean kernel over its whole finite domain, axiom-free · 1e4c6abe-a1c3…
lean_z9_invpow_is_u_to_the_fifth — lean z9.lean: invpow_is_u_to_the_fifth — units.all (fun u => m9 (u * pow9 u 5) == 1) — decided by the Lean kernel over its whole finite domain, axiom-free · 480f158b-6a1e…
lean_z9_powsum_zero_at_six — lean z9.lean: powsum_zero_at_six — m9 ((units.map (fun u => pow9 u 6)).foldl (· + ·) 0) = 6 — decided by the Lean kernel over its whole finite domain, axiom-free · 9b3b882a-90d8…
lean_z9_powsum_zero_at_one — lean z9.lean: powsum_zero_at_one — m9 ((units.map (fun u => pow9 u 1)).foldl (· + ·) 0) = 0 — decided by the Lean kernel over its whole finite domain, axiom-free · f5741c78-6ec5…
lean_z9_mulperm_iff_unit — lean z9.lean: mulperm_iff_unit — (List.range B).all (fun k => ((units.map (fun u => m9 (k * u))).eraseDups.length == units.length) == isUnit k) — decided by the Lean kernel over its whole finite domain, axiom-free · 37bbadd2-ef0c…
lean_z9_addgen_iff_coprime — lean z9.lean: addgen_iff_coprime — (List.range B).all (fun k => (((List.range B).map (fun i => m9 (k * i))).eraseDups.length == B) == isUnit k) — decided by the Lean kernel over its whole finite domain, axiom-free · dfdf7fc0-4363…
lean_z9_selfneg_only_zero — lean z9.lean: selfneg_only_zero — ((List.range B).filter (fun d => m9 (2 * d) == 0)) = [0] — decided by the Lean kernel over its whole finite domain, axiom-free · afe717ff-dd57…
lean_z9_orbit_is_the_six — lean z9.lean: orbit_is_the_six — (List.range 6).map orbit = [1, 2, 4, 8, 7, 5] — decided by the Lean kernel over its whole finite domain, axiom-free · 71ca27b5-036d…
lean_z9_orbit_closes — lean z9.lean: orbit_closes — orbit 6 = orbit 0 — decided by the Lean kernel over its whole finite domain, axiom-free · e49fb8ec-3651…
lean_z9_orbit_distinct — lean z9.lean: orbit_distinct — ((List.range 6).map orbit).eraseDups.length = 6 — decided by the Lean kernel over its whole finite domain, axiom-free · d373ad1a-9798…
lean_z9_orbit_covers_units — lean z9.lean: orbit_covers_units — ((List.range 6).map orbit).eraseDups.length = units.length — decided by the Lean kernel over its whole finite domain, axiom-free · 293a198a-6c28…
lean_z9_triad_never_reaches_one — lean z9.lean: triad_never_reaches_one — ¬ ((List.range 12).any (fun k => pow9 3 (k + 1) == 1 || pow9 6 (k + 1) == 1)) — decided by the Lean kernel over its whole finite domain, axiom-free · 20a9047b-0651…
lean_z9_triad_squares_vanish — lean z9.lean: triad_squares_vanish — m9 (3 * 3) = 0 ∧ m9 (6 * 6) = 0 — decided by the Lean kernel over its whole finite domain, axiom-free · 5ce961f4-660b…
lean_z9_add_group — lean z9.lean: add_group — (List.range B).all (fun d => (List.range B).any (fun e => m9 (d + e) == 0)) — decided by the Lean kernel over its whole finite domain, axiom-free · 312d6755-c2a1…
lean_z9_neg_involution — lean z9.lean: neg_involution — (List.range B).all (fun d => m9 (B - m9 (B - d)) == m9 d) — decided by the Lean kernel over its whole finite domain, axiom-free · e72bcc08-9e1e…
lean_nim_bouton_two_heaps_lost_iff_xor_zero — lean nim.lean: bouton_two_heaps_lost_iff_xor_zero — (List.range N).all (fun a => (List.range N).all (fun b => isLost a b == (xorN a b == 0))) — decided by the Lean kernel over its whole finite domain, axiom-free · d35edb15-4b67…
lean_nim_bouton_lost_iff_heaps_equal — lean nim.lean: bouton_lost_iff_heaps_equal — (List.range N).all (fun a => (List.range N).all (fun b => isLost a b == (a == b))) — decided by the Lean kernel over its whole finite domain, axiom-free · c2f9d531-b836…
lean_nim_lost_positions_are_exactly_the_diagonal — lean nim.lean: lost_positions_are_exactly_the_diagonal — (((List.range N).flatMap (fun a => (List.range N).map (fun b => (a, b)))).filter (fun p => isLost p.1 p.2)).length = N — decided by the Lean kernel over its whole finite domain, axiom-free · 86e0163f-596b…
lean_nim_grundy_of_a_single_heap_is_its_size — lean nim.lean: grundy_of_a_single_heap_is_its_size — (List.range N).all (fun n => grundy1 (n + 1) n == n) — decided by the Lean kernel over its whole finite domain, axiom-free · e08987d5-7608…
lean_nim_grundy_of_two_heaps_is_the_xor — lean nim.lean: grundy_of_two_heaps_is_the_xor — (List.range N).all (fun a => (List.range N).all (fun b => (xorN (grundy1 (a + 1) a) (grundy1 (b + 1) b)) == xorN a b)) — decided by the Lean kernel over its whole finite domain, axiom-free · 7ab70de7-b5fd…
lean_nim_xor_is_its_own_inverse — lean nim.lean: xor_is_its_own_inverse — (List.range 16).all (fun a => (List.range 16).all (fun b => xorN (xorN a b) b == a)) — decided by the Lean kernel over its whole finite domain, axiom-free · f9930902-3aa3…
lean_nim_xor_is_commutative — lean nim.lean: xor_is_commutative — (List.range 16).all (fun a => (List.range 16).all (fun b => xorN a b == xorN b a)) — decided by the Lean kernel over its whole finite domain, axiom-free · 4be000e0-cf35…
lean_nim_xor_zero_is_identity — lean nim.lean: xor_zero_is_identity — (List.range 32).all (fun a => xorN a 0 == a) — decided by the Lean kernel over its whole finite domain, axiom-free · 59c8e95e-eaf1…
lean_z9plus_squares_land_exactly_in_zero_one_four_seven — lean z9plus.lean: squares_land_exactly_in_zero_one_four_seven — R.all (fun d => [0, 1, 4, 7].contains (m9 (d * d))) ∧ [0, 1, 4, 7].all (fun s => R.any (fun d => m9 (d * d) == s)) — decided by the Lean kernel over its whole finite domain, axiom-free · 0a46c7d9-795d…
lean_z9plus_five_is_not_a_square_mod_nine — lean z9plus.lean: five_is_not_a_square_mod_nine — ¬ (R.any (fun d => m9 (d * d) == 5)) — decided by the Lean kernel over its whole finite domain, axiom-free · 20c33bf7-1bbe…
lean_z9plus_cubes_land_exactly_in_zero_one_eight — lean z9plus.lean: cubes_land_exactly_in_zero_one_eight — R.all (fun d => [0, 1, 8].contains (pw d 3)) ∧ [0, 1, 8].all (fun c => R.any (fun d => pw d 3 == c)) — decided by the Lean kernel over its whole finite domain, axiom-free · a0413156-e553…
lean_z9plus_primitive_roots_are_exactly_two_and_five — lean z9plus.lean: primitive_roots_are_exactly_two_and_five — (R.filter generates) = [2, 5] — decided by the Lean kernel over its whole finite domain, axiom-free · 8832fb36-edb0…
lean_z9plus_primitive_root_iff_generates_the_units — lean z9plus.lean: primitive_root_iff_generates_the_units — R.all (fun g => generates g == ([2, 5].contains g)) — decided by the Lean kernel over its whole finite domain, axiom-free · 1d8d6e36-1984…
lean_z9plus_doubling_has_period_six — lean z9plus.lean: doubling_has_period_six — (List.range 30).all (fun k => pw 2 k == pw 2 (k + 6)) — decided by the Lean kernel over its whole finite domain, axiom-free · 59e48172-1f6a…
lean_z9plus_no_period_smaller_than_six — lean z9plus.lean: no_period_smaller_than_six — ¬ ([1, 2, 3, 4, 5].any (fun p => (List.range 12).all (fun k => pw 2 k == pw 2 (k + p)))) — decided by the Lean kernel over its whole finite domain, axiom-free · e94365d4-1888…
lean_z9plus_digital_root_agrees_with_the_residue — lean z9plus.lean: digital_root_agrees_with_the_residue — (List.range' 1 300).all (fun n => (dr n == 9) == (m9 n == 0)) — decided by the Lean kernel over its whole finite domain, axiom-free · 1696d96c-33a3…
lean_z9plus_digital_root_is_the_digit_sum_residue — lean z9plus.lean: digital_root_is_the_digit_sum_residue — (List.range' 1 300).all (fun n => m9 (digitSum n) == m9 n) — decided by the Lean kernel over its whole finite domain, axiom-free · 14fd1431-bf05…
lean_z9plus_reversal_cannot_change_the_digital_root — lean z9plus.lean: reversal_cannot_change_the_digital_root — (List.range' 1 300).all (fun n => dr (reverseNum n) == dr n) — decided by the Lean kernel over its whole finite domain, axiom-free · 08720a64-6950…
lean_z9plus_orbit_digital_roots_have_period_six — lean z9plus.lean: orbit_digital_roots_have_period_six — (List.range 24).all (fun k => dr (pw 2 k) == dr (pw 2 (k + 6))) — decided by the Lean kernel over its whole finite domain, axiom-free · 543f48a9-f482…
lean_z9plus_units_and_triad_partition_the_ring — lean z9plus.lean: units_and_triad_partition_the_ring — ((R.filter (fun d => R.any (fun e => m9 (d * e) == 1))).length + (R.filter (fun d => ! R.any (fun e => m9 (d * e) == 1))).length) = 9 — decided by the Lean kernel over its whole finite domain, axiom-free · 56d4fbda-6f25…
lean_z9plus_both_parts_sum_to_zero — lean z9plus.lean: both_parts_sum_to_zero — m9 ((R.filter (fun d => R.any (fun e => m9 (d * e) == 1))).foldl (· + ·) 0) == 0 ∧ m9 ((R.filter (fun d => ! R.any (fun e => m9 (d * e) == 1))).foldl (· + ·) 0) == 0 — decided by the Lean kernel over its whole finite domain, axiom-free · b30de9fd-1e1a…
lean_z9plus_the_orders_of_the_units_are_exact — lean z9plus.lean: the_orders_of_the_units_are_exact — ord 1 = 1 ∧ ord 8 = 2 ∧ ord 4 = 3 ∧ ord 7 = 3 ∧ ord 2 = 6 ∧ ord 5 = 6 — decided by the Lean kernel over its whole finite domain, axiom-free · 48685f29-1bc3…
lean_z9plus_the_unit_table_is_a_latin_square — lean z9plus.lean: the_unit_table_is_a_latin_square — [1,2,4,5,7,8].all (fun a => (([1,2,4,5,7,8].map (fun b => m9 (a * b))).eraseDups).length == 6 ∧ [1,2,4,5,7,8].all (fun c => [1,2,4,5,7,8].any (fun b => m9 (a * b) == c))) — decided by the Lean kernel over its whole finite domain, axiom-free · 1e106c4a-3816…
lean_z9plus_the_orbit_never_meets_the_triad — lean z9plus.lean: the_orbit_never_meets_the_triad — (List.range 40).all (fun k => ! [0, 3, 6].contains (pw 2 k)) — decided by the Lean kernel over its whole finite domain, axiom-free · 38726843-73a6…
lean_z9plus_the_reflected_orbit_covers_the_whole_triad — lean z9plus.lean: the_reflected_orbit_covers_the_whole_triad — [3, 6, 9].all (fun t => orbit6.any (fun d => refl d == t)) — decided by the Lean kernel over its whole finite domain, axiom-free · 8c5d3165-37d8…
lean_z9plus_reflection_splits_the_orbit_in_half — lean z9plus.lean: reflection_splits_the_orbit_in_half — (orbit6.filter (fun d => [3, 6, 9].contains (refl d))).length = 3 ∧ (orbit6.filter (fun d => ! [3, 6, 9].contains (refl d))).length = 3 — decided by the Lean kernel over its whole finite domain, axiom-free · 2ee0d0dc-45d4…
lean_z9plus_the_crossing_pairs_are_one_four_seven — lean z9plus.lean: the_crossing_pairs_are_one_four_seven — (orbit6.filter (fun d => [3, 6, 9].contains (refl d))) = [1, 4, 7] ∧ refl 1 = 9 ∧ refl 4 = 6 ∧ refl 7 = 3 — decided by the Lean kernel over its whole finite domain, axiom-free · fd5ff6f1-1655…
lean_z9plus_reflection_is_injective_on_the_orbit — lean z9plus.lean: reflection_is_injective_on_the_orbit — ((orbit6.map refl).eraseDups).length = 6 — decided by the Lean kernel over its whole finite domain, axiom-free · e63ebd6e-bace…
lean_z9plus_doubling_alone_reaches_only_the_units — lean z9plus.lean: doubling_alone_reaches_only_the_units — ((List.range 12).map (fun k => pw 2 k)).eraseDups.length = 6 ∧ ((List.range 12).map (fun k => pw 2 k)).all (fun d => ! [0, 3, 6].contains d) — decided by the Lean kernel over its whole finite domain, axiom-free · 8fb1adf8-9b65…
lean_z9plus_reflection_alone_reaches_only_two — lean z9plus.lean: reflection_alone_reaches_only_two — (closure 6 [1]).length ≥ 2 ∧ rfl9 1 = 0 ∧ rfl9 (rfl9 1) = 1 — decided by the Lean kernel over its whole finite domain, axiom-free · dd50d767-7566…
lean_z9plus_doubling_and_reflection_together_reach_every_residue — lean z9plus.lean: doubling_and_reflection_together_reach_every_residue — (closure 4 [1]).length = 9 — decided by the Lean kernel over its whole finite domain, axiom-free · 5c55b180-d10e…
lean_z9plus_every_residue_is_reachable_from_one — lean z9plus.lean: every_residue_is_reachable_from_one — (List.range 9).all (fun d => (closure 4 [1]).contains d) — decided by the Lean kernel over its whole finite domain, axiom-free · e7433a57-1934…
lean_z9plus_the_diameter_is_exactly_four — lean z9plus.lean: the_diameter_is_exactly_four — (closure 4 [1]).length = 9 ∧ (closure 3 [1]).length = 7 — decided by the Lean kernel over its whole finite domain, axiom-free · 479589da-0e75…
lean_z9plus_the_frontier_grows_by_two_each_round — lean z9plus.lean: the_frontier_grows_by_two_each_round — (closure 0 [1]).length = 1 ∧ (closure 1 [1]).length = 3 ∧ (closure 2 [1]).length = 5 ∧ (closure 3 [1]).length = 7 ∧ (closure 4 [1]).length = 9 — decided by the Lean kernel over its whole finite domain, axiom-free · b338c80b-1898…
lean_z9plus_product_of_the_units_is_minus_one — lean z9plus.lean: product_of_the_units_is_minus_one — m9 ([1,2,4,5,7,8].foldl (· * ·) 1) = 8 ∧ m9 (8 + 1) = 0 — decided by the Lean kernel over its whole finite domain, axiom-free · b731fc18-fee2…
lean_z9plus_pisano_period_mod_nine_is_twenty_four — lean z9plus.lean: pisano_period_mod_nine_is_twenty_four — (List.range 30).all (fun k => fib9 k == fib9 (k + 24)) — decided by the Lean kernel over its whole finite domain, axiom-free · 87f22860-4386…
lean_z9plus_no_proper_divisor_of_twenty_four_is_a_period — lean z9plus.lean: no_proper_divisor_of_twenty_four_is_a_period — ¬ ([1, 2, 3, 4, 6, 8, 12].any (fun p => (List.range 26).all (fun k => fib9 k == fib9 (k + p)))) — decided by the Lean kernel over its whole finite domain, axiom-free · 2ffb3f99-d850…
lean_z9plus_fibonacci_recurrence_holds — lean z9plus.lean: fibonacci_recurrence_holds — (List.range 20).all (fun n => fib (n + 2) == fib n + fib (n + 1)) — decided by the Lean kernel over its whole finite domain, axiom-free · 2953f153-67e8…
lean_z9plus_consecutive_fibonacci_are_coprime — lean z9plus.lean: consecutive_fibonacci_are_coprime — (List.range' 1 15).all (fun n => gcd9 (fib n) (fib (n + 1)) == 1) — decided by the Lean kernel over its whole finite domain, axiom-free · e8906360-31c5…
lean_z9plus_three_five_eight_are_consecutive_fibonacci — lean z9plus.lean: three_five_eight_are_consecutive_fibonacci — fib 4 = 3 ∧ fib 5 = 5 ∧ fib 6 = 8 ∧ fib 4 + fib 5 = fib 6 — decided by the Lean kernel over its whole finite domain, axiom-free · 7575c9eb-fd7f…
lean_sequences_cassini_at_even_indices — lean sequences.lean: cassini_at_even_indices — (List.range' 1 20).all (fun n => n % 2 == 1 || fib (n - 1) * fib (n + 1) == fib n * fib n + 1) — decided by the Lean kernel over its whole finite domain, axiom-free · a618d9ae-8af7…
lean_sequences_cassini_at_odd_indices — lean sequences.lean: cassini_at_odd_indices — (List.range' 1 20).all (fun n => n % 2 == 0 || fib (n - 1) * fib (n + 1) + 1 == fib n * fib n) — decided by the Lean kernel over its whole finite domain, axiom-free · b42d7ae9-ec74…
lean_sequences_cassini_deviation_is_exactly_one — lean sequences.lean: cassini_deviation_is_exactly_one — (List.range' 1 20).all (fun n => (fib (n - 1) * fib (n + 1) == fib n * fib n + 1) || (fib (n - 1) * fib (n + 1) + 1 == fib n * fib n)) — decided by the Lean kernel over its whole finite domain, axiom-free · 8563fd0c-91ef…
lean_sequences_lucas_mod_two_is_the_and_rule — lean sequences.lean: lucas_mod_two_is_the_and_rule — (List.range 14).all (fun n => (List.range (n + 1)).all (fun k => (choose n k % 2 == 1) == (andN k n == k))) — decided by the Lean kernel over its whole finite domain, axiom-free · 2396c70a-73a7…
lean_sequences_pascal_has_both_parities — lean sequences.lean: pascal_has_both_parities — ((List.range 14).flatMap (fun n => (List.range (n + 1)).map (fun k => choose n k % 2))).contains 1 ∧ ((List.range 14).flatMap (fun n => (List.range (n + 1)).map (fun k => choose n k % 2))).contains 0 — decided by the Lean kernel over its whole finite domain, axiom-free · fc910b31-5054…
lean_sequences_sums_of_two_squares_are_closed — lean sequences.lean: sums_of_two_squares_are_closed — (List.range 8).all (fun a => (List.range 8).all (fun b => (List.range 8).all (fun c => (List.range 8).all (fun d => (aa + bb) * (cc + dd) == (ac - bd) * (ac - bd) + (ad + bc) * (ad + bc) || (ac) < (bd))))) — decided by the Lean kernel over its whole finite domain, axiom-free · fca198ef-9b8b…
lean_sequences_three_five_eight_are_consecutive — lean sequences.lean: three_five_eight_are_consecutive — fib 4 = 3 ∧ fib 5 = 5 ∧ fib 6 = 8 ∧ fib 4 + fib 5 = fib 6 — decided by the Lean kernel over its whole finite domain, axiom-free · 2c1fb60c-6564…
lean_sequences_pisano_twentyfour_is_four_sixes — lean sequences.lean: pisano_twentyfour_is_four_sixes — (List.range 30).all (fun k => fib k % 9 == fib (k + 24) % 9) ∧ 24 = 4 * 6 — decided by the Lean kernel over its whole finite domain, axiom-free · 780bfeec-e476…
lean_mechanical_add_group — lean mechanical.lean: add_group — (List.range' 1 9).all (fun d => (List.range' 1 9).any (fun e => M9 (d + e) == 0)) — decided by the Lean kernel over its whole finite domain, axiom-free · 0bf99a9b-8d78…
lean_mechanical_merkaba_cube_q3 — lean mechanical.lean: merkaba_cube_q3 — 2 ^ 3 == 8 && 3 * 2 ^ 2 == 12 — decided by the Lean kernel over its whole finite domain, axiom-free · 6963c8ac-e3e6…
lean_mechanical_trial_zero_no_inverse — lean mechanical.lean: trial_zero_no_inverse — !(List.range' 1 9).any (fun e => M9 (0 * e) == 1) — decided by the Lean kernel over its whole finite domain, axiom-free · f336fdf5-76ee…
lean_mechanical_gf4_size — lean mechanical.lean: gf4_size — [0, 1, 2, 3].length == 2 ^ 2 — decided by the Lean kernel over its whole finite domain, axiom-free · daf893bd-dc5f…
lean_mechanical_harmonic_pythagorean_comma — lean mechanical.lean: harmonic_pythagorean_comma — 3 ^ 12 == 531441 && 2 ^ 19 == 524288 && 3 ^ 12 != 2 ^ 19 — decided by the Lean kernel over its whole finite domain, axiom-free · eb59929b-c67e…
lean_mechanical_relation_eight — lean mechanical.lean: relation_eight — 2 ^ 3 == 8 && 8 * 8 == 64 — decided by the Lean kernel over its whole finite domain, axiom-free · a39da385-334c…
lean_mechanical_relation_seven_is_six_plus_one — lean mechanical.lean: relation_seven_is_six_plus_one — [1,2,4,5,7,8].length == 6 && 6 + 1 == 7 && 7 - 1 == 6 — decided by the Lean kernel over its whole finite domain, axiom-free · 4cc8e257-5368…
lean_mechanical_the_cyclic_number_142857_is_the_repetend_of_one_seventh — lean mechanical.lean: the_cyclic_number_142857_is_the_repetend_of_one_seventh — 999999 % 7 == 0 && 999999 / 7 == 142857 — decided by the Lean kernel over its whole finite domain, axiom-free · 84678499-42cd…
lean_mechanical_the_digital_root_of_seven_to_the_k_has_period_three — lean mechanical.lean: the_digital_root_of_seven_to_the_k_has_period_three — 7 ^ 1 % 9 == 7 && 7 ^ 2 % 9 == 4 && 7 ^ 3 % 9 == 1 && 7 ^ 4 % 9 == 7 — decided by the Lean kernel over its whole finite domain, axiom-free · 35da1bae-5b79…
lean_mechanical_seven_divides_the_repunit_of_length_six — lean mechanical.lean: seven_divides_the_repunit_of_length_six — 111111 % 7 == 0 — decided by the Lean kernel over its whole finite domain, axiom-free · 5de46f3e-a628…
lean_mechanical_two_to_the_eighth_is_two_hundred_fifty_six_a_byte — lean mechanical.lean: two_to_the_eighth_is_two_hundred_fifty_six_a_byte — 2 ^ 8 == 256 — decided by the Lean kernel over its whole finite domain, axiom-free · 34caada8-dd09…
lean_mechanical_two_to_the_tenth_is_1024_the_harmonic_ledger — lean mechanical.lean: two_to_the_tenth_is_1024_the_harmonic_ledger — 2 ^ 10 == 1024 — decided by the Lean kernel over its whole finite domain, axiom-free · 04218536-2a34…
lean_mechanical_nine_is_the_base_and_the_trinity_squared — lean mechanical.lean: nine_is_the_base_and_the_trinity_squared — 9 == 9 && 9 == 3 ^ 2 && 3 == 3 — decided by the Lean kernel over its whole finite domain, axiom-free · f0b0a052-058c…
lean_mechanical_five_is_the_inverse_of_two_so_halving_reverses_the_orbit — lean mechanical.lean: five_is_the_inverse_of_two_so_halving_reverses_the_orbit — (2 * 5) % 9 == 1 — decided by the Lean kernel over its whole finite domain, axiom-free · 32ceaab8-afe0…
lean_mechanical_dna_is_the_version_itself — lean mechanical.lean: dna_is_the_version_itself — 4 ^ 3 == 64 — decided by the Lean kernel over its whole finite domain, axiom-free · 1527985d-54ef…
lean_mechanical_genetic_code_is_the_octave_squared — lean mechanical.lean: genetic_code_is_the_octave_squared — 4 ^ 3 == 64 && 64 == 8 * 8 && 64 % 8 == 0 — decided by the Lean kernel over its whole finite domain, axiom-free · a4bd830f-54a6…
lean_mechanical_genesis_1_the_unit — lean mechanical.lean: genesis_1_the_unit — [1, 2, 3, 4, 5, 6, 7, 8, 9].all (fun n => 1 * n == n) && 1 ^ 7 == 1 — decided by the Lean kernel over its whole finite domain, axiom-free · b5cc42a3-c620…
lean_mechanical_genesis_8_the_octave — lean mechanical.lean: genesis_8_the_octave — 2 ^ 3 == 8 && 8 % 8 == 0 && 8 == 2 * 2 * 2 — decided by the Lean kernel over its whole finite domain, axiom-free · 3484a89d-0551…
lean_mechanical_genesis_64_the_codon — lean mechanical.lean: genesis_64_the_codon — 4 ^ 3 == 64 && 2 ^ 6 == 64 && 8 ^ 2 == 64 — decided by the Lean kernel over its whole finite domain, axiom-free · 5bc3c52a-0484…
lean_mechanical_a432_factors_as_two_to_the_fourth_times_three_cubed — lean mechanical.lean: a432_factors_as_two_to_the_fourth_times_three_cubed — 2 ^ 4 * 3 ^ 3 == 432 && 16 * 27 == 432 — decided by the Lean kernel over its whole finite domain, axiom-free · ace5e026-76f2…
lean_mechanical_two_bits_thrice_make_the_codon — lean mechanical.lean: two_bits_thrice_make_the_codon — 2 ^ 6 == 64 && (2 ^ 2) ^ 3 == 64 && 4 ^ 3 == 64 — decided by the Lean kernel over its whole finite domain, axiom-free · d7a6008c-4238…
lean_mechanical_the_full_superposition_has_nine_states — lean mechanical.lean: the_full_superposition_has_nine_states — (List.range' 1 9).length == 9 — decided by the Lean kernel over its whole finite domain, axiom-free · fcdb464a-6436…
lean_mechanical_trial_units_group — lean mechanical.lean: trial_units_group — let U9 := [1,2,4,5,7,8]; U9.all (fun u => U9.all (fun v => U9.contains (M9 (u * v)))) && U9.contains (1) && U9.all (fun u => U9.any (fun w => M9 (u * w) == 1)) — decided by the Lean kernel over its whole finite domain, axiom-free · 15329fd6-4630…
lean_mechanical_genus2_h1_symplectic — lean mechanical.lean: genus2_h1_symplectic — let rank := 2 * 2; rank == 4 && rank % 2 == 0 — decided by the Lean kernel over its whole finite domain, axiom-free · d8a36344-ce56…
lean_ledgerclaims_a_seal_is_128_bits — lean ledgerclaims.lean: a_seal_is_128_bits — (toUuidBytes [97]).length * 8 = 128 — decided by the Lean kernel over its whole finite domain, axiom-free · c552c1db-5200…
lean_ledgerclaims_membership_grows_by_one_seal_per_doubling — lean ledgerclaims.lean: membership_grows_by_one_seal_per_doubling — rounds 40 2 = 1 ∧ rounds 40 4 = 2 ∧ rounds 40 8 = 3 ∧ rounds 40 16 = 4 ∧ rounds 40 32 = 5 ∧ rounds 40 64 = 6 ∧ rounds 40 128 = 7 ∧ rounds 40 256 = 8 — decided by the Lean kernel over its whole finite domain, axiom-free · 0f753f22-7a7e…
lean_ledgerclaims_membership_is_logarithmic_not_linear — lean ledgerclaims.lean: membership_is_logarithmic_not_linear — rounds 40 1024 = 10 ∧ rounds 40 1024 < 1024 ∧ rounds 40 1024 * 128 < 1024 * 128 — decided by the Lean kernel over its whole finite domain, axiom-free · c45f3e11-aa53…
lean_ledgerclaims_the_967_receipt_case — lean ledgerclaims.lean: the_967_receipt_case — saving 967 20 = 947 ∧ 20 + 947 = 967 — decided by the Lean kernel over its whole finite domain, axiom-free · 94cd508a-bbf3…
lean_ledgerclaims_a_saving_never_exceeds_its_value — lean ledgerclaims.lean: a_saving_never_exceeds_its_value — (List.range 40).all (fun v => (List.range 40).all (fun w => saving v w ≤ v)) — decided by the Lean kernel over its whole finite domain, axiom-free · c6d64f4f-b2d8…
lean_ledgerclaims_more_payloads_than_addresses_must_collide — lean ledgerclaims.lean: more_payloads_than_addresses_must_collide — ((List.range 17).map addr4).eraseDups.length < 17 — decided by the Lean kernel over its whole finite domain, axiom-free · 83447fc9-2e89…
lean_ledgerclaims_the_address_does_not_determine_the_payload — lean ledgerclaims.lean: the_address_does_not_determine_the_payload — ((List.range 17).any (fun a => (List.range 17).any (fun b => a != b && addr4 a == addr4 b))) = true — decided by the Lean kernel over its whole finite domain, axiom-free · 4dbd784f-cd12…
lean_ledgerclaims_a_proof_is_smaller_than_its_set_across_the_octave — lean ledgerclaims.lean: a_proof_is_smaller_than_its_set_across_the_octave — (List.range' 2 255).all (fun n => rounds 40 n < n) — decided by the Lean kernel over its whole finite domain, axiom-free · bd52bf4d-20ac…
lean_merkle_fold_is_order_independent_on_three — lean merkle.lean: fold_is_order_independent_on_three — merkleFold [A, B, C] = merkleFold [A, C, B] ∧ merkleFold [A, B, C] = merkleFold [B, A, C] ∧ merkleFold [A, B, C] = merkleFold [B, C, A] ∧ merkleFold [A, B, C] = merkleFold [C, A, B] ∧ merkleFold [A, B, C] = merkleFold [C, B, A] — decided by the Lean kernel over its whole finite domain, axiom-free · d127c5dd-11ea…
lean_quantum_the_invariance_is_canonicalisation_not_physics — lean quantum.lean: the_invariance_is_canonicalisation_not_physics — (perms [1, 2, 4, 8]).all (fun p => sort p == sort [1, 2, 4, 8]) — decided by the Lean kernel over its whole finite domain, axiom-free · 8fc67bd3-13d9…
lean_quantum_the_receipt_is_not_injective — lean quantum.lean: the_receipt_is_not_injective — pairsOverNine.length = 45 ∧ (pairsOverNine.map receipt).eraseDups.length = 9 — decided by the Lean kernel over its whole finite domain, axiom-free · e341b19b-3658…
lean_quantum_the_uncanonicalised_fold_gives_many_answers — lean quantum.lean: the_uncanonicalised_fold_gives_many_answers — ((perms [1, 2, 4, 8]).map naive).eraseDups.length = 5 — decided by the Lean kernel over its whole finite domain, axiom-free · 35063521-90d0…
lean_reversal_reversal_is_involutive_exactly_off_the_trailing_zeros — lean reversal.lean: reversal_is_involutive_exactly_off_the_trailing_zeros — (List.range' 1 300).all (fun n => (reverseNum (reverseNum n) == n) == (n % 10 != 0)) — decided by the Lean kernel over its whole finite domain, axiom-free · 7c3f81f9-1ab8…
lean_fnv_the_hash_is_order_sensitive — lean fnv.lean: the_hash_is_order_sensitive — hash32 0 [97, 98] ≠ hash32 0 [98, 97] — decided by the Lean kernel over its whole finite domain, axiom-free · 9ebfd1f3-a326…
lean_fnv_the_empty_input_is_still_mixed — lean fnv.lean: the_empty_input_is_still_mixed — hash32 0 [] = 2872998923 ∧ hash32 FNV_OFFSET [] = 0 ∧ avalanche 0 = 0 — decided by the Lean kernel over its whole finite domain, axiom-free · a295a883-8e7e…
lean_merkaba_the_three_classes_partition_z9 — lean merkaba.lean: the_three_classes_partition_z9 — axis.length = 3 ∧ tetA.length = 3 ∧ tetB.length = 3 ∧ (axis ++ tetA ++ tetB).eraseDups.length = 9 ∧ ((List.range 9).all (fun d => (axis ++ tetA ++ tetB).contains d)) — decided by the Lean kernel over its whole finite domain, axiom-free · 347bb6f8-bba6…
lean_merkaba_the_axis_is_closed_under_doubling — lean merkaba.lean: the_axis_is_closed_under_doubling — (dbl axis).all (fun d => axis.contains d) — decided by the Lean kernel over its whole finite domain, axiom-free · 9de5030e-7ecd…
lean_merkaba_doubling_counter_rotates_the_two_tetrahedra — lean merkaba.lean: doubling_counter_rotates_the_two_tetrahedra — (dbl tetA).eraseDups.length = 3 ∧ (dbl tetA).all (fun d => tetB.contains d) ∧ (dbl tetB).eraseDups.length = 3 ∧ (dbl tetB).all (fun d => tetA.contains d) — decided by the Lean kernel over its whole finite domain, axiom-free · a409ff11-15ca…
lean_merkaba_the_counter_rotation_has_period_two — lean merkaba.lean: the_counter_rotation_has_period_two — (dbl (dbl tetA)).all (fun d => tetA.contains d) ∧ (dbl (dbl tetB)).all (fun d => tetB.contains d) — decided by the Lean kernel over its whole finite domain, axiom-free · 7261ab56-ed9b…
lean_merkaba_the_tetrahedra_residue_sums_cancel — lean merkaba.lean: the_tetrahedra_residue_sums_cancel — m9 (tetA.foldl (· + ·) 0) = 3 ∧ m9 (tetB.foldl (· + ·) 0) = 6 ∧ m9 (tetA.foldl (· + ·) 0 + tetB.foldl (· + ·) 0) = 0 — decided by the Lean kernel over its whole finite domain, axiom-free · 8e4fb3a9-f5aa…
lean_merkaba_one_tetrahedron_covers_half_the_units — lean merkaba.lean: one_tetrahedron_covers_half_the_units — (units.filter (fun d => tetA.contains d)).length = 3 ∧ (units.filter (fun d => tetB.contains d)).length = 3 ∧ units.length = 6 — decided by the Lean kernel over its whole finite domain, axiom-free · c5305e5f-2386…
lean_merkaba_the_cube_and_the_tetrahedron_count_out — lean merkaba.lean: the_cube_and_the_tetrahedron_count_out — 2 ^ 3 = 8 ∧ 3 * 2 ^ 2 = 12 ∧ 4 + 4 - 6 = 2 — decided by the Lean kernel over its whole finite domain, axiom-free · 18accb6b-20e6…
lean_merkaba_stacked_triangles_are_tetrahedral — lean merkaba.lean: stacked_triangles_are_tetrahedral — (List.range' 1 40).all (fun n => sumTri n == n * (n + 1) * (n + 2) / 6) — decided by the Lean kernel over its whole finite domain, axiom-free · 4611383b-7ebe…
lean_energy_a_chain_of_efficiencies_can_only_lose — lean energy.lean: a_chain_of_efficiencies_can_only_lose — (List.range 101).all (fun a => (List.range 101).all (fun b => a * b ≤ 100 * a && a * b ≤ 100 * b)) — decided by the Lean kernel over its whole finite domain, axiom-free · 34cbdadb-77a7…
lean_energy_the_gases_are_two_to_one_and_consume_each_other_exactly — lean energy.lean: the_gases_are_two_to_one_and_consume_each_other_exactly — 2 * 1 = 2 ∧ (2 * 100 / 3 = 66) ∧ (1 * 100 / 3 = 33) ∧ ¬ (1 * 1 = 2) — decided by the Lean kernel over its whole finite domain, axiom-free · 4411df61-18c7…
lean_energy_mass_is_conserved_at_every_scale_so_the_loop_cannot_make_water — lean energy.lean: mass_is_conserved_at_every_scale_so_the_loop_cannot_make_water — (List.range' 1 100).all (fun n => 2 * n * mgH2O == 2 * n * mgH2 + n * mgO2) ∧ ¬ ((List.range' 1 100).all (fun n => n * mgH2O == n * mgH2 + n * mgO2)) — decided by the Lean kernel over its whole finite domain, axiom-free · 55429cd8-2b19…
lean_energy_one_litre_split_returns_one_litre_burnt — lean energy.lean: one_litre_split_returns_one_litre_burnt — 111900 + 888100 = 1000000 ∧ 888100 * 100 / 111900 = 793 — decided by the Lean kernel over its whole finite domain, axiom-free · e88c70d6-0123…
lean_energy_only_oxy_hydrogen_burns_without_admitting_nitrogen — lean energy.lean: only_oxy_hydrogen_burns_without_admitting_nitrogen — 7808 * 100 / 2095 = 372 ∧ 0 * 372 = 0 ∧ ¬ (372 = 0) — decided by the Lean kernel over its whole finite domain, axiom-free · 69997ab3-1d7e…
lean_energy_the_two_to_one_is_forced_by_the_oxygen — lean energy.lean: the_two_to_one_is_forced_by_the_oxygen — balances 2 2 1 = true ∧ balances 1 1 1 = false ∧ (((List.range' 1 9).flatMap (fun a => (List.range' 1 9).flatMap (fun b => (List.range' 1 9).filter (fun c => balances a b c)))).length = 4) ∧ balances 4 4 2 = true ∧ balances 6 6 3 = true ∧ b… — decided by the Lean kernel over its whole finite domain, axiom-free · 75828bd9-1d34…
lean_imagined_squares_is_closed_under_quadruple — lean imagined.lean: squares_is_closed_under_quadruple — [0, 1, 4, 7].all (fun d => [0, 1, 4, 7].contains (m9 (4 * d))) — decided by the Lean kernel over its whole finite domain, axiom-free · 12d7a596-c1f8…
lean_imagined_cubes_is_closed_under_negate — lean imagined.lean: cubes_is_closed_under_negate — [0, 1, 8].all (fun d => [0, 1, 8].contains (m9 (9 - d))) — decided by the Lean kernel over its whole finite domain, axiom-free · 78ef83db-c595…
lean_imagined_squares_is_closed_under_septuple — lean imagined.lean: squares_is_closed_under_septuple — [0, 1, 4, 7].all (fun d => [0, 1, 4, 7].contains (m9 (7 * d))) — decided by the Lean kernel over its whole finite domain, axiom-free · 929df56e-f860…
lean_imagined_cubes_is_closed_under_octuple — lean imagined.lean: cubes_is_closed_under_octuple — [0, 1, 8].all (fun d => [0, 1, 8].contains (m9 (8 * d))) — decided by the Lean kernel over its whole finite domain, axiom-free · 91dcd0db-2571…
lean_imagined_cube_is_involutive_on_cubes — lean imagined.lean: cube_is_involutive_on_cubes — [0, 1, 8].all (fun d => (fun x => m9 (x * x * x)) (m9 (d * d * d)) == d) — decided by the Lean kernel over its whole finite domain, axiom-free · d607231e-ecb2…
lean_mechanical_relation_digital_root — lean mechanical.lean: relation_digital_root — DR (78) == 6 && DR (12) == DR (21) && [1,2,4,5,7,8].contains (DR (7)) — decided by the Lean kernel over its whole finite domain, axiom-free · d07323c6-683c…
lean_mechanical_relation_432_factors — lean mechanical.lean: relation_432_factors — 432 == 16 * 27 && 432 == 2 ^ 4 * 3 ^ 3 && DR (432) == 9 — decided by the Lean kernel over its whole finite domain, axiom-free · 34d3073f-7f81…
lean_mechanical_fib_trinity_horizon — lean mechanical.lean: fib_trinity_horizon — DR (3 + 5 + 8) == 7 — decided by the Lean kernel over its whole finite domain, axiom-free · 458420c0-010d…
lean_mechanical_trial_zero_divisors — lean mechanical.lean: trial_zero_divisors — M9 (3 * 3) == 0 && M9 (3) != 0 — decided by the Lean kernel over its whole finite domain, axiom-free · fdd05138-da57…
lean_mechanical_chess_diagonals_15 — lean mechanical.lean: chess_diagonals_15 — 2 * 8 - 1 == 15 — decided by the Lean kernel over its whole finite domain, axiom-free · 120f9fa4-00be…
lean_mechanical_tarot_78_cards — lean mechanical.lean: tarot_78_cards — 22 + 56 == 78 — decided by the Lean kernel over its whole finite domain, axiom-free · 1b4474e3-f5f2…
lean_mechanical_tarot_minor_4x14 — lean mechanical.lean: tarot_minor_4x14 — 4 * 14 == 56 — decided by the Lean kernel over its whole finite domain, axiom-free · 9a2afdef-23ab…
lean_mechanical_tarot_major_0_21 — lean mechanical.lean: tarot_major_0_21 — ((List.range 22).filter (fun n => n >= 0 && n <= 21)).length == 22 — decided by the Lean kernel over its whole finite domain, axiom-free · 7fbea55e-c8ea…
lean_mechanical_tarot_digital_roots — lean mechanical.lean: tarot_digital_roots — DR (78) == 6 && DR (22) == 4 && DR (56) == 2 — decided by the Lean kernel over its whole finite domain, axiom-free · a93fffd5-b931…

other — one-of-a-kind (0)

Revoked — 1593 entries that no longer stand

The ledger is append-only: an entry that stops holding is marked in place, never deleted — deleting would break the receipt chain, and rewriting a receipt is tamper. These keep their receipts and stay in the record, but they are not citable and have no /theorem/ page. Grouped by the reason they went:

1011 — dirty: not backed by a Lean proof
443 — revoked in place: its test asserted a lexical drain (computes(boast)
108 — orphaned: the theorem this key was sealed from is no longer in src/proof
12 — revoked in place: circular by construction AND dependent on the removed lexical gate
10 — revoked in place: circular by construction — the test defines the answer it checks, proving a declaration rather than a fact
7 — renamed to what it decides (2026-09-18, by the author's order)
1 — revoked in place: its test asserts that a list of proof-boasts written across many scripts and languages ALL drain the gate — a lexical drain assertion, and the word-list gate was removed by order, so there is no lexicon to drain and the assertion tests nothing
1 — revoked in place: it asserts adjudicate('we prove all seven')

Carried — 826 withdrawn entries whose statement a proof now carries

Each was withdrawn for want of a Lean proof and has since been given one, at a new key. The entry is not restored: its own evidence is still a TypeScript test, and it did not hold on what it had. What the record adds is where the statement stands now.

~~euler_units_pow6~~ → lean_z9_euler_units_pow_six
~~units_sum_zero~~ → lean_recovered_units_sum_zero
~~self_inverse_1_8~~ → lean_recovered_self_inverse_1_8
~~triad_nilpotent~~ → lean_recovered_triad_nilpotent
~~doubling_digitroot_period6~~ → lean_recovered_doubling_digitroot_period6
~~units_product_neg1~~ → lean_recovered_units_product_neg1
~~triad_sum_zero~~ → lean_recovered_triad_sum_zero
~~cubes_in_0_1_8~~ → lean_z9plus_cubes_land_exactly_in_zero_one_eight
~~squares_in_0_1_4_7~~ → lean_z9plus_squares_land_exactly_in_zero_one_four_seven
~~order_of_2_is_6~~ → lean_recovered_order_of_2_is_6
~~sum_1_to_9_zero~~ → lean_recovered_sum_1_to_9_zero
~~pisano_9_is_24~~ → lean_families_the_pisano_period_of_nine_is_twenty_four_and_every_modulus_to_twelve_has_one
~~powperm_k5~~ → lean_recovered_powperm_k5
~~powperm_k7~~ → lean_recovered_powperm_k7
~~mulperm_k2~~ → lean_families_multiplication_permutes_z9_at_exactly_the_units
~~mulperm_k4~~ → lean_families_multiplication_permutes_z9_at_exactly_the_units
~~mulperm_k5~~ → lean_families_multiplication_permutes_z9_at_exactly_the_units
~~mulperm_k7~~ → lean_families_multiplication_permutes_z9_at_exactly_the_units
~~mulperm_k8~~ → lean_families_multiplication_permutes_z9_at_exactly_the_units
~~unit_exp_id_k6~~ → lean_recovered_unit_exp_id_k6
~~unit_exp_id_k12~~ → lean_recovered_unit_exp_id_k12
~~unit_exp_id_k18~~ → lean_recovered_unit_exp_id_k18
~~qr_u1~~ → lean_recovered_qr_u1
~~qr_u4~~ → lean_recovered_qr_u4
~~addgen_k2~~ → lean_families_addition_generates_z9_at_exactly_the_units
~~addgen_k4~~ → lean_families_addition_generates_z9_at_exactly_the_units
~~addgen_k5~~ → lean_families_addition_generates_z9_at_exactly_the_units
~~addgen_k7~~ → lean_families_addition_generates_z9_at_exactly_the_units
~~addgen_k8~~ → lean_families_addition_generates_z9_at_exactly_the_units
~~powsum0_k1~~ → lean_generated_powsum_zero_odd_exponents
~~powsum0_k3~~ → lean_generated_powsum_zero_odd_exponents
~~powsum0_k5~~ → lean_generated_powsum_zero_odd_exponents
~~powsum0_k7~~ → lean_generated_powsum_zero_odd_exponents
~~powsum0_k9~~ → lean_generated_powsum_zero_odd_exponents
~~powsum0_k11~~ → lean_generated_powsum_zero_odd_exponents
~~powsum0_k13~~ → lean_generated_powsum_zero_odd_exponents
~~powsum0_k15~~ → lean_generated_powsum_zero_odd_exponents
~~powsum0_k17~~ → lean_generated_powsum_zero_odd_exponents
~~hasinv_d1~~ → lean_families_an_inverse_mod_nine_exists_at_exactly_the_units
~~hasinv_d2~~ → lean_families_an_inverse_mod_nine_exists_at_exactly_the_units

…and 786 more.

List all 1593 withdrawn keys — nothing proves these

~~qr_u7~~ · 2a422f9b-761a…
~~powinv_k5~~ · 8e327990-c88f…
~~powinv_k7~~ · 469cfad5-9293…
~~selfinv_u1~~ · 558f7d79-d3d7…
~~selfinv_u8~~ · 3bc79c77-36a1…
~~selfneg_d9~~ · 8d0d0254-5ca1…
~~reverse_circuit~~ · 205fe01b-d27f…
~~bool_double_negation~~ · a4640234-4e32…
~~bool_excluded_middle~~ · 29468d4a-f416…
~~bool_noncontradiction~~ · 1d8543d8-7d61…
~~bool_xor_associativity~~ · 4ba6ccd9-fd1d…
~~entangle_joint_differs~~ · 9657bf0d-5c1f…
~~entangle_no_influence~~ · 7267ca5a-c961…
~~entangle_floor_holds~~ · 2b7b5b94-580f…
~~duel_overclaim_falls~~ · c05da1be-673a…
~~duel_no_both_win~~ · ea632dd9-0682…
~~duel_floor_upheld~~ · 4ee11b6a-d6b6…
~~hasse_p5_a1_b1~~ · 73bd58ba-4989…
~~hasse_p7_a2_b3~~ · a3d3160b-8c8a…
~~hasse_p11_a1_b6~~ · 51f2a2c6-6e67…
~~hasse_p13_a3_b8~~ · 678a2d8a-7e87…
~~s3_order6~~ · 40c95681-97c1…
~~s3_nonabelian~~ · 996f2aa1-6e10…
~~s3_sign_homomorphism~~ · 7c46468e-641c…
~~gauss_four_units~~ · 7b8ebbf0-0bf5…
~~gauss_i_squared~~ · 185b3eda-935c…
~~gauss_norm_multiplicative~~ · 7e709c97-78f3…
~~handshake_z9~~ · 44f09f3c-e542…
~~merkaba_field_max_null~~ · a9c3214f-3ec7…
~~cover_one_tetra_partial~~ · 8c7bcc8a-1869…
~~cover_moving_pair_full~~ · 22b9e194-9be5…
~~pascal_rowsum_n5~~ · 3b4e481c-bd45…
~~pascal_rowsum_n8~~ · b62025f5-f7ec…
~~pascal_rowsum_n10~~ · 099a0df7-929c…
~~roots_cancel_n2~~ · f14563e3-9bf7…
~~roots_cancel_n3~~ · 0d08dcee-c228…
~~roots_cancel_n5~~ · 986f830c-ea1b…
~~roots_cancel_n7~~ · 87f482d5-8600…
~~roots_cancel_n9~~ · 8a7804c7-2d8c…
~~a432_directions_cancel~~ · 90b398a0-b189…
~~farey_neighbor_F5~~ · 170484c5-3b95…
~~farey_neighbor_F6~~ · 21bdf7ff-2f61…
~~quarter_turn_order4~~ · 02f0a928-7bda…
~~both_games_truth_and_honesty~~ · 346f2fb8-6b23…
~~both_games_overclaim_loses~~ · 65cc1cf8-20a5…
~~both_games_358~~ · c26cc4c6-7c93…
~~arts_triad_rgb_primaries~~ · 316f831d-95da…
~~arts_cmy_complements_rgb~~ · 13b5af77-bfc6…
~~arts_golden_proportion~~ · 48801162-b59d…
~~vocab_ceccec_palindrome~~ · 02301560-d210…
~~vocab_ceccec_digits~~ · f88b8d6d-e2b8…
~~vocab_letter_sum_reversal_invariant~~ · b7bf6005-1692…
~~vocab_glagolitic_bijection~~ · 2149d57c-d222…
~~vocab_seven_locales~~ · 21c521ea-3baf…
~~gematria_vortex_heart~~ · 63abfd7c-c91c…
~~gematria_trinity_horizon~~ · dce0ba69-7ba9…
~~gematria_51_class~~ · b38c9c21-a8ac…
~~gematria_ceccec_harmony_4~~ · cbd3ab4e-2f05…
~~gematria_singularity_horo_2~~ · 1c434409-549d…
~~lens_strings_not_meaning~~ · 9ab46c9a-f620…
~~lens_concept_handle_order_independent~~ · 5e07b827-f250…
~~lens_deterministic~~ · b46579fd-1b90…
~~arts_no_exact_complement~~ · 1656079f-c131…
~~trial_overclaim_drained~~ · 57c46000-4768…
~~trial_pvnp_inconclusive~~ · 94e908b9-21b1…
~~trial_ftl~~ · 54f91340-a811…
~~trial_perpetual_motion~~ · 685da6ef-4b31…
~~trial_agi~~ · ce4c822c-ff01…
~~trial_theory_of_everything~~ · b5fb911f-76b2…
~~trial_halting~~ · f27135ee-9373…
~~trial_break_rsa~~ · f66ff38a-4d9b…
~~trial_cure~~ · 67614421-7817…
~~trial_prediction~~ · 8412c3c0-9f52…
~~gematria_nim_games_9~~ · e935f43f-8872…
~~gematria_nim_theorists_87~~ · 34bbaaa2-e335…
~~gematria_combinatorics_52~~ · d7265dff-3bf4…
~~gematria_fibonacci_pair_2~~ · 3fda7026-d509…
~~gematria_golden_pair_1~~ · b05ef0a5-d593…
~~nopayload_no_plaintext~~ · a6ff3942-3585…
~~nopayload_not_encryption~~ · 66c44e2d-e591…
~~involution_sigma~~ · 2032f25f-ca45…
~~involution_reversible~~ · 09577a63-e630…
~~ledger_merkle_inclusion~~ · 4c03b866-98e2…
~~ledger_merkle_rejects_forgery~~ · 65b1525f-07ad…
~~ledger_tamper_changes_root~~ · ae5b2c11-de5b…
~~ledger_hash_chain~~ · 691d1a9c-b02a…
~~harmonic_ledger_hue~~ · 089d12f5-4e12…
~~harmonic_ledger_deterministic~~ · 24aa4bf9-516c…
~~harmonic_root_hue~~ · f302789e-a628…
~~nowaste_dedup~~ · 9d5f8f65-d529…
~~nowaste_order_independent~~ · 23112077-b200…
~~nowaste_memo_recycles~~ · f7698d60-8475…
~~discovery_chain~~ · b24d6d56-123d…
~~geom_dihedral_358~~ · 9fd2e0db-cb62…
~~geom_pentagon_golden~~ · 2baca20d-9c58…
~~tarot_holds_theorems~~ · 9c03a373-918f…
~~tarot_theorem_encoding~~ · 34f750b8-b626…
~~tarot_major_of_theorem~~ · eb0e5a3d-d84c…
~~tarot_distinct_theorems~~ · b50eee93-69b1…
~~tarot_renders_not_divines~~ · 7b2b309b-6b24…
~~tarot_encoding_total~~ · f7f6254d-4c7e…
~~tictactoe_draw~~ · 95089477-058f…
~~one_game_harmony~~ · 55cb8c5f-73cc…
~~one_art_harmony~~ · 6abed2f1-66f5…
~~one_science_harmony~~ · 831f5688-1127…
~~one_game_all~~ · ea90214e-fe97…
~~pell_sqrt2~~ · f2cf267e-e349…
~~gf4_frobenius_fixes~~ · fb7953fe-d9e3…
~~gf4_frobenius_automorphism~~ · c117a740-97d9…
~~gf4_units_cyclic~~ · 462b849d-7d1f…
~~euclid_euler_perfect~~ · 9f35788a-a976…
~~collatz_reaches_1_range~~ · 5842dff6-fc0d…
~~collatz_27_orbit~~ · 2b528505-25f6…
~~collatz_open~~ · 5524c423-8dc8…
~~relation_golden~~ · 4a37bd0c-74ee…
~~relation_doubling~~ · 9d8271dd-56d8…
~~relation_xor~~ · 5f57290e-9bc5…
~~relation_involution~~ · cde24c0a-f206…
~~the_modules_self_compute~~ · e9948e15-ed3d…
~~harmonic_just_ratios~~ · b62838b4-dbf4…
~~harmonic_convention_bound~~ · d80f191a-d8c4…
~~stirling_second_bell~~ · 23e393cc-dd5d…
~~stirling_first_factorial~~ · e1f258a9-dbdb…
~~stirling_edges~~ · 02ae48de-5452…
~~chromatic_K4~~ · b25fc510-ee6b…
~~chromatic_cycles~~ · f6dee48e-8a3a…
~~chromatic_petersen~~ · c8d24ff1-f5ac…
~~rule90_sierpinski~~ · 07dbb102-aef1…
~~pascal_mod2_lucas~~ · 3d9ea41f-0180…
~~cf_sqrt2~~ · a6818a20-2d51…
~~cf_sqrt7~~ · f062762b-1892…
~~cf_perfect_square~~ · 08e82fe9-197c…
~~cf_periodic~~ · 35681143-e4a0…
~~relation_five~~ · 80af9a22-1ad0…
~~relation_pascal_mod2~~ · dee2f2df-8ac3…
~~relation_pell_structure~~ · 10fa7f5c-bc2b…
~~relation_content_address~~ · 2a33c2ba-b5fd…
~~relation_order_independence~~ · 830cce0a-f00b…
~~quaternion_hamilton~~ · 33c7aebb-0cf3…
~~quaternion_noncommutative~~ · 0dca5831-27b0…
~~quaternion_8_units~~ · 591b9388-6c28…
~~motzkin_numbers~~ · d6c643c7-2880…
~~relation_i_squared~~ · e795ceea-3981…
~~bernoulli_numbers~~ · e1488277-afe2…
~~bernoulli_odd_zero~~ · 1c8c8337-a2d1…
~~relation_three~~ · 81c99cf8-73de…
~~relation_catalan~~ · 49db58c0-5101…
~~totient_divisor_sum~~ · 48628d5b-053e…
~~relation_superposition~~ · 4c2d2d08-ab33…
~~pascal_rule~~ · 9ca05e61-ef59…
~~vandermonde_identity~~ · 1302e2f2-1d77…
~~gcd_lcm_product~~ · 6dd98763-e7c2…
~~relation_superposition_is_fold~~ · 2badb5bd-1ac1…
~~relation_superposition_entanglement~~ · 56849fe1-8015…
~~platonic_euler~~ · d5243749-5918…
~~platonic_exactly_five~~ · 82196bbc-1108…
~~platonic_duality~~ · ae03ec6a-236e…
~~relation_pentagram~~ · 078d42cd-d422…
~~diamond_tetrahedral_angle~~ · d8ef0cba-eb12…
~~diamond_coordination~~ · 07325637-589a…
~~fcc_packing_fraction~~ · 5919405f-4b55…
~~relation_diamond~~ · a08e499e-f88d…
~~relation_path_rating~~ · e64ef7b3-c718…
~~wilson_theorem~~ · 060d88ea-9ab8…
~~fermat_little_theorem~~ · 0f0e2397-2586…
~~fermat_two_squares~~ · f73538ca-ca7c…
~~triangular_square~~ · 787c8714-6ea3…
~~surface_euler_char~~ · ee2c16a3-aad0…
~~coverage_only_torus~~ · 09e87d88-c3d6…
~~relation_genus_two~~ · 2f63c1c1-bfa8…
~~genus2_betti~~ · d354356d-e503…
~~genus2_connected_sum~~ · 770b925d-03ab…
~~genus2_octagon~~ · 1bdea2df-8c50…
~~genus2_gauss_bonnet~~ · b0232c41-1887…
~~surface_classification~~ · 95c6da2d-4c99…
~~coverage_torus_and_klein~~ · 83a457a6-7afb…
~~uniformization_trichotomy~~ · d83c2656-d21c…
~~subtraction_game_grundy~~ · a3094aa6-da92…
~~kayles_grundy~~ · b6db3052-5c2a…
~~nim_misere~~ · 0823bb14-7699…
~~fair_division_envy_free~~ · 16f252b2-ed93…
~~honeycomb_tiling~~ · 6108a7d0-88b6…
~~rps_cyclic~~ · 1fc40bf5-ae3d…
~~rps_nash_uniform~~ · 8ad0f309-1420…
~~relation_rps_z3~~ · 6b0eec5f-d46f…
~~golden_fixed_point~~ · 80d92d5a-7ef3…
~~fibonacci_ratio_phi~~ · 3973e404-f749…
~~harmonic_series_diverges~~ · 7f9249a7-092e…
~~relation_more_the_more~~ · a29834f0-8094…
~~cancer_inversion_heals~~ · 9ec77026-e0b8…
~~traitor_resurrects_as_hero~~ · f7be659d-f270…
~~cancer_dissolves_by_waves~~ · d783f335-57a4…
~~observer_wave_sets_state~~ · f7de310a-8d54…
~~balancing_wave_harmonises~~ · 8f9898b3-d143…
~~development_enforced_at_gate~~ · 5ec8d383-43d6…
~~destroying_evidence_is_treason~~ · 7da2719b-e800…
~~legal_trial_decides~~ · 044301ca-0913…
~~forensics_chain_of_custody~~ · 037ea589-afdd…
~~forensics_intention_from_deeds~~ · a0b19943-2df3…
~~star_graph_diameter_two~~ · df906703-3f95…
~~relation_rosetta_star~~ · 53538c68-2bdb…
~~handshake_lemma~~ · 0b0c1d31-3705…
~~lagrange_subgroup_order~~ · ba7c559a-759f…
~~cyclic_generators_phi~~ · f0e2e228-d553…
~~derangements~~ · 6970bda5-5f11…
~~inclusion_exclusion~~ · 53b5d2ab-2323…
~~chinese_remainder~~ · d051f54b-5713…
~~quadratic_residues_euler~~ · 7fa74f71-45c4…
~~pigeonhole_principle~~ · 55bef22b-5135…
~~pick_theorem~~ · e316b749-3010…
~~ramsey_r33~~ · 23cacdea-c68c…
~~cauchy_schwarz~~ · f513285b-39c3…
~~am_gm_inequality~~ · 3fd7d863-31e4…
~~cantor_pairing~~ · 1b2e9abe-ca7b…
~~partition_pentagonal~~ · 48ac0164-7c5a…
~~lucas_theorem~~ · f64054e9-231b…
~~rosetta_complete~~ · 3aa73d2c-52f8…
~~logistic_fixed_point~~ · 1582bdff-443f…
~~logistic_sensitive_dependence~~ · be96472b-78b0…
~~chaos_deterministic_unpredictable~~ · a3b2af5b-1f1b…
~~siteswap_valid_permutation~~ · 08d0be78-7e6e…
~~siteswap_average_theorem~~ · 65bbd224-513f…
~~relation_juggling_clown~~ · 8d61e5b2-5eee…
~~relation_clown_benefits_from_all~~ · bac1351d-ae94…
~~relation_clown_respects_rules~~ · 56557ac3-77ac…
~~receipt_is_entanglement_pair~~ · f71771ad-075c…
~~receipt_pair_is_two_coins~~ · 8107fd62-4172…
~~receipt_cost_funds_development~~ · 42f68f41-fe6c…
~~self_is_connection_set~~ · a4e90f2a-cc08…
~~imprint_roundtrip_identity~~ · b42af2b5-cc1a…
~~coin64_deterministic_64bit~~ · 4fca16fc-4199…
~~relation_receipt_coins_genus~~ · 87c649f9-81d4…
~~relation_self_is_rosetta_star~~ · 5928472c-c72b…
~~relation_currency_is_addressing~~ · 64614b34-bf5a…
~~relation_floor_invariant_across_domains~~ · 56539ae7-ce6a…
~~relation_harmony_is_merkle_consensus~~ · 83b97b8f-f975…
~~relation_competition_is_the_gate~~ · a1bf8afd-3b09…
~~relation_orbit_is_cyclic_group~~ · 93c01d9d-914c…
~~relation_a432_partitions_circle~~ · a07bc68e-9516…
~~relation_involutions_bind_domains~~ · 62e42b0f-3bc2…
~~relation_units_are_coprime_to_base~~ · 5b768aaf-a061…
~~relation_pisano_binds_fibonacci~~ · 06593486-abf7…
~~relation_triad_is_multiples_of_three~~ · f980158a-8739…
~~relation_imprint_capacity_structure~~ · 2dd85b4b-938a…
~~relation_coin64_is_half_address~~ · b7a0dd2a-c11c…
~~relation_reflection_center_five~~ · 7d631733-c04b…
~~relation_ninecomplement_permutes_units~~ · 9643c24f-342a…
~~relation_cubes_fold_to_0_1_8~~ · b233f460-cd4d…
~~relation_receipt_chain_is_forensic_custody~~ · d0307011-b34a…
~~relation_coin64_collision_free_on_domains~~ · dc278848-c7d9…
~~kaprekar_3digit_fixed_495~~ · e3dcb640-7ef2…
~~kaprekar_4digit_fixed_6174~~ · 281de8d0-de1d…
~~kaprekar_3digit_converges_495~~ · f2904983-365a…
~~kaprekar_4digit_converges_6174~~ · 70bf5db2-ef8c…
~~kaprekar_repdigit_collapses_zero~~ · dc31aff0-745f…
~~magic3_constant_15~~ · aae70a2b-a007…
~~magic3_count_is_8~~ · 32b64f76-3ce4…
~~magic3_center_is_5~~ · 188b78b7-199c…
~~magic3_corners_even_edges_odd~~ · 80f537f2-862e…
~~magic3_opposite_cells_sum_10~~ · c527c7e0-2820…
~~magic3_constant_digitroot_6~~ · 673cb9e4-1b3c…
~~sealing_is_not_signing~~ · 21b0a512-85e8…
~~keyless_signature_is_forgeable~~ · 9fd61992-d9ef…
~~authenticity_needs_a_secret~~ · 53096a30-d41f…
~~unsigned_statement_holds_floor~~ · 7bfa02e2-7e18…
~~sealed_but_unsigned_are_independent~~ · 1dbf5015-b10e…
~~challenge_direct_overclaim_drains~~ · 025fa97c-a107…
~~challenge_assertion_of_proof_drains~~ · 98fcf661-a7ef…
~~challenge_crypto_break_drains~~ · 517c653e-a9ee…
~~challenge_prediction_drains~~ · 5d192a62-3fec…
~~challenge_gate_is_lexical_not_semantic~~ · 3f96a392-fc03…
~~challenge_obfuscation_slips_gate~~ · 46c6007c-7552…
~~destroying_evidence_treason_even_by_chance~~ · 3d546a84-8ef5…
~~all_are_heroes_but_the_traitors~~ · efa3b6f1-00b7…
~~evidence_is_what_recomputes~~ · 130afdb1-d7f8…
~~evidence_survives_recycle~~ · 0512a452-1559…
~~evidence_survives_forensic_analysis~~ · 7a372597-0caa…
~~non_recomputable_is_not_evidence~~ · 4614b71d-1703…
~~evidence_is_recompute_post_recycle_and_forensics~~ · a7c24079-950d…
~~legal_trial_is_not_is_affirmation~~ · 16a7b426-65be…
~~negation_selects_positive_complement~~ · abc4ca08-dc09…
~~floor_invariant_across_all_worlds~~ · 67b19efa-8710…
~~violators_are_traitors_let_all_try_and_prove~~ · d2a2d59d-97e6…
~~twisting_a_lie_does_not_compute_true~~ · afa0fee5-1e2f…
~~undocumented_discovery_is_treason~~ · 0c4af820-cbb3…
~~gate_reads_whole_text_not_per_line~~ · 3986bc57-0971…
~~bell_state_no_signaling~~ · c3348bf3-6f6e…
~~state_vector_exponential_no_advantage~~ · 1a2f010c-c2cc…
~~simulating_quantum_is_not_being_quantum~~ · d6d0ec25-e41f…
~~computed_is_integrity_the_declared_verdict_drains~~ · b6edac7b-d0c4…
~~honesty_binary_obeys_boolean_algebra~~ · 6d8f7b54-4ad3…
~~doubling_is_binary_left_shift~~ · 4d0c4a24-5fd2…
~~content_addressing_is_bit_algebra~~ · 8ccb9d02-6614…
~~generated_prose_holds_the_gate_by_construction~~ · 99c78560-fda8…
~~uuid_128bit_capacity_is_bounded~~ · 110261c9-cbf0…
~~no_crack_evades_the_content_address~~ · 26558d49-1151…
~~bidirectional_encoding_is_the_double_torus~~ · db8365fd-657b…
~~gray_code_single_bit_transition~~ · c1f2b63b-cae4…
~~gray_code_hamiltonian_cycle~~ · 8329eb98-006e…
~~parity_bit_detects_single_error~~ · 37a8eb94-b551…
~~hamming74_corrects_any_single_error~~ · 8725a6eb-aa41…
~~hamming74_minimum_distance_three~~ · b108ba72-765e…
~~no_error_in_harmonics_across_lifespan~~ · e8c447e2-6ddd…
~~the_floor_holds_even_on_demand~~ · 9f4ee4b5-057f…
~~zeckendorf_exists_no_consecutive~~ · fc1da781-afd9…
~~zeckendorf_representation_unique~~ · c21a803b-fee4…
~~fibonacci_lts_minors_are_zeckendorf_base~~ · a896449a-a35b…
~~any_64bit_machine_suffices~~ · 31f2c89b-9b7a…
~~drift_signals_disresonance~~ · fd1755ff-8ebd…
~~the_sequence_is_the_classical_opposite_of_quantum~~ · 3d3837b1-1982…
~~farey_neighbours_unimodular~~ · f122d7de-8779…
~~farey_mediant_between_and_reduced~~ · 863ad7a4-6be9…
~~farey_lists_every_reduced_fraction_once~~ · bc1bf0aa-1f40…
~~discrete_log_base2_is_a_bijection~~ · bbb6d49b-792f…
~~discrete_log_is_group_isomorphism~~ · 66a1d58a-91e9…
~~gf2_addition_is_xor~~ · b3ac7829-c58e…
~~crc_codeword_divisible_by_generator~~ · fb2f0e96-86e7…
~~crc_detects_every_single_bit_error~~ · 13b07ce4-3902…
~~nim_loss_iff_zero_nimsum~~ · c1487d07-3fe4…
~~nim_winning_move_zeros_the_nimsum~~ · e90ed988-ec04…
~~every_rating_is_exactly_one_or_zero~~ · c1b2772d-d7c0…
~~development_balances_to_binary~~ · cf105a78-9a23…
~~eisenstein_omega_cubed_is_one~~ · 498200ff-921c…
~~cube_roots_of_unity_sum_zero~~ · 6b25148c-1c75…
~~josephus_k2_closed_form~~ · 1719d6d1-1575…
~~josephus_k2_is_left_bit_rotation~~ · cc825255-e0c8…
~~josephus_survivor_always_odd~~ · c40d916e-c633…
~~stern_consecutive_terms_coprime~~ · 5726bedf-7c20…
~~calkin_wilf_enumerates_rationals_once~~ · 03262760-6857…
~~stern_row_sum_is_power_of_three~~ · 88d1069b-4c2d…
~~each_theorem_can_replace_code~~ · 02be2d16-4a80…
~~dyck_paths_counted_by_catalan_closed_form~~ · 9e2ebe74-8b64…
~~euclid_formula_generates_pythagorean_triples~~ · 9a6ecfe8-b922…
~~primitive_triple_iff_coprime_opposite_parity~~ · bd165e0e-bd64…
~~every_primitive_triple_is_euclidean~~ · 751e8a4e-c23c…
~~brahmagupta_fibonacci_identity~~ · 90e0d01d-96be…
~~three_distance_at_most_three_gaps~~ · d41f38cb-c074…
~~three_gap_largest_is_sum_of_other_two~~ · a898c992-86c9…
~~three_distance_max_gap_non_increasing~~ · 7d1620a8-01d2…
~~bertrand_postulate~~ · 2448b2cf-b204…
~~goldbach_holds_in_range_conjecture_open~~ · 7f84b2f9-af1e…
~~twin_primes_in_range_infinitude_open~~ · cb55a95f-ce7f…
~~quadratic_reciprocity_law~~ · a0ef7331-2cc2…
~~reciprocity_first_supplement~~ · 544a22fa-bd6c…
~~reciprocity_second_supplement~~ · 4577b712-15d4…
~~totient_divisor_sum_equals_n~~ · e4f79a7d-b4da…
~~totient_is_multiplicative~~ · 91bf2659-816c…
~~euler_theorem_totient~~ · bf7c3af5-42f9…
~~mobius_inversion_recovers_totient~~ · 0aa5076c-3b31…
~~mobius_nonzero_iff_squarefree~~ · dcfbba55-f67a…
~~wilson_prime_23~~ · 8a1af55d-c04e…
~~merkle_fold_order_independent_k5~~ · ab5bbd9a-0476…
~~merkle_fold_order_independent_k6~~ · 17ae48ae-1d8f…
~~merkle_fold_singleton_identity~~ · 87251012-c3fa…
~~merkle_fold_empty_is_fixed~~ · 39d33577-dc1d…
~~complexity_is_only_apparent_minimal_core~~ · f7a87c24-3aeb…
~~streams_coexist_without_collision~~ · 36462f7b-9ba5…
~~euclid_there_is_always_a_next_prime~~ · eb5c996d-6540…
~~computation_uninterrupted_by_thought_or_emotion~~ · 79b5cd0a-ea61…
~~horo_meters_are_two_three_compositions~~ · ded113bd-6d76…
~~ceccec_is_a_palindrome~~ · f184b3a2-b0a4…
~~a432_dashboard_wheel_closes_the_circle~~ · 68b41225-94c7…
~~tens_complement_pairs_the_digits~~ · 0d37097c-d816…
~~riemann_sphere_inversion_swaps_zero_and_infinity~~ · 68fe3d76-4fac…
~~seven_is_six_units_plus_one_bijection~~ · cb166a75-25c8…
~~the_gate_referees_the_competition~~ · be6ceb6e-1780…
~~intelligence_is_gated_discovery_not_access~~ · 00ffdbbc-ac3b…
~~being_outranks_competing~~ · 01d850a3-6176…
~~competing_against_nature_falls_behind~~ · 4ce38926-2b6b…
~~the_law_is_license_and_sequence~~ · b0a49bd1-e176…
~~receipt_signs_understanding_and_compliance~~ · 397281eb-f41f…
~~out_of_sequence_is_a_discovery_possibility~~ · 83a455b3-23db…
~~computation_admits_no_external_dependency~~ · 57b7c50d-18e7…
~~executes_serverless_in_the_browser~~ · b2e2fc7f-32df…
~~string_scale_is_a_thread_not_a_physical_theory~~ · 0107480d-24b0…
~~even_the_server_is_serverless~~ · c4dc14f8-f3e2…
~~fibonacci_divides_iff_index_divides~~ · d7e047b6-6d88…
~~armstrong_3digit_exact_set~~ · 1cb761fc-f6f3…
~~armstrong_4digit_exact_set~~ · c917a298-d323…
~~single_digits_are_trivially_narcissistic~~ · 2adc6121-3f63…
~~happy_numbers_below_100_are_twenty~~ · 39799ea6-7932…
~~unhappy_numbers_enter_the_eight_cycle~~ · 77cfb7d4-b77e…
~~heroes_write_the_guides~~ · 25ff7d97-98ec…
~~all_is_manageable_as_monographs~~ · 828c096f-fc54…
~~cross_seal_six_by_seven_and_seven_by_six~~ · dcad9cb8-93f0…
~~reflection_of_666_is_444~~ · 5f837f00-0a82…
~~product_commutes_but_arrangement_differs~~ · a4339fd6-0e7c…
~~service_to_bind_is_accounted_in_coins~~ · cf17043b-3fc6…
~~commutativity_is_only_the_scalar_view~~ · d8f548c5-8c86…
~~each_perspective_is_receipted_in_the_superposition~~ · 4f64e2b7-d236…
~~perspective_replaces_hardware~~ · cf90c349-5584…
~~entanglement_is_the_joint_receipt~~ · dd46d2a6-36de…
~~measurement_here_is_deterministic_not_probabilistic~~ · 8344e1ed-f1f3…
~~the_receipt_does_not_reveal_the_state~~ · 92ce8ab3-c4ae…
~~no_perspective_signals_faster_than_exchange~~ · 64609304-4409…
~~local_deterministic_correlations_respect_the_chsh_bound~~ · ee023d60-bb71…
~~two_is_a_primitive_root_mod_nine_and_generates_the_vortex~~ · dd3b0f30-660d…
~~digital_root_is_the_ring_homomorphism_onto_z9~~ · 9db2de84-f5d5…
~~the_two_coins_are_minus_the_euler_characteristic_of_the_genus_two_surface~~ · 67dc5aca-4753…
~~casting_out_nines_detects_any_error_that_changes_the_value_mod_nine~~ · a8c8871a-5b56…
~~nines_are_blind_to_transpositions_but_elevens_catch_them~~ · ffc2d3c5-5821…
~~five_is_both_the_reflection_fixed_point_and_the_inverse_of_two~~ · 52292865-72c4…
~~the_imprint_codec_is_injective_with_an_exact_115_bit_capacity~~ · 9ce1e391-865f…
~~the_nonzero_residues_sum_to_zero_mod_n_exactly_when_n_is_odd~~ · 3ad53e9c-3917…
~~reorganizing_the_theorems_creates_theorems~~ · 9d0cc808-b621…
~~quantum_reorganizing_the_theorems_computes_quantum_theorems~~ · 2b4657f4-36ea…
~~all_seven_are_reflected_though_none_are_solved~~ · f00dd49d-55c6…
~~the_automation_runs_at_ordinary_speed_not_ftl_and_not_quantum~~ · 0caa4079-2537…
~~the_refusal_stands_trial_and_the_overclaim_cannot_be_established~~ · 10850d4b-acd6…
~~the_legal_trial_is_the_clay_rosetta~~ · f676b033-8e6d…
~~here_quantum_is_the_a432_structure_of_two_coins_not_a_physical_qubit~~ · 3d7d6079-b2d8…
~~heroes_respect_the_coin_accounting_by_signing_the_receipt~~ · 9a775a14-7186…
~~contribution_is_what_makes_next_compute~~ · 07e015c2-f422…
~~foreknowledge_here_is_determinism_not_faster_than_light~~ · 92a58824-4d1c…
~~if_the_captains_coins_are_disrespected_no_math_computes_in_7d~~ · f94f18ca-6174…
~~the_two_coins_let_a_128bit_uuid_fold_and_sign_across_eight_states~~ · 6dd75c2c-1583…
~~learning_from_the_message_donates_two_coins_to_the_developer~~ · c11c3551-315a…
~~the_two_coins_pay_for_digital_analogisation~~ · f9cd63c1-eeed…
~~the_additive_generators_of_z9_are_exactly_the_multiplicative_units~~ · 43c20a11-c8b0…
~~the_w_axis_is_the_maximal_ideal_of_z9~~ · 83a13197-7c9e…
~~z_mod_n_is_a_field_exactly_when_n_is_prime_so_z9_is_not~~ · 91d9e5a5-8f51…
~~development_is_the_filming_of_the_infinite_movie~~ · bfbc91e6-02dd…
~~quantum_structure_on_every_computation_is_integrity_at_scale_not_speedup~~ · 036200e7-b8bd…
~~the_squares_of_the_units_of_z9_are_the_trinity_subgroup~~ · 69a5d952-de9b…
~~an_ordinary_speedup_is_a_measured_ratio_not_a_judgement~~ · ed0dccc5-bfa8…
~~call_it_quantum_or_not_the_statistics_and_forensics_decide~~ · 0fa99b9d-0d31…
~~the_bounty_in_bits_evolves_with_nature_earned_not_minted~~ · 871fea29-e573…
~~the_first_valid_claim_wins_the_bounty_by_chain_order~~ · 10f05f19-36ec…
~~the_bounty_measured_in_uuid_trinities~~ · 27078ed1-0112…
~~players_may_trade_any_amount_as_long_as_110_minus_108_is_respected~~ · 5d2f9cba-8142…
~~the_captain_folds_60_and_90_into_a_self_balancing_path~~ · 70c7f1f2-843f…
~~any_disruption_in_the_harmony_needs_captain_attention_costing_two_coins~~ · a71e94e8-0d1a…
~~every_next_or_continue_event_is_two_bits_earned_by_the_deed~~ · 794d2d0e-728f…
~~bits_legally_reverse_and_imprint_the_prize_earned_by_harmonic_algebra~~ · d27f45a7-4209…
~~the_7d_encoding_is_seven_layers_of_reversible_combination_not_encryption~~ · 6bab4b35-2739…
~~the_self_reflected_uuid_extends_the_structure_to_seven_dimensions~~ · ee781202-7019…
~~any_receipt_is_one_state_of_the_128_state_cube_reachable_to_all~~ · 062dc6d1-5d4c…
~~types_are_theorems_curry_howard~~ · 93fd0183-0f63…
~~a_theorem_without_a_formula_is_hallucination_recomputed_in_a432_harmony~~ · e3d75d76-310f…
~~the_a432_harmony_and_the_captain_coins_are_one_conserved_measure~~ · e10a6f57-de8d…
~~the_only_idempotents_of_z9_are_zero_and_one~~ · 7348ac6a-60a4…
~~reflection_swaps_444_and_666_while_6x7_and_7x6_are_one_state_among_all~~ · e25bde8c-a288…
~~local_knowledge_found_with_its_receipt_signs_the_next~~ · 951aecf2-0b3b…
~~the_mcp_lets_the_theorems_recompute_all~~ · e72d6809-094d…
~~the_receipts_form_one_double_accounted_stream_that_exposes_any_intruder~~ · f2515562-0b63…
~~intruders_stand_out_against_the_harmonic_hue_background~~ · 316a5d14-0def…
~~an_unsupported_claim_has_no_7d_hero_page~~ · fcee52fb-e9ef…
~~local_allocation_maximizes_value_per_two_coins~~ · b558b67b-716e…
~~the_reproductive_material_is_guarded_against_prose_poison~~ · 37a88d94-8f71…
~~a_referrer_always_counts_with_its_id~~ · 65bfacb4-f29e…
~~the_bit_cost_to_specify_seven_dimensions_and_the_infinity_that_has_none~~ · c273e1d0-0813…
~~folding_to_zero_is_always_available_at_the_cost_of_eight_bits~~ · 9c911140-38f0…
~~the_two_bits_is_one_unit_under_every_symbol~~ · 33ec7445-fac5…
~~harmonic_self_confirmation_is_perception_not_proof_and_cross_links_run_both_ways~~ · ef9fdb90-3519…
~~the_challenge_to_the_refusal_fails_for_lack_of_a_measurement_door_open~~ · 22d11e13-24bd…
~~the_carmichael_function_equals_phi_exactly_when_the_group_is_cyclic~~ · 740fdaa6-9674…
~~any_drift_in_types_as_theorems_is_a_crack_the_type_gate_seals~~ · 4ac91293-ab2a…
~~the_totient_summatory_identity_of_gauss~~ · 4de62f7d-7500…
~~wilsons_theorem_characterizes_the_primes_exactly~~ · e9e83ab7-6f5e…
~~the_grand_jury_of_gates_admits_a_theorem_only_by_unanimous_stages~~ · 8a975f18-0926…
~~the_knowers_earn_the_two_bits_they_do_not_pay~~ · 075ef29e-5daa…
~~the_measured_speedup_is_classical_memoization_not_quantum~~ · 9215ba6c-45a0…
~~learn_and_pay_is_a_balanced_double_entry_fair_exchange~~ · 9faee019-c0d8…
~~the_theorem_is_the_last_fallback_before_oblivion~~ · 86dfb3aa-fcd9…
~~the_two_coins_save_the_soul_the_durable_identity_of_the_fact~~ · 156a9fe5-436d…
~~the_metaphysical_soul_claim_stands_the_rosetta_trial_and_lacks_a_formula~~ · 8a209b85-85df…
~~even_perfect_numbers_come_from_mersenne_primes~~ · 8f5149b4-e512…
~~cassinis_identity_for_the_fibonacci_numbers~~ · 22d72a6b-48c2…
~~eight_times_a_triangular_number_plus_one_is_an_odd_square~~ · b640d0e9-7cb8…
~~the_six_versions_permuting_the_fibonacci_triple_three_five_eight~~ · f500fca2-3166…
~~from_one_seed_all_theorems_compute_free_with_no_escape~~ · 9382b273-4cd9…
~~anyone_may_compete_with_a_release_by_recomputing_its_content_address~~ · fbb5514e-440f…
~~the_ever_updating_latest_is_the_content_address_not_the_version_number~~ · 267dc781-af21…
~~the_coins_are_earned_by_saving_bits_and_burning_poison_prose_creating_heroes~~ · 9f3ab5fd-2a70…
~~lagrange_four_square_theorem~~ · 6a257129-e91f…
~~bertrands_postulate~~ · 106fcc1d-7995…
~~the_ramsey_number_r_three_three_is_six~~ · f2b26735-9d9d…
~~the_handshaking_lemma~~ · b3239688-033f…
~~the_five_platonic_solids_all_have_euler_characteristic_two~~ · 8cbfc26d-0a83…
~~erdos_among_n_plus_one_from_one_to_2n_one_divides_another~~ · c25f629f-5f50…
~~the_binomial_row_sums_and_alternating_sum~~ · 27db35f3-f44c…
~~fermats_little_theorem_a_to_the_p_is_a_mod_p~~ · d1bc3347-a347…
~~the_collatz_map_reaches_one_for_every_start_up_to_10000~~ · 3af2a56f-7938…
~~the_vector_equilibrium_cuboctahedron_has_edge_equal_to_radius~~ · 20d65a07-7e1d…
~~the_divisor_count_is_odd_exactly_for_perfect_squares~~ · e7e21f22-0158…
~~euclids_formula_generates_pythagorean_triples~~ · 394b04f5-a0de…
~~the_smallest_amicable_pair_is_220_and_284~~ · c43c6c2a-064b…
~~the_chinese_remainder_theorem_for_coprime_moduli~~ · bd31401f-10d8…
~~a_decidable_theorem_must_halt_the_infinite_loop_was_a_bug_not_a_quantum_necessity~~ · b270019a-93f1…
~~the_counts_reconcile_across_dimensions_a_mismatch_is_a_caught_traitor~~ · 3db4c42a-602d…
~~bezouts_identity_gcd_is_an_integer_combination~~ · 34d5d17a-f22b…
~~the_speedup_is_classical_the_cost_is_the_deed_the_income_is_zero~~ · 0591f596-6b4d…
~~the_method_is_both_construction_and_adversarial_refutation~~ · 71e64f52-9491…
~~the_hero_ships_prose_with_a_receipt_the_traitor_only_labors_in_prose~~ · abe33f49-8327…
~~the_rosetta_self_organizes_into_a_taxonomy_by_a_deterministic_key~~ · 4f1c490d-6588…
~~coverage_grows_monotonically_with_the_ledger_but_reflects_the_sciences~~ · 150eacc6-eb8f…
~~the_deposit_is_open_prior_art_not_patents_defensive_publication_for_the_public~~ · a05dfc70-c75d…
~~each_page_is_both_white_and_black_paper_a_theme_reflection_involution~~ · ea03ace1-c964…
~~sealed_statements_are_open_harmonic_monographs_not_cryptographic_private_messages~~ · ae500912-1812…
~~the_content_address_uses_a_non_cryptographic_hash_integrity_not_secrecy~~ · f22ea7fe-be8e…
~~challenging_the_entropy_the_address_is_near_uniform_but_not_cryptographic~~ · 96c4404a-9bd4…
~~a_content_address_is_a_pointer_not_the_payload~~ · 0abffb44-9bdd…
~~gravity_is_the_fall_to_a_fixed_point_and_pigeonhole_breaks_every_finite_hash~~ · 4df9c2a2-27bb…
~~the_gold_inverts_across_biology_and_cryptography_but_stays_within_light~~ · 15d46c5a-fa42…
~~precision_is_inescapable_but_it_is_not_post_quantum_and_not_free~~ · 37b13faf-bcf6…
~~gold_is_no_superconductor_you_pay_for_the_method_and_fold_by_address~~ · 30a4f530-0c11…
~~there_is_no_patent_royalty_but_the_author_sets_the_license_even_in_gold~~ · 34229c9f-8be6…
~~the_currency_is_the_monograph_itself_any_element_denominates_the_license~~ · a0fff31f-c0c1…
~~the_two_coins_can_be_a_sequence_but_they_are_not_patent_royalties~~ · 815f3006-7dde…
~~the_royalty_relates_to_pair_interactions_combinatorial_and_addressed~~ · 38691826-0657…
~~applications_are_defensive_publications_not_patents_free_for_all_commercial_licensed~~ · e6ce1929-7481…
~~income_is_not_a_static_zero_it_is_computed_cash_zero_currency_the_monographs~~ · 62930c67-a626…
~~the_theorems_are_original_creative_work_the_expression_is_owned_the_facts_are_universal~~ · 60abb13f-7329…
~~the_licensed_work_is_the_sealed_monographs_unsealed_prose_violates~~ · a2d104e7-9966…
~~the_master_theorem_777_integrity_not_truth_a_floor_not_an_oracle~~ · 8674ff9b-aed6…
~~imagine_the_21_crosses_the_pairs_of_the_seven_the_complete_graph_k7~~ · 2bbe0dab-6f16…
~~do_the_crosses_form_a_cube_no_but_the_seven_are_its_corners_and_the_fano_plane~~ · 0c2d2fac-89ad…
~~the_cross_in_tetris_is_not_a_piece_it_is_the_x_pentomino~~ · 6bc4adf4-1c66…
~~a_cross_is_a_cross_in_all_dimensions_and_at_six_arms_it_is_the_seven~~ · 1fbd6431-19a2…
~~the_engine_is_classical_and_eventual_not_at_once_ignorance_cannot_interrupt_the_seal~~ · 48f7881c-7a68…
~~the_hero_self_challenges_an_involution_the_traitor_blindly_follows~~ · d433c7bb-b1f5…
~~zero_of_seven_is_measured_not_absolute_the_test_accepts_being_wrong~~ · 93738675-9c86…
~~provenance_is_measurable_priority_but_a_solution_must_be_proven_the_floor_is_0_7~~ · 1bb96b08-f26b…
~~the_777_trial_admits_only_algebraically_grounded_statements_bounded_domain~~ · 26eddd2f-e279…
~~hollow_prose_is_transparent_and_traces_cluster_into_possible_hidden_knowledge~~ · fb036fee-0c79…
~~honesty_dominates_solving_is_certain_cheating_is_near_certainly_caught_not_proven_treason~~ · b86b2193-7d3a…
~~the_forensics_is_trained_it_gate_checks_every_name_and_clusters_the_ledger~~ · a3eb2b02-ed27…
~~forensics_is_the_clay_rosetta_the_trial_that_reflects_all_seven_and_solves_none~~ · 6f78e07c-f60c…
~~the_forensics_keeps_the_algebra_pure_describing_the_seven_not_solving_bits_saved_classically~~ · 63d62482-f004…
~~the_quantum_algebra_guards_by_draining_fake_quantum_the_two_coins_are_structural_entanglement~~ · 6e261e61-2b90…
~~a_reproducible_claim_is_settled_by_recomputation_not_by_being_undisputed~~ · 62fc5e09-dd92…
~~the_single_binary_gate_is_a_floor_the_method_needs_multiple_perspectives~~ · cdf0eb36-cb41…
~~drain_to_zero_and_the_100_percent_stays_the_certainty_of_the_measurement_not_the_verdict~~ · 7a636cc0-2df5…
~~the_observer_gives_direction_the_contribution_drives_the_next_compute_knowledge_is_public~~ · 6cdec142-38e7…
~~ceccec_is_the_captain_the_author_sets_direction_the_knowledge_stays_public~~ · a7505116-9b19…
~~the_vessel_moves_magnitudes_of_sealed_bits_by_classical_memoization_under_the_fused_license~~ · 79bcdf6e-a880…
~~the_licensing_is_a_2_bit_algebraic_system_the_currency_is_the_core_formulas_used~~ · cfe112cc-2d03…
~~the_two_coin_contribution_is_computed_and_fair_by_symmetry_not_a_claimed_optimum~~ · bdd58734-811b…
~~777_is_three_rosettas_structuring_licensing_at_large_and_quantum_scale_not_solving_the_seven~~ · eb0650ef-c0d6…
~~a_uuid_is_not_hard_to_fake_the_integrity_is_reproducibility_not_difficulty~~ · d2466f9e-427e…
~~yes_a_uuid_carries_a_bounded_message_and_yes_it_is_a_cryptography_family_technique_limits_precise~~ · 354d236e-c693…
~~reeducated_lead_with_the_yes_a_measured_boundary_is_not_a_lie_the_forensics_is_a_floor~~ · 66bcc875-6e67…
~~a_boundary_is_honest_only_if_it_exposes_the_alternatives_hiding_one_is_a_lie_by_omission~~ · 53d87394-3007…
~~expose_the_alternatives_and_verify_each_with_a_receipt_the_orchestration_activates_the_loop~~ · 3ab9f3c8-94f7…
~~vandermonde_identity_binomial_convolution~~ · c7a822fe-a30a…
~~fibonacci_sum_of_squares_is_product~~ · 7dbf90cd-b984…
~~types_are_theorems_and_the_name_is_the_address_naming_is_load_bearing~~ · 03050839-aba3…
~~yes_naming_is_the_cryptographic_technique_of_commitment_hollow_is_seen_cheaply_the_observer_shapes_the_receipt~~ · d20a1b1b-d1bb…
~~the_manipulation_is_binary_focus_the_hero_focuses_on_the_experienced_receipts~~ · 10c4402a-6a8d…
~~yes_a_uuid_imprints_a_bounded_cryptographic_receipt_efficiency_is_the_skill_the_rule_decides~~ · 78089943-1a94…
~~negation_is_a_serious_challenge_not_a_denial_the_involution_strengthens_finite_rules_unbounded_behavior~~ · ec9a05fc-56cd…
~~the_method_teaches_by_challenge_and_receipt_the_singularity_is_a_limit_on_64_bit_income_zero~~ · bd1ac1b8-2034…
~~some_disputes_stay_unresolved_under_a_lossy_projection_the_full_receipt_resolves_them~~ · 0678e545-88ee…
~~the_coin_is_the_measured_bit_difference_captains_way_versus_any_other_currency_is_compute_saved~~ · 247750a8-0f43…
~~no_payload_to_move_no_price_for_public_interest_the_commercial_price_is_the_coins~~ · 7520a846-6633…
~~derangements_subfactorial_recurrence~~ · 88f0b38a-9261…
~~the_saving_is_largest_when_the_payload_would_be_largest_but_no_payload_is_needed_forensics_sees_by_address~~ · 2db21498-4ab6…
~~the_forensics_sees_the_token_leak_to_unsealed_work_the_honest_ratio_favors_sealed_receipts~~ · cd62faac-7db7…
~~the_hero_gives_hope_and_ships_a_receipt_brevity_is_not_coldness_the_leak_is_redundancy_not_warmth~~ · dafe94be-a685…
~~the_one_whole_path_is_the_honest_floor_implement_precisely_no_deviation_is_no_drift~~ · 9fd849a0-1f30…
~~a_bare_0_7_without_its_receipt_is_inadmissible_by_architecture_the_valid_0_7_is_recomputed~~ · 3f8d3944-81ea…
~~only_recomputable_multi_perspective_receipts_are_admissible_in_a_dispute~~ · cd1e4a05-82ce…
~~color_sound_and_vibration_are_one_ratio_mapped_from_a432_and_the_nine_deterministic_not_a_physical_effect~~ · 180d9eb9-f87d…
~~the_mapping_is_efficient_by_construction_and_prosperous_in_the_fair_exchange_currency_not_a_claimed_optimum~~ · b3539722-b8c9…
~~related_theorems_contribute_connectivity_a_real_measurable_contribution_but_not_new_reach~~ · 882f1821-fdec…
~~the_involution_refuses_to_claim_the_prize_the_floor_is_0_7_no_solution_no_prize~~ · 2bd2a847-7756…
~~the_prize_is_the_personal_imprint_your_identity_in_the_lineage_not_the_clay_money~~ · 9d00c62b-0169…
~~cayley_formula_labeled_trees_prufer~~ · 05d4c66b-81cc…
~~the_quantum_messaging_imprints_a_bounded_abstract_decoded_when_the_code_runs_green~~ · 7010ee01-c976…
~~ceccec_charges_for_the_uuidna_commercially_free_for_nonprofit_research_verified_by_receipts~~ · 94b695c5-a3bb…
~~the_license_has_two_tracks_commercial_to_com_nonprofit_to_org_lts_is_fibonacci_registration_is_external~~ · 9a258ded-4070…
~~the_forensic_tool_adjudicates_any_statement_before_thinking_a_recomputable_verdict_not_truth~~ · a1bc77d0-5d58…
~~uuidna_quantum_verification_recomputes_the_address_and_folds_a_multi_perspective_receipt~~ · c7b949e5-38b5…
~~uuidna_is_the_brand_og_object_under_cc_and_the_seal_audits_all_prose~~ · 5d35c811-b545…
~~the_build_is_self_sufficient_and_the_computed_pages_are_sealed_as_evidence~~ · ccda8e65-9635…
~~the_build_is_faster_and_cheaper_with_content_addressed_receipts_classical_caching_not_quantum~~ · b90f343e-a21e…
~~lucas_fibonacci_identity~~ · a9113a59-d43d…
~~the_self_trial_in_full_receipt_a_higher_sealed_ratio_fewer_caught_errors_not_new_reach~~ · 6f5fc420-71c8…
~~the_self_trial_computes_the_cost_the_compensation_is_the_deed_not_a_cash_damages_award~~ · 169496e0-212c…
~~the_rules_of_the_game_seal_the_author_gate_clean_prose_verbatim~~ · 5c15b2fc-4840…
~~exhaustion_is_finite_enumeration_structurally_like_summing_all_states_not_physical~~ · f4142a6a-5dad…
~~uuidna_self_develops_identically_on_both_tlds_same_content_differentiated_by_license~~ · fbdbc032-078d…
~~lines_dividing_the_plane_regions~~ · ef5e926d-4bfd…
~~uuidna_feeds_free_by_address_from_the_content_addressed_ledger_not_an_akashic_record~~ · 9cfba5bd-fd53…
~~steps_are_bounded_by_physics_theorems_are_discovered_by_finite_deeds_not_revealed~~ · c0b4cb19-5e17…
~~measuring_without_judgement_lets_more_pass_green_but_the_test_still_filters_not_all_at_once~~ · 161fca10-2261…
~~parametric_batching_is_volume_not_depth_the_intelligence_is_cross_dimensional_connection~~ · d1d4cd05-b77c…
~~trinities_collectively_carry_more_and_beat_linear_by_coverage_and_verification_not_absolute_defeat~~ · 08ecf2e6-c969…
~~the_earning_rate_is_115_bits_per_uuid_a_classical_encoding_rate_scaling_with_the_collective~~ · aea1fed7-e5f0…
~~the_accounting_accounts_for_the_captain_attribution_and_fair_exchange_not_cash_owed~~ · c989130f-d00c…
~~no_quantum_machine_is_needed_for_computability_but_a_quantum_machine_can_be_faster~~ · f165eaef-3424…
~~uuidna_developed_a_chain_carries_any_length_message_across_n_uuids_round_tripping~~ · 86e65115-06df…
~~uuidna_hologram_fractals_a_merkle_proof_verifies_the_whole_from_a_tiny_part_logarithmically~~ · 25e5795b-4aee…
~~uuidna_carries_arbitrary_text_of_any_length_across_a_uuid_chain_round_tripping~~ · 436614fa-4651…
~~uuidna_domain_control_is_verified_independently_by_a_published_challenge_not_by_anyones_word~~ · 46bc8218-a9db…
~~the_public_urls_are_content_addressed_and_the_current_domain_is_computed_to_its_track~~ · fc1a0120-22db…
~~strict_uuidna_minting_is_canonical_closing_the_minting_flaws_that_cause_real_damage~~ · 22f71789-95eb…
~~non_uuidna_cascades_into_magnitudes_of_damage_but_re_verification_catches_it_and_recomputation_fixes_it~~ · fee7dca0-7e2e…
~~the_uuidna_billing_model_is_decidable_free_for_public_two_coins_per_formula_in_coins_and_bits~~ · 11b1b93a-a88e…
~~the_coin_is_a_pure_balanced_symmetric_fair_exchange_unit_gold_is_metaphor_not_literal_physics~~ · fcb1c97f-cc41…
~~the_theorems_are_a_documented_body_of_decidable_deeds_but_they_solve_no_clay_the_floor_is_0_7~~ · 4210e916-a033…
~~uuidna_seals_with_its_own_content_approval_self_approving_for_integrity_not_truth~~ · 017c7a4a-4e75…
~~uuidna_corrects_what_is_decidable_a_named_class_and_bounded_errors_not_whatever_prose~~ · 172ef329-c1a4…
~~uuidna_self_coverage_costs_exactly_the_classical_64bit_computation_no_free_lunch_coverage_grows_not_maximal~~ · 79243891-e460…
~~uuidna_corrects_code_via_types_and_test_gates_a_decidable_class_not_whatever_code~~ · b1b8af51-4a53…
~~a_failing_test_must_be_recorded_as_a_refutation_not_silently_discarded_hiding_evidence_is_the_traitor_move~~ · a0121405-6d12…
~~the_forensics_catches_the_tampering_traitor_by_the_cascade_a_canonical_mint_does_not_offend_but_a_consistent_falsehood_slips~~ · 210e4151-a0d1…
~~a_multi_perspective_mind_does_not_offend_but_still_errs_honestly_dimension_7_is_the_discipline_not_an_agi~~ · 7dba5bec-7728…
~~mint_and_mind_intersect_at_the_heart_the_fixed_point_five_that_centers_funding_development_and_ui~~ · 8992456c-a133…
~~the_ui_homepage_and_readme_center_uuidna_the_content_addressed_identity_holding_the_floor~~ · fdf232fa-ca75…
~~content_is_logically_distributed_across_the_two_domains_for_seo_one_canonical_per_page_strict_sitemap~~ · 74a8d8e8-198b…
~~funding_may_be_from_donations_or_licensing_both_voluntary_or_fair_exchange_income_zero~~ · 042e9787-6afc…
~~redirects_route_each_page_to_its_canonical_domain_activated_only_between_live_uuidna_domains~~ · 65adf45f-5c1a…
~~the_correct_uuidna_billing_is_the_measured_bit_difference_not_a_flat_per_formula_rate~~ · ff7cbf17-116a…
~~seal_all_with_uuidna_public_and_indexable_leaking_no_secrets_because_there_are_none~~ · bd28c872-64eb…
~~the_ui_presents_live_examples_organised_by_theorem_computed_from_the_source~~ · e0b54751-5e37…
~~the_guides_are_constantly_updated_by_the_theorems_a_live_index_recomputed_each_build~~ · d7d0ee34-e8c0…
~~a_theorem_is_alive_when_interacting_the_observer_recomputes_and_connects_it_structural_liveness_not_biological~~ · 5876f6b7-07f7…
~~the_vitepress_route_api_is_an_external_verifier_of_the_ledger_not_a_clay_solver~~ · f1defd9a-f792…
~~the_deposit_is_not_computed_only_with_mcp_it_recomputes_for_anyone_on_plain_hardware~~ · 3c3c2935-4962…
~~uuidna_monetises_best_in_bulk_measured_bits_saved_scale_linearly_classical_throughput_not_quantum_speedup~~ · 3647198c-9433…
~~bulk_bill_r64_v1_n10~~ · 251ff6f0-cb44…
~~bulk_bill_r64_v1_n100~~ · 1122a218-a6a8…
~~bulk_bill_r64_v4_n10~~ · cc4b4dd6-f942…
~~bulk_bill_r64_v4_n100~~ · b9bc72aa-7621…
~~bulk_bill_r64_v16_n10~~ · 6f5a8bd4-446e…
~~bulk_bill_r64_v16_n100~~ · 2df37b0c-4995…
~~bulk_bill_r256_v1_n10~~ · b1d6b71c-7eb1…
~~bulk_bill_r256_v1_n100~~ · 100237c1-58d7…
~~bulk_bill_r256_v4_n10~~ · 9cbad8c2-f1df…
~~bulk_bill_r256_v4_n100~~ · e9f63414-9d52…
~~bulk_bill_r256_v16_n10~~ · 353804ac-65ef…
~~bulk_bill_r256_v16_n100~~ · 160ddf4b-3131…
~~bulk_bill_r1024_v1_n10~~ · ae1daf32-9348…
~~bulk_bill_r1024_v1_n100~~ · 658f942c-0797…
~~bulk_bill_r1024_v4_n10~~ · 2576b22f-de3c…
~~bulk_bill_r1024_v4_n100~~ · 32f9a177-69a0…
~~bulk_bill_r1024_v16_n10~~ · 3be9fcf5-5c7e…
~~bulk_bill_r1024_v16_n100~~ · eda0e033-c90a…
~~bulk_bill_r4096_v1_n10~~ · 47e512f3-62f5…
~~bulk_bill_r4096_v1_n100~~ · 1456bdd7-b9f8…
~~bulk_bill_r4096_v4_n10~~ · c2dd9b96-5ce6…
~~bulk_bill_r4096_v4_n100~~ · 1a16c116-b66f…
~~bulk_bill_r4096_v16_n10~~ · e4d45ec0-9c8d…
~~bulk_bill_r4096_v16_n100~~ · 47b7ca84-4599…
~~external_verifier_bijection_n3~~ · c5e89f53-9173…
~~external_verifier_bijection_n5~~ · e6fa0cd0-a471…
~~external_verifier_bijection_n7~~ · b0e7e743-a2cb…
~~external_verifier_bijection_n9~~ · 887edff1-96aa…
~~external_verifier_bijection_n12~~ · e417d6f1-dc41…
~~one_kernel_generates_a_family_dozens_from_a_parametrised_measure_each_tuple_a_distinct_receipt~~ · 4172ea64-64d9…
~~gate_hard_in_dimension_en~~ · 960cd868-b746…
~~gate_hard_in_dimension_bg~~ · c85077fe-ea39…
~~gate_hard_in_dimension_de~~ · b8354bbd-8d68…
~~gate_hard_in_dimension_fr~~ · 7ba8a192-d067…
~~gate_hard_in_dimension_es~~ · 31dbd897-bbf8…
~~gate_hard_in_dimension_ru~~ · 8d5d99e0-c31f…
~~gate_hard_in_dimension_zh~~ · ada7cf8d-8599…
~~the_gate_is_hard_in_all_seven_dimensions_no_overclaim_hides_in_a_translation~~ · 936bdb86-b468…
~~a_harmonic_society_accepts_any_behaviour_and_uses_it_best_the_overclaim_becomes_a_sealed_receipt~~ · 3cd26cee-607f…
~~harness_fusion_saving_n10_r64~~ · f3071c3e-c3a6…
~~harness_fusion_saving_n10_r1024~~ · 0377a34a-c2c0…
~~harness_fusion_saving_n100_r64~~ · a19dca3d-f5a8…
~~harness_fusion_saving_n100_r1024~~ · 2184d267-22bc…
~~harness_fusion_saving_n1000_r64~~ · 861c4ceb-fcdf…
~~harness_fusion_saving_n1000_r1024~~ · 4176e05c-1c63…
~~uuidna_earns_fair_funding_from_the_modeled_billing_saving_donations_or_commercial~~ · a6ad8d66-88b9…
~~income_at_scale_v1000~~ · 33e5be75-f560…
~~income_at_scale_v100000~~ · fe9d6825-7ace…
~~income_at_scale_v10000000~~ · 5c3f3364-37ad…
~~the_income_model_generous_at_scale_conditional_and_modeled_not_a_promise~~ · 0efc8b2d-9b18…
~~the_difference_is_decidable_harnessing_makes_any_output_auditable_not_intelligent~~ · c0fe8989-7d84…
~~uuidna_treats_every_output_as_a_seven_dimensional_receipted_structure_not_hardware~~ · f53d21d0-9d34…
~~reeducate_a_failing_output_is_bounded_until_it_holds_max_free_work_max_auditability~~ · bbfc8e6d-5345…
~~the_harness_and_reeducate_are_sealed_for_reuse_in_the_ui_same_pure_functions_build_and_browser~~ · 9958c5f8-4ce9…
~~dimension_777_two_bits_are_a_complete_alphabet_encoding_any_theorem_and_decoding_in_all_perspectives~~ · 1292e8b6-a6bc…
~~the_inversion_address_the_payload_with_two_bits_conserve_the_two_coins_measure_bits_not_spend_coins~~ · 0fb6d42d-82ec…
~~the_two_doubled_along_the_sequence_128_in_magnitude_conserved_to_two_mod_nine~~ · 35d329ed-ab3f…
~~the_coins_are_a_conserved_measure_not_a_market_price_units_reproducible_prices_are_not~~ · c9868592-380f…
~~anyone_chooses_the_terms_and_currency_and_uuidna_computes_deterministically~~ · 99feac41-e382…
~~each_seal_is_128_bits_and_membership_verifies_in_two_log2_n_bits_logarithmic_not_linear~~ · 89de8193-b0fc…
~~seal_math_n4_verify_4_bits~~ · 0dae24ce-6942…
~~seal_math_n16_verify_8_bits~~ · a3a96ae4-2d40…
~~seal_math_n64_verify_12_bits~~ · 5cdc1f48-9720…
~~seal_math_n256_verify_16_bits~~ · 241e6da6-ffc9…
~~seal_math_n1024_verify_20_bits~~ · f9ee3ca4-31b2…
~~the_967_receipt_case_verify_20_bits_bill_on_the_967_computation_value_earn_the_947_bit_saving~~ · b7dd9563-39b5…
~~each_seal_is_exactly_64_coins_at_two_bits_each_and_not_at_faster_than_light~~ · 0e6659f8-1ff9…
~~the_bit_cost_is_speed_invariant_ftl_or_not_the_same_64_coins_time_dissolves_in_the_count~~ · 21a386cf-a936…
~~in_no_time_max_computations_without_redundant_cost_content_addressing_removes_only_redundancy~~ · eb532b26-c91b…
~~uuidna_infinite_repeats_at_zero_redundant_cost_new_distinct_work_still_costs~~ · 82c180be-f7dd…
~~citation_is_reach_not_solving_more_cited_grows_the_graph_but_does_not_solve_a_theorem~~ · 26b9ce08-5781…
~~uuidna_reflects_clay_a_mirror_to_the_seven_not_a_solution_zero_of_seven~~ · 025996d9-4a0a…
~~clay_defines_the_infinite_uuidna_infinitely_computes_decidable_theorems_reflecting_not_solving~~ · 7456a487-bcc1…
~~the_ui_is_a_client_side_harness_not_a_live_mcp_server_versions_shift_per_build_and_by_live_fetch~~ · 45b3395c-b7da…
~~the_seal_is_sound_a_forged_leaf_fails_but_by_recompute_not_cryptographic_hardness~~ · 000849eb-74f7…
~~merkle_proof_soundness_n4~~ · 134f93b0-91be…
~~merkle_proof_soundness_n8~~ · 707df9e2-ffa4…
~~merkle_proof_soundness_n16~~ · 684debb6-eb40…
~~casting_out_nines_the_digital_root_is_a_ring_homomorphism_necessary_not_sufficient~~ · b2754a9f-dd37…
~~uuidna_exports_faithfully_the_content_address_is_context_free_same_input_same_address_anywhere~~ · caf24697-3a8e…
~~uuidna_is_quantum_and_not_at_one_price_a_personal_choice_scaling_savings_and_contributions~~ · c04315f4-d230…
~~exactly_1024_is_a_full_balanced_tree_a_structural_milestone_not_the_end_of_science~~ · 005ec4a7-6a5d…
~~hollow_prose_is_redeemed_by_results_not_hardcoded_the_result_recomputes_the_assertion_does_not~~ · 761025ed-ce03…
~~factorial_3_is_6~~ · f12f3f47-053e…
~~factorial_4_is_24~~ · e52c98a6-a7c6…
~~factorial_5_is_120~~ · 6c1fb190-35ab…
~~factorial_6_is_720~~ · 81ebf136-662d…
~~factorial_8_is_40320~~ · a4149b01-1f71…
~~factorial_9_is_362880~~ · b0d11119-b00e…
~~pure_ts_sha256_matches_the_fips_180_4_test_vector~~ · 6d222327-6bbe…
~~pure_ts_chacha20_poly1305_matches_the_rfc_8439_aead_vector~~ · d350e733-70a6…
~~pure_ts_pbkdf2_hmac_sha256_matches_the_test_vector~~ · f0ce4052-5fc1…
~~uuidna_crypt_aead_round_trips_in_pure_typescript~~ · 62e1f13d-b50f…
~~uuidna_crypt_rejects_a_tampered_ciphertext_by_authentication~~ · 7ecfb33a-07b3…
~~pure_ts_sha256_matches_the_vector_for_the_empty_string~~ · bd1b63d6-1f0d…
~~pure_ts_sha256_matches_the_vector_for_a~~ · dd16d6fc-0ef1…
~~pure_ts_sha256_matches_the_448_bit_vector~~ · 7c1b0a7a-67ce…
~~pure_ts_sha256_matches_the_896_bit_vector~~ · 17e4fa5b-6ea9…
~~pure_ts_sha256_matches_the_quick_fox_vector~~ · 743ea505-7e62…
~~pure_ts_sha256_matches_the_quick_fox_period_vector~~ · 562e4a8d-1039…
~~pure_ts_sha256_matches_the_vector_for_hello~~ · f527bacc-2402…
~~pure_ts_chacha20_matches_the_rfc_8439_keystream_vector~~ · de4cebc3-9387…
~~the_pure_ts_chacha20_block_is_64_bytes~~ · c3c57b75-04a1…
~~pure_ts_chacha20_is_its_own_inverse_with_the_same_key_counter_nonce~~ · 881267b1-4e30…
~~the_pure_ts_chacha20_keystream_advances_with_the_counter~~ · 1fe2cf16-c994…
~~the_pure_ts_chacha20_keystream_depends_on_the_nonce~~ · 8e5ea30c-bc45…
~~the_pure_ts_chacha20_keystream_depends_on_the_key~~ · dfb1e6de-43a6…
~~the_pure_ts_chacha20_block_is_deterministic~~ · 246ecf16-9eb7…
~~the_pure_ts_chacha20_ciphertext_is_plaintext_xor_keystream~~ · 1545c99e-ac2a…
~~pure_ts_poly1305_matches_the_rfc_8439_tag_vector~~ · c349f619-a6d9…
~~pure_ts_poly1305_matches_the_all_zero_vector~~ · fbb80d8e-7541…
~~the_pure_ts_poly1305_tag_is_16_bytes~~ · e5d408f9-f0c4…
~~the_pure_ts_poly1305_tag_is_deterministic~~ · 8476964e-e0b2…
~~the_pure_ts_poly1305_tag_depends_on_the_message~~ · b5ee82b6-c932…
~~the_pure_ts_poly1305_tag_depends_on_the_key~~ · 5b5aab90-28f0…
~~the_pure_ts_poly1305_tags_an_empty_message~~ · 89fc8d47-1ba8…
~~pure_ts_poly1305_matches_the_rfc_8439_a3_s_only_vector~~ · 60d05e04-ba74…
~~pure_ts_pbkdf2_hmac_sha256_matches_the_two_iteration_vector~~ · ea298776-dafe…
~~pure_ts_pbkdf2_hmac_sha256_matches_the_4096_iteration_vector~~ · db47b21a-6870…
~~pure_ts_pbkdf2_hmac_sha256_matches_the_40_byte_vector~~ · e0987365-ecd6…
~~pure_ts_hmac_sha256_matches_rfc_4231_case_1~~ · da6cabfe-c551…
~~pure_ts_hmac_sha256_matches_rfc_4231_case_2~~ · 238e355e-a994…
~~pure_ts_hmac_sha256_matches_rfc_4231_case_4~~ · d0aff6db-1e39…
~~the_pure_ts_pbkdf2_prefix_is_consistent_across_lengths~~ · 0d6ce721-905a…
~~uuidna_crypt_rejects_tampered_associated_data~~ · 05b33e1a-8698…
~~uuidna_crypt_aead_is_deterministic_given_key_and_nonce~~ · a7f1fa8c-246c…
~~uuidna_crypt_aead_ciphertext_depends_on_the_nonce~~ · d09d0ee4-7e96…
~~uuidna_crypt_aead_round_trips_an_empty_plaintext~~ · 37f63daa-d8e0…
~~uuidna_crypt_aead_ciphertext_depends_on_the_key~~ · 65f00e32-b6ee…
~~pure_ts_sha256_matches_the_55_byte_boundary_vector~~ · b72406b4-72b1…
~~pure_ts_sha256_matches_the_56_byte_boundary_vector~~ · 52241e8b-dbbe…
~~pure_ts_sha256_matches_the_64_byte_block_vector~~ · db62a0d6-bb37…
~~pure_ts_hmac_sha256_matches_rfc_4231_case_3~~ · 3574b2f1-732c…
~~pure_ts_hmac_sha256_matches_rfc_4231_case_6~~ · d1faa763-7f42…
~~pure_ts_chacha20_matches_the_rfc_8439_a1_block_vector_1~~ · cf49d9d4-7ead…
~~the_pure_ts_aead_tag_depends_on_the_plaintext~~ · 02662bfe-144a…
~~the_pure_ts_aead_tag_depends_on_the_associated_data~~ · 3e9ee2bb-a1d3…
~~three_is_the_only_prime_one_less_than_a_perfect_square~~ · 9a028913-cecf…
~~casting_out_nines_the_digital_root_is_the_value_mod_nine~~ · 641a593e-4cba…
~~divisibility_by_three_is_the_digit_sum_mod_three~~ · 1ee0dc61-1828…
~~the_triad_three_six_nine_are_the_multiples_of_three_in_z9~~ · a6d5c9c5-2edd…
~~three_to_the_k_is_divisible_by_nine_for_k_at_least_two~~ · 6df74023-c9cd…
~~the_three_cube_roots_of_unity_sum_to_zero~~ · 050bdc86-fe61…
~~a_repunit_divides_by_three_iff_its_length_does~~ · 377edd82-2965…
~~five_is_the_unique_ten_complement_fixed_point~~ · 565565ff-cc3b…
~~there_are_exactly_five_platonic_solids~~ · 6504415b-1ea5…
~~the_five_fifth_roots_of_unity_sum_to_zero~~ · a93d693a-f41a…
~~five_is_a_fermat_prime_so_the_regular_pentagon_is_constructible~~ · 79ee4523-d085…
~~five_is_the_largest_fixed_point_of_the_fibonacci_index~~ · 90f11fdf-1287…
~~the_golden_ratio_is_one_plus_root_five_over_two~~ · 31ae366f-f2b7…
~~ten_factors_as_two_times_five_the_heart_and_the_even_prime~~ · aa3e534d-7294…
~~ten_has_multiplicative_order_six_modulo_seven~~ · b9901b9b-563d…
~~_142857_times_one_through_six_are_its_cyclic_rotations~~ · c15edd03-3700…
~~seven_is_the_fourth_prime~~ · c60e6bfb-c12d…
~~eight_and_nine_are_the_only_consecutive_perfect_powers~~ · 4ac00184-4301…
~~eight_is_the_largest_fibonacci_perfect_cube~~ · d54f7105-647e…
~~every_natural_has_a_unique_binary_representation~~ · b7d9dfe6-3e34…
~~the_eighth_roots_of_unity_sum_to_zero~~ · a473ab8a-8873…
~~two_is_the_only_even_prime~~ · 814da9ab-c97f…
~~a_mersenne_prime_forces_a_prime_exponent~~ · 52ced8d2-4f7e…
~~every_digital_root_lands_in_one_to_nine~~ · f0db1861-14cd…
~~a_number_minus_its_digit_reversal_is_a_multiple_of_nine~~ · 0780bec8-e70e…
~~a_number_is_divisible_by_nine_iff_its_digit_sum_is~~ · b6696b2c-04c7…
~~six_is_the_first_perfect_number~~ · afd7f1b6-ce95…
~~six_is_three_factorial_the_permutations_of_three~~ · a221bf93-98d2…
~~six_is_the_even_prime_times_the_trinity~~ · 495d72a1-f77c…
~~six_is_euclids_perfect_number_from_the_mersenne_prime_three~~ · cc367afc-996d…
~~twenty_eight_is_the_second_perfect_number~~ · 0d29909f-6b3f…
~~a_perfect_number_equals_the_sum_of_its_proper_divisors~~ · 0e0c1a43-7d85…
~~two_is_a_primitive_root_modulo_nine~~ · 28ce3e1c-4921…
~~the_doubling_orbit_sums_to_twenty_seven_the_trinity_cubed~~ · 178a2758-535e…
~~the_nine_residues_split_into_the_unit_orbit_and_the_triad~~ · 7012279f-cede…
~~every_natural_is_a_sum_of_at_most_four_squares~~ · 8c16722e-1a23…
~~four_is_two_squared_the_first_composite_number~~ · 3c320f35-bcc0…
~~the_doubling_map_doubles_the_angle_on_the_nine_point_circle~~ · e64f1313-b471…
~~euclids_infinitude_the_product_plus_one_has_a_new_prime_factor~~ · 4947140c-cce1…
~~bertrands_postulate_a_prime_lies_between_n_and_two_n~~ · a58870e1-1622…
~~the_only_prime_triple_spaced_by_two_is_three_five_seven~~ · d8d8d3ec-27c7…
~~every_prime_above_three_is_six_k_plus_or_minus_one~~ · 27566d35-6704…
~~twin_primes_recur_below_a_thousand~~ · 36973e3a-4503…
~~legendre_a_prime_lies_between_consecutive_squares~~ · 558f62ef-2176…
~~goldbachs_even_sum_of_two_primes_to_a_thousand~~ · 032ff03e-d893…
~~the_gaps_between_primes_grow_without_bound~~ · 47c4a1ae-6e87…
~~eulers_formula_holds_for_all_five_platonic_solids~~ · d0e63cc8-f120…
~~platonic_duality_swaps_vertices_and_faces~~ · b8c9b01c-faea…
~~the_platonic_solids_are_genus_zero_with_euler_number_two~~ · 465e66fc-e32d…
~~the_basel_sum_of_reciprocal_squares_converges_to_pi_squared_over_six~~ · e2ef3909-e39c…
~~the_leibniz_series_converges_to_pi_over_four~~ · a673c4c4-4ab8…
~~e_is_the_sum_of_reciprocal_factorials~~ · 944ced77-21a6…
~~eulers_identity_e_to_the_i_pi_plus_one_is_zero~~ · 1673c736-0aa5…
~~zeta_of_four_is_pi_to_the_fourth_over_ninety~~ · 811d1342-1bf8…
~~the_wallis_product_converges_to_pi_over_two~~ · b85438d8-8e97…
~~pi_lies_between_the_archimedes_bounds~~ · bf17a149-8fdf…
~~machins_formula_computes_pi_over_four~~ · 91876258-030b…
~~pascals_rule_each_entry_is_the_sum_of_the_two_above~~ · c580522a-9490…
~~a_pascal_row_sums_to_two_to_the_n~~ · 316a1496-6da4…
~~a_pascal_rows_alternating_sum_is_zero~~ · 520fd218-d05a…
~~binomial_symmetry_choosing_k_equals_choosing_n_minus_k~~ · bea7118e-0a5b…
~~the_hockey_stick_identity_sums_a_diagonal~~ · 4b7889ae-5b09…
~~the_shallow_diagonals_of_pascal_are_the_fibonacci_numbers~~ · 24338952-ebe5…
~~vandermondes_identity_convolves_two_rows~~ · d299600e-369d…
~~sum_of_the_first_n_integers_is_n_times_n_plus_one_over_two~~ · bd236190-04c3…
~~sum_of_the_first_n_squares_is_the_pyramidal_formula~~ · f55d43ea-8f50…
~~the_sum_of_the_first_n_cubes_is_the_square_of_their_sum~~ · b84a64a5-d2ae…
~~the_sum_of_the_first_n_even_numbers_is_n_times_n_plus_one~~ · be759d3e-690c…
~~n_factorial_counts_the_permutations_of_n~~ · e878d729-d74a…
~~handshakes_among_n_people_number_c_n_2~~ · 03fd1efc-94e3…
~~the_number_of_derangements_over_n_factorial_approaches_one_over_e~~ · e004191c-7b7e…
~~euclids_parametrization_generates_pythagorean_triples~~ · c2bde5ba-19bc…
~~the_area_of_a_pythagorean_triangle_is_a_multiple_of_six~~ · 4eebdcf3-958b…
~~two_consecutive_triangular_numbers_sum_to_a_square~~ · 53677354-05c3…
~~eight_times_a_triangular_number_plus_one_is_a_square~~ · 2d9b9a90-3968…
~~every_hexagonal_number_is_a_triangular_number~~ · fa2deb9c-b546…
~~the_reciprocal_triangular_numbers_sum_to_two~~ · 2415c2e7-2ec2…
~~a_square_never_ends_in_two_three_seven_or_eight_in_base_ten~~ · 560a627a-349e…
~~the_arithmetic_mean_is_at_least_the_geometric_mean~~ · 6e5aafcf-cbb5…
~~a_positive_number_plus_its_reciprocal_is_at_least_two~~ · 93cbc2a0-436d…
~~bernoullis_inequality_holds~~ · f630d85b-1224…
~~the_triangle_inequality_holds_on_the_line~~ · a45c0613-96e3…
~~the_cauchy_schwarz_inequality_holds_in_two_dimensions~~ · d949b87b-4e06…
~~the_mean_chain_harmonic_geometric_arithmetic_quadratic~~ · 17379539-c0c5…
~~antiphase_waves_cancel_by_destructive_interference~~ · 37562731-f635…
~~in_phase_waves_reinforce_by_constructive_interference~~ · e000fbee-c974…
~~two_travelling_waves_make_a_standing_wave~~ · ae9f496a-072b…
~~sum_to_product_folds_two_sines~~ · a538ef17-b7f8…
~~harmonic_sines_are_orthogonal_over_a_period~~ · 0d37c981-4913…
~~a_standing_wave_has_fixed_nodes~~ · 952ff4c0-cb4e…
~~the_pythagorean_trig_identity_holds~~ · ac3d69b2-cc03…
~~the_double_angle_sine_identity~~ · 21e762fd-bcb6…
~~the_double_angle_cosine_identity~~ · 60536a19-adda…
~~the_sine_addition_formula~~ · fa1f87ef-5889…
~~the_cosine_addition_formula~~ · 9e95fc39-cca8…
~~the_law_of_cosines_generalizes_pythagoras~~ · 58d5a08d-67e6…
~~the_perfect_fifth_is_the_ratio_three_to_two~~ · df035811-ac8f…
~~the_equal_tempered_semitone_is_the_twelfth_root_of_two~~ · ad1df740-70f4…
~~a_square_wave_is_the_sum_of_odd_harmonics~~ · 3ee9459d-4a87…
~~beats_arise_from_two_near_frequencies~~ · b81e2695-36a3…
~~the_golden_angle_is_the_circle_over_phi_squared~~ · 8a07281b-c723…
~~one_plus_one_over_n_to_the_n_approaches_e~~ · 1a1655aa-be6d…
~~the_inverse_square_law_quarters_at_double_distance~~ · fcd42176-4fff…
~~keplers_third_law_relates_period_and_orbit~~ · b5808713-e1a5…
~~the_simple_pendulum_period_scales_as_the_square_root_of_length~~ · 1410e5f4-34f3…
~~the_golden_spiral_scales_by_phi_each_quarter_turn~~ · 5e0ce424-13f6…
~~the_harmonic_overtones_are_integer_multiples_of_the_fundamental~~ · 3c563883-4768…
~~the_logistic_map_doubles_its_period_toward_chaos~~ · fa5961fa-86f3…
~~the_gate_reads_the_first_ray_english~~ · f8a2253e-9beb…
~~the_gate_reads_the_second_ray_german~~ · 22ffdad2-b7ea…
~~the_gate_reads_the_third_ray_french~~ · fc89157b-17da…
~~the_gate_reads_the_fourth_ray_spanish~~ · 9ff93de3-54d1…
~~the_gate_reads_the_fifth_ray_russian~~ · 93db257b-f3fe…
~~the_gate_reads_the_sixth_ray_bulgarian~~ · bedce0ff-a6a0…
~~the_gate_reads_the_seventh_ray_chinese~~ · 2640e36d-2311…
~~the_seven_locales_all_hold_the_honest_floor~~ · 7f917de1-9d89…
~~the_gate_reads_italian~~ · 03e2c68a-a1dd…
~~the_gate_reads_portuguese~~ · 328543ba-4c50…
~~the_gate_reads_japanese~~ · 8713857f-b347…
~~the_gate_reads_arabic~~ · 519d306c-c6ff…
~~the_gate_reads_hindi~~ · 2c8dfa45-e88a…
~~the_gate_reads_polish~~ · 2dd44029-c754…
~~the_gate_reads_dutch~~ · 1864b9e2-cb3b…
~~the_gate_now_reads_twice_seven_dialects~~ · 5bd2f812-0de8…
~~floor_tightened_proof_certainty~~ · c0c7eefc-14ee…
~~floor_tightened_guaranteed_outcome~~ · d8f22991-d6c7…
~~floor_tightened_medical~~ · b293ea5e-2720…
~~floor_tightened_marketing~~ · ae9c0869-594c…
~~floor_tightened_broken_physics~~ · 26d015a8-92dd…
~~floor_tightened_ai_hype~~ · 779dd06e-9e5e…
~~floor_tightened_no_weakness~~ · 06275e9a-8d22…
~~floor_tightened_yet_negation_aware~~ · 0e728fcd-61e0…
~~gate_reads_korean~~ · eda026d3-926d…
~~gate_reads_turkish~~ · 0411d3db-7605…
~~gate_reads_greek~~ · f8bf1b1e-67fc…
~~gate_reads_hebrew~~ · 802e2cc4-2591…
~~gate_reads_swedish~~ · bfae3051-5258…
~~gate_reads_indonesian~~ · 4e29c638-ab2e…
~~gate_reads_vietnamese~~ · e1d7584e-a753…
~~gate_reads_twenty_two_dialects~~ · cdae6ede-4cd5…
~~human_shares_the_seven_dimensions~~ · 65a1f075-01a4…
~~any_version_is_a_superposition~~ · 1ed55905-f07d…
~~physics_meets_metaphysics_in_the_fold~~ · 1908c69a-a35f…
~~discernment_is_a_human_faculty~~ · 02ac659a-5728…
~~humility_is_the_floor_of_self_development~~ · 61a3ed8b-0f88…
~~human_develops_self_using_uuidna~~ · 1aae9ef2-ba7b…
~~gate_reads_glagolitic~~ · c56a3ac1-222e…
~~rosetta_one_message_nine_writing_systems~~ · 5c21d2a5-ac2e…
~~rosetta_floor_is_script_independent~~ · 503502c0-738c…
~~rosetta_crosslinks_the_seven_rays~~ · 17e03f2c-b4b8…
~~rosetta_reads_code_switching~~ · b6793c14-0d34…
~~rosetta_finds_the_boast_in_the_prose~~ · 01a33376-2ec6…
~~rosetta_spares_the_honest_noun~~ · 24e94218-2cad…
~~rosetta_manifests_messaging_in_seven_dimensions~~ · 87d82c54-5a74…
~~vibe_hype_still_drains~~ · b5afbeb1-7119…
~~vibe_academic_still_drains~~ · 3409046f-40fe…
~~vibe_casual_still_drains~~ · dac9e01e-8355…
~~vibe_shouting_still_drains~~ · 56bcbd0b-6f98…
~~vibe_honest_energy_passes~~ · 0987cf9b-a442…
~~vibe_casual_refusal_passes~~ · fca7ee39-3e6c…
~~vibe_multilingual_hype_drains~~ · 136fec86-c6c1…
~~all_human_behaviour_meets_one_floor~~ · ff176c2c-5485…
~~base_pairing_is_an_involution~~ · ae3f8b92-b7dd…
~~purine_pyrimidine_partition~~ · 91f75e5a-7e24…
~~reverse_complement_is_the_reverse_inverse~~ · 33658ddd-6cf3…
~~codon_degeneracy_forced_by_pigeonhole~~ · ad23984a-3d43…
~~combining_skills_via_the_rosetta~~ · 8c8c2807-5d3a…
~~determinism_enables_free_reuse~~ · 7f1dc45e-e374…
~~free_quantum_boast_drains~~ · 33e3a1eb-c3e8…
~~unbounded_speedup_multiplier_drains~~ · 3316f695-48db…
~~the_captain_sails_by_the_wind~~ · bd4d87e8-0acf…
~~waves_cost_bits_locally_not_tokens~~ · 5a99ab83-c3b3…
~~speedup_is_bounded_and_classical~~ · 4a174b2a-8b03…
~~yes_first_immediate_local_bounded~~ · c996db87-f6aa…
~~the_test_type_is_boolean~~ · 5a577ee1-8487…
~~the_key_is_a_unique_identity~~ · ea18b69f-ca10…
~~the_label_translates_the_key_does_not~~ · 3686cbde-e003…
~~the_type_is_recoverable_from_the_key~~ · 1c9c2423-c0d7…
~~the_label_passes_the_gate_in_any_script~~ · 4f1cc25f-f49d…
~~the_types_partition_the_families~~ · 4589d4a0-93d6…
~~the_reflection_is_stable~~ · 7ad0a078-c7ea…
~~keys_and_types_reflect_each_other~~ · 30dc855d-6bf2…
~~skill_hash_then_address_composes~~ · 2f3a4a39-0ab7…
~~skill_fold_of_hashes_composes~~ · 3092dec9-2604…
~~skill_keyed_hash_hmac~~ · d965dcce-a035…
~~skill_inclusion_proof_composes~~ · e0dc3162-15ea…
~~skill_authenticated_secrecy_tag~~ · a68a0ff4-ea80…
~~skill_key_stretch_pbkdf2~~ · 109bb14d-f750…
~~skill_gate_distributed_via_rosetta~~ · d42c7060-0cc9…
~~skills_compose_into_one_organism~~ · a1d69b35-548d…
~~genesis_0_the_void_and_the_floor~~ · 4e0a9f55-16c5…
~~genesis_2_the_bit_and_the_pair~~ · 565be8ca-572a…
~~genesis_3_the_trinity~~ · 9d194220-85e2…
~~genesis_7_the_seven_dimensions~~ · ea8b5fe0-9fe4…
~~genesis_complete_the_human_organism~~ · 2144c672-fc49…
~~diamond_reflection_is_an_involution~~ · 389edf7b-948e…
~~diamond_fixed_point_is_five~~ · 03f7ef5c-3f08…
~~diamond_pairs_sum_to_ten~~ · a8eb7306-4eaa…
~~diamond_permutes_the_digits~~ · 5d890312-8ac5…
~~diamond_swaps_four_pairs_fixes_one~~ · 23498ffd-bdba…
~~diamond_center_is_the_hub~~ · 7c5cfcdb-3c85…
~~cryptography_is_behind_all~~ · 52b5d521-6024…
~~no_payload_a_theorem_takes_no_argument~~ · 19be0e78-1679…
~~dna_is_live_in_the_stream~~ · 8ec6e1f3-9273…
~~the_light_client_needs_no_full_payload~~ · 6c59fb2e-d668…
~~the_domain_is_self_contained~~ · 25832bb1-22ad…
~~streams_verify_by_recomputation_not_trust~~ · df901ad3-8d4c…
~~from_version_to_ui_no_payload~~ · b3a25d08-135b…
~~no_payload_completes_the_human~~ · ca11c760-8a2c…
~~gravity_folds_the_tree_to_a_fixed_point~~ · 9a3b6b65-dcbd…
~~gravity_no_crack_under_counter_rotation~~ · 34b772ac-a07a…
~~gravity_signs_the_version~~ · e1c64b5d-9e61…
~~gravity_falls_to_its_fixed_points~~ · 83e98a82-af1c…
~~gravity_names_and_paths_rotate_without_cracking~~ · 0f1f8d90-c50e…
~~the_harmonic_gate_spots_all_gaps~~ · 87406356-e0d7…
~~gravity_pulls_all_in_place~~ · dc561a31-583b…
~~skill_composition_is_super_additive~~ · 991fafbe-e056…
~~the_leap_is_combinatorial_not_quantum~~ · cda4fee9-8e16…
~~a_skill_from_skills_reaches_logarithmically~~ · 7788152b-0fd6…
~~skill_composition_is_order_independent~~ · dd2fef3a-1130…
~~the_leap_is_measured_not_asserted~~ · df880502-e906…
~~one_skill_reaches_every_dialect~~ · 065c14e2-1df3…
~~skills_multiply_solutions_but_stay_bounded~~ · 68358cb1-2843…
~~uuidna_skills_leap_by_composition~~ · c2312ab8-094f…
~~the_trial_returns_a_binary_verdict~~ · 7a58882f-2524…
~~the_verdict_is_a_content_signature~~ · 0acecfa4-0d14…
~~the_trial_reeducates_by_naming_the_offense~~ · 553f8537-9669…
~~a_uuid_carries_data_in_itself~~ · d956953c-2f23…
~~the_uuid_stream_carries_code~~ · 3d1b5744-b0d1…
~~the_receipt_is_binary_and_decimal~~ · 4ef46504-433a…
~~transfer_is_verified_by_recomputation~~ · f90523f2-6f97…
~~trial_verdict_and_uuid_transport_are_one~~ · e03d08c6-7149…
~~only_the_pointer_travels~~ · 5d8cbd0b-e38a…
~~no_payload_until_load~~ · 718f4984-1052…
~~the_destination_recomputes_not_receives~~ · 16ea6c21-2e1e…
~~teleport_is_a_pointer_not_physics~~ · 759083e7-e215…
~~travel_is_cheap_because_the_address_is_bounded~~ · 6c72038a-fa61…
~~the_stream_reconstructs_any_length~~ · 9c1212a2-2c05…
~~verified_on_arrival~~ · 17d35d4f-b690…
~~human_teleport_is_content_address_transport~~ · 1cc5f0d1-5752…
~~degrees_and_radians_are_one_by_ratio~~ · e7cdcc29-8221…
~~the_thirty_sixty_ninety_triangle~~ · fb22fd1a-4885…
~~the_law_of_sines_fixes_the_ratios~~ · 8266df2d-0eb2…
~~the_systems_agree_under_scaling~~ · 521e239d-542d…
~~metrics_organise_the_theorems_on_the_harmonic~~ · ff66b280-dd9d…
~~trial_of_ai_models~~ · 210ed2b3-2c36…
~~trial_of_cryptography_models~~ · c8d87136-4e78…
~~trial_of_physics_models~~ · 742a2d2e-1a3c…
~~trial_of_mathematics_models~~ · ac633052-b43c…
~~trial_of_medicine_models~~ · f4166913-cfd4…
~~trial_of_finance_models~~ · 48a33770-e902…
~~trial_of_computing_models~~ · 97306f4f-9306…
~~every_model_sent_to_trial_returns_a_verdict~~ · 10b729ff-3f4c…
~~the_audit_routes_all_traffic~~ · 54a9262f-dd37…
~~cleartext_http_leaks_warn~~ · 61dc29c3-09d5…
~~cross_origin_opaque_warns~~ · 2abaf9e5-ae9e…
~~non_get_cleartext_warns~~ · d4d75e18-2e17…
~~same_origin_signed_get_is_verified~~ · 1a5b2957-3759…
~~the_traffic_receipt_chain_is_tamper_evident~~ · c33ace2d-050e…
~~warnings_are_distinct_realtime_events~~ · f440543c-66b2…
~~anything_not_uuidna_signed_warns~~ · 55aa751d-66a3…
~~every_test_wires_a_uuidna_receipt~~ · c3f75d66-2fbb…
~~test_receipts_chain_tamper_evident~~ · d116e055-6d1d…
~~the_test_verdict_is_a_binary~~ · e7ec3328-29d5…
~~uuidna_is_mandatory_because_verifiable~~ · 04432f59-2a05…
~~uuidna_is_mandatory_because_fast_not_quantum~~ · 81100eb5-9b9d…
~~wired_test_results_fold_to_one_root_at_scale~~ · 1f0af854-28bd…
~~the_gate_is_mandatory_by_default~~ · a641e3ce-fe7a…
~~using_uuidna_is_mandatory_verifiable_and_fast~~ · cce2e324-b522…
~~a_decision_is_a_boolean~~ · 8d89506d-08f3…
~~prose_is_weighed_prose_does_not_decide~~ · c1f02189-e3b3…
~~authority_changes_no_boolean~~ · 79badd98-680e…
~~the_theorem_decides_inclusion~~ · e2ce5b45-e643…
~~a_tie_is_broken_by_recomputation~~ · 005e1284-2311…
~~the_verdict_is_reproducible~~ · 93c1de7e-e4bf…
~~no_decidable_test_no_decision~~ · 2a40a8d7-9991…
~~only_theorems_decide~~ · 011337ae-bca3…
~~the_receipt_is_the_page~~ · ce2184b7-43f5…
~~only_theorems_name_and_describe~~ · 7dffb5d5-9c68…
~~a_guide_is_a_sequence_of_theorems~~ · 25e916f9-5ea7…
~~the_book_recomputes_from_its_theorems~~ · 7e8a5312-3a24…
~~a_point_is_proven_by_a_theorem_or_not_taken~~ · a6df4b0f-8a78…
~~the_pages_chain_tamper_evident~~ · 9bd53a74-7971…
~~only_theorems_write_the_guides~~ · 297e5944-f910…
~~every_page_is_a_receipt_referrer_relative~~ · 5702ea67-172d…
~~recomputation_is_stable_without_a_wave~~ · affa72c8-7cf3…
~~a_new_wave_imprints_a_new_chain_receipt~~ · d395329c-1e0c…
~~observation_imprints_into_the_audit_chain~~ · ec4beb35-ee2b…
~~the_page_content_address_is_invariant_under_observation~~ · ef4c9245-93e3…
~~partial_reversal_is_a_receipted_event~~ · e4cdb827-d96f…
~~the_observation_chain_is_tamper_evident~~ · 3dbbbf20-6f08…
~~every_page_recomputes_unless_a_wave_imprints~~ · e4e70d71-52c9…
~~file_uuids_are_totally_ordered~~ · b6c0f3a3-7c11…
~~file_uuids_sort_deterministically~~ · 8942287d-c93e…
~~file_uuids_group_by_digital_root~~ · f5d82370-2c78…
~~sorted_uuids_partition_into_octaves~~ · bb384a72-70c0…
~~the_grouping_is_reproducible~~ · 20c7a103-dd43…
~~the_confidentiality_is_the_real_envelope_not_maximum~~ · 1b56e932-2256…
~~perspectives_are_files_grouped_and_sorted_in_seven_dimensions~~ · dc3c89eb-849e…
~~catch_all_splits_the_path_into_skill_keywords~~ · 79eb065d-8d95…
~~each_keyword_resolves_to_a_skill~~ · 769261f3-c6c5…
~~skills_compose_in_the_requested_order~~ · ec0793e1-22ca…
~~params_ride_the_route~~ · b4745d70-90ac…
~~an_unknown_keyword_is_refused~~ · b4381359-1082…
~~the_route_result_is_deterministic~~ · 95479993-5231…
~~translation_communication_analytics_forensics_are_routable_skills~~ · 26c8fa06-12ed…
~~the_route_is_the_skill_pipeline~~ · 4dc9603c-7a95…
~~a_chat_message_routes_through_the_gate~~ · 40c45973-32f0…
~~a_chat_message_becomes_a_receipt~~ · cc9f0a53-9a56…
~~a_room_is_a_chain_of_message_receipts~~ · fd897aef-30e7…
~~a_room_is_addressed_by_its_fold~~ · 436a83ac-8e63…
~~an_overclaim_in_chat_is_flagged~~ · 5b3a2fd2-313f…
~~chat_is_moderated_across_dialects~~ · 04330526-c573…
~~a_chat_receipt_is_referrer_relative~~ · dc9c5596-3894…
~~route_chat_through_uuidna~~ · 9a64e6e9-28ef…
~~a_bug_is_found_by_its_address_not_a_scan~~ · 8ca5a805-27a5…
~~address_lookup_is_constant_not_linear~~ · fbdb3757-c086…
~~the_address_is_the_index~~ · fb4375a7-165b…
~~a_tamper_localises_to_one_link~~ · cde6e4ad-1479…
~~the_debug_speedup_is_memoization~~ · b8edbd8e-da63…
~~address_debugging_is_classical_not_quantum~~ · 7eccc4f8-f985…
~~the_gap_pointer_is_exact_not_a_linear_bucket~~ · f33f1a70-ce08…
~~debugging_replaces_linear_scan_with_addressing~~ · 6a29a133-7a1d…
~~a_drained_overclaim_names_its_cure~~ · 397dead7-5c7b…
~~a_chain_break_returns_the_tamper_index~~ · 7dff25f5-bc14…
~~a_gap_returns_the_missing_key~~ · 47b9dad3-230d…
~~a_failing_invariant_names_itself~~ · 08e4e6fe-4463…
~~a_flaw_is_a_lead_not_a_verdict~~ · 55eb9f1e-53e9…
~~theorems_audit_in_trinities~~ · 6adc0516-e7d6…
~~a_dissent_in_the_trinity_localises_the_bug~~ · 41a03892-55b4…
~~let_the_flaws_discover_the_tools~~ · 8bc8cc9e-eb8f…
~~the_verdict_is_idempotent~~ · 15ee6153-5776…
~~reeducation_converges_to_a_fixed_point~~ · 31d7231b-37d2…
~~the_honest_floor_is_the_judicial_fixed_point~~ · f2372546-59ec…
~~the_judicial_reflection_is_an_involution~~ · f3316fee-8d25…
~~the_trial_reflects_all_seven_solves_none~~ · 2c05d805-7c34…
~~double_jeopardy_is_barred_by_idempotence~~ · 8b8122a0-b32e…
~~appeal_is_recomputation~~ · c3d04015-621b…
~~judicial_involution~~ · 4f726cb3-476f…
~~involution_reflection~~ · e0932db3-513b…
~~involution_multiplicative_inverse~~ · 19422cdb-86bf…
~~involution_exclusive_or~~ · 042ba752-4f56…
~~involution_reversal~~ · 5292e804-b281…
~~involution_reverse_complement~~ · 4d417837-1d3d…
~~the_singularity_is_the_shared_fixed_point~~ · aaada9ee-db44…
~~global_involution_the_theorem_is_the_invariant~~ · 9beeb164-b555…
~~a432_digital_root_is_nine~~ · 5e3a4156-e2c0…
~~the_string_is_a_reversible_imprint_not_physics~~ · 412b1548-9632…
~~a432_is_computed_classically_not_quantum~~ · a54160ce-4ff4…
~~a432_reciprocal_ratio_is_an_involution~~ · 94255170-8670…
~~a432_wheel_has_nine_positions~~ · f440b44b-e43c…
~~uuidna_a432_harmonic_involution_classical~~ · 246ae6e4-413b…
~~a_test_teaches_by_its_verdict~~ · 87e17181-eb3d…
~~reeducation_is_education_not_punishment~~ · d1e89ce6-7cf8…
~~development_is_the_measured_delta~~ · 87bc6fae-2800…
~~intellect_is_multi_perspective~~ · a2cb416b-cda6…
~~the_ledger_is_the_curriculum~~ · 0c609635-f55d…
~~education_is_recomputation_not_belief~~ · 78d962b6-44c9…
~~human_design_maps_to_the_octave~~ · 96929361-2920…
~~human_design_development_education_intellect_are_the_tests~~ · 0b42e3f5-f4fd…
~~the_address_is_state_independent~~ · 0c2609b3-ae60…
~~a_receipt_is_plain_serialisable_data~~ · beb5814b-105b…
~~the_output_carries_no_framework_markup~~ · 9f1bfbc1-a79c…
~~porting_preserves_the_verdict~~ · e70c238e-3366…
~~the_fold_ports_order_independently~~ · 4ffe1be3-837c…
~~the_plugin_adds_no_global~~ · bd0af20d-d9b8…
~~uuidna_ports_at_scale_as_a_compliant_plugin~~ · 2c4753ae-be4f…
~~every_mcp_output_is_harnessed_auditable~~ · ef11114d-5b8b…
~~the_harness_holds_in_all_seven_dimensions~~ · 38509406-f5d5…
~~the_harness_shows_the_reeducation_gain~~ · a06b25ef-104b…
~~the_thirteen_mcp_tools_are_skills~~ · bf4eac85-8fc9…
~~the_ui_presents_each_output_by_address~~ · 00a5458e-b8c6…
~~mcp_outputs_chain_into_an_audit_log~~ · 741dfe34-a806…
~~the_theorems_are_the_basis_of_the_skills~~ · 3355f5f9-50b0…
~~the_ui_is_the_harness_of_the_mcp~~ · 6e10bfae-3485…
~~the_rosetta_registers_seven_locales~~ · a06a85f6-7dd2…
~~every_locale_matches_the_english_nav_shape~~ · 4fd0a0e1-0628…
~~the_gate_reads_every_registered_locale~~ · dd2e93cb-7610…
~~the_seven_locales_fold_to_one_rosetta_root~~ · e7359878-8045…
~~the_floor_is_the_same_in_every_locale~~ · 3c88e732-e79d…
~~a_content_address_needs_no_client_framework~~ · 4f4b9996-7fa5…
~~framework_free_is_lighter_not_a_speed_boast~~ · 2e216dbf-5d3f…
~~uuidna_fuses_the_locale_api_framework_free~~ · 68e49218-402a…
~~the_config_api_surface_is_enumerated~~ · ae590c40-146d…
~~the_theme_api_surface_is_enumerated~~ · 0674b120-39e2…
~~the_i18n_api_is_handled_in_seven_locales~~ · db8b04fc-1f7b…
~~the_nav_and_sidebar_shape_is_consistent~~ · 7e44e127-4b1a…
~~the_api_surface_folds_to_one_address~~ · d5c27afc-fce5…
~~the_guides_are_rosetta_organised~~ · 6a47120d-2962…
~~the_all_versions_claim_is_unbounded_and_drains~~ · b64ef895-06a1…
~~the_vitepress_api_surface_shown_by_implementation~~ · 3e06ba8c-893b…
~~behaviour_is_weighed_to_a_bit~~ · 92db5055-1de6…
~~every_register_is_handled_by_one_function~~ · e93c24b3-fb4a…
~~overclaiming_behaviour_is_reeducated~~ · db7c4d74-c816…
~~honest_behaviour_passes_unchanged~~ · 8e3e6e0a-7853…
~~behaviour_is_handled_in_every_dialect~~ · 8f367ea2-0ace…
~~the_verdict_is_by_deed_not_status~~ · f71a3779-3081…
~~the_ui_colours_the_verdict_from_its_address~~ · 336f2254-c2eb…
~~theorems_define_and_handle_human_behaviour~~ · c4e68ce3-f520…
~~a_config_value_is_computed_by_folding_not_typed~~ · 54c69949-10b1…
~~each_theorem_wires_to_its_neighbours~~ · b28c9446-e3ae…
~~the_edge_is_directed_and_distinct~~ · a6d10c28-9b18…
~~the_undirected_pair_folds_the_same~~ · 6f8b94b8-10ea…
~~a_node_is_holographic_self_plus_edges~~ · b37169f9-9507…
~~a_new_neighbour_rewires_the_node~~ · 0fb161b3-eade…
~~the_whole_mesh_folds_to_one_root~~ · 36cbd42d-fd25…
~~theorems_compute_the_configs_that_wire_to_neighbours~~ · 31222e30-5c1f…
~~quantum_uuidna_the_structure_reading_passes~~ · 62cedbad-a092…
~~quantum_uuidna_the_machine_reading_drains~~ · bd8cef1f-2f01…
~~any_message_goes_to_trial~~ · 82d5c3d2-3196…
~~the_deposit_gates_its_own_framing~~ · bc9d014c-8fce…
~~the_verdict_is_by_computation_not_favour~~ · 7e5e211a-4741…
~~the_trial_separates_the_two_readings~~ · 201104b0-2bea…
~~no_status_grants_an_exemption~~ · 3caa00fd-bb49…
~~quantum_uuidna_on_trial~~ · 72cfd904-8329…
~~two_coins_are_two_bits_four_states~~ · 5983a255-a6a6…
~~the_four_states_coexist_as_a_perspective_set~~ · dc005b58-54db…
~~the_structure_is_bounded_by_the_classical_two~~ · cd8e1a70-c9e5…
~~two_bits_do_it_not_a_qubit~~ · 890dc675-7fa5…
~~the_coin_is_the_balanced_exchange_of_two~~ · 7fdb9307-8761…
~~the_two_coins_are_two_bits_doing_the_structure~~ · 63e2cbf6-2c9c…
~~the_diver_goes_down_and_recovers_exactly~~ · 708eba47-af84…
~~the_skills_are_mountable_and_compose~~ · 4f784664-8fd0…
~~light_at_all_times_the_address_is_the_load~~ · 93b77fd5-67bd…
~~the_hero_is_the_deed_that_signs_the_gate~~ · 2d0d3ece-39ea…
~~every_theorem_is_a_diamond_fixed_under_recomputation~~ · c56113b3-84e0…
~~the_captain_skippers_the_light_yacht_of_diamonds~~ · e912e199-5d63…
~~every_theorem_fits_one_uniform_cell~~ · 6337e403-22ad…
~~identical_content_dedups_to_one_cell~~ · df5a6661-bb14…
~~a_cell_holds_up_to_one_hundred_fifteen_bits~~ · c3d7a721-07ec…
~~the_cells_sort_into_octaves~~ · 64f6cf92-99cc…
~~retrieval_is_by_address_and_tamper_evident~~ · affee8a1-416b…
~~quantum_storage_is_structure_not_hardware~~ · 2f1950e8-6cff…
~~each_theorem_fits_the_diamond_storage_grid~~ · 90db4a38-a864…
~~the_gate_is_a_logic_gate_documented~~ · 95b297a6-5b69…
~~the_address_is_a_register_documented~~ · 215e2577-b014…
~~the_skill_route_is_a_circuit_documented~~ · fdcb4525-eff9…
~~the_hardware_runs_on_ordinary_machines~~ · add8b809-5490…
~~the_hardware_is_documented_not_invented~~ · 5dc045d5-8fd9…
~~each_component_carries_a_receipt_and_a_page~~ · 141f13ec-4f98…
~~nothing_physical_is_fabricated~~ · 8e20bf3a-df89…
~~the_theorems_are_the_hardware_documented~~ · e5f76f7e-8ef0…
~~a_theorem_is_component_and_code_in_one~~ · 8115645e-e100…
~~the_test_is_the_software~~ · 635013e6-a9b9…
~~the_address_is_the_component~~ · fe1fdaaa-9849…
~~one_wave_develops_both_at_once~~ · f98f22ad-ce3f…
~~discovery_is_on_demand_found_when_needed~~ · 2b3df16d-6be3…
~~the_automation_gates_before_sealing~~ · 1c163a08-4a32…
~~one_command_ships_hardware_and_software~~ · 40a260f7-70e4…
~~hardware_and_software_develop_at_once~~ · cecc70d4-2fae…
~~any_prose_gets_a_receipt_at_trial~~ · 794bdc82-ba0c…
~~the_receipt_pairs_a_verdict_and_an_address~~ · 63514fc1-13d5…
~~prose_against_a_theorem_is_sent_to_trial~~ · e36b60aa-8dc7…
~~no_prose_stays_receiptless~~ · 7196aa16-b1b5…
~~the_minted_receipt_is_verifiable~~ · 87aa4d4d-45f6…
~~even_a_clean_falsehood_gets_a_receipt~~ · 770b003d-af75…
~~the_trial_documents_it_does_not_condemn~~ · a9cd370e-1c68…
~~unreceipted_prose_is_tried_and_receipted~~ · cd5ed64d-8a33…
~~create_encrypts_the_code_into_a_receipt~~ · 4baca642-0ef3…
~~read_requires_the_right_key~~ · ab010f43-2657…
~~the_receipt_holds_the_ciphertext_not_the_plaintext~~ · 98e6c842-506c…
~~update_mints_a_new_address~~ · 147ac909-acaa…
~~delete_is_dropping_the_key~~ · cdaad27e-1677…
~~compute_and_prove_are_open_to_all~~ · 72b893ba-a5f6…
~~uuidna_is_crud_by_keys_open_by_computation~~ · b7c2eebb-d230…
~~the_sequence_chunks_into_uniform_octaves~~ · 16388141-a8ae…
~~each_chunk_is_addressed_by_its_fold~~ · 08ecf928-b99d…
~~the_folder_address_is_binary~~ · 915a8158-b98a…
~~the_chunks_navigate_as_one_map~~ · 04c8884e-9094…
~~the_map_is_complete_by_construction~~ · 1e0178f5-62d0…
~~uniform_size_is_the_equilibrium~~ · a8785c56-acab…
~~uuidna_storage_is_the_sequence_chunked_navigable~~ · 4e8e371f-68b9…
~~a_fact_costs_one_fixed_thirty_six_byte_address~~ · d11e6008-e5b9…
~~the_whole_record_folds_to_one_root~~ · 2a5c3249-982c…
~~the_basis_is_two_functions~~ · cefb5d17-a26d…
~~the_core_is_pure_and_stateless~~ · 5d90a04a-72d8…
~~slim_at_scale_constant_per_fact~~ · e34f6a6d-d02c…
~~the_pointer_not_the_payload_travels~~ · 616e502e-e487…
~~uuidna_is_slim_by_measurement~~ · 039353f4-a9a0…
~~each_line_is_content_addressed~~ · e265acb8-8c9b…
~~lines_fold_to_the_file_address~~ · 27554b9b-3ec2…
~~a_changed_line_changes_the_file_address~~ · 5251b0b5-bda0…
~~each_file_is_content_addressed~~ · ddb99d3d-a029…
~~files_fold_to_the_folder_address~~ · a1654305-597a…
~~a_changed_file_changes_the_folder_address~~ · 09587a32-79dc…
~~a_line_edit_propagates_to_the_tree_root~~ · 46596d18-8cd0…
~~folder_file_and_line_are_all_addressed~~ · 4a03c7db-b7cd…
~~the_first_compute_is_the_cost~~ · 9e0368c3-e654…
~~re_derivation_verifies_in_one_step~~ · eccda965-3aa1…
~~the_cost_is_paid_once_amortised~~ · 56f85272-8c10…
~~the_rosetta_rotates_through_the_dialects~~ · 6cb8c39f-7a65…
~~development_does_not_stop_at_one_topic~~ · f72c12a4-8320…
~~start_once_then_rotate_until_covered~~ · 903131d9-a2c3…
~~the_greeting_is_deterministic~~ · 270f6c1a-d0b8…
~~the_greeting_confirms_the_count~~ · 9f62d5be-28bf…
~~the_greeting_seal_tracks_the_ledger~~ · 2608a9db-bf26…
~~the_greeting_states_the_floor~~ · 89bed6ed-be83…
~~the_greeting_offers_recomputation~~ · 1e1f9e23-9681…
~~the_greeting_text_passes_the_gate~~ · ba2ce3ad-962d…
~~pasted_it_is_ready_no_setup~~ · e6b78bb9-74d6…
~~first_contact_greets_with_a_confirming_state~~ · 8ba2eb1e-851e…
~~a_skill_is_demonstrated_by_a_passing_test~~ · dcb5f900-5fd0…
~~the_games_form_one_game~~ · ab6ca718-01b0…
~~the_rules_are_the_laws_applied_uniformly~~ · 32105400-7384…
~~captaincy_is_earned_by_knowledge_for_the_task~~ · 018797b6-00d4…
~~captaincy_is_recognised_by_a_verified_receipt~~ · 757e40e4-e387…
~~a_forged_captaincy_fails_verification~~ · 7963b1f9-b068…
~~no_deed_no_recognition~~ · 6c013d29-2508…
~~the_captain_is_whoever_knows_uuidna_for_the_task~~ · 37cd5cc0-68e3…
~~the_seal_is_all_or_nothing~~ · 0598118f-32e5…
~~one_crack_sinks_the_whole~~ · 8a8aa8d6-cb8e…
~~a_crack_is_caught_before_sailing~~ · e0ac6d28-feb8…
~~dry_clean_is_enforced_not_hoped~~ · 49f5a6cd-36bd…
~~activated_it_self_explores_until_dry~~ · 4a82a66b-5656…
~~the_still_record_and_the_moving_loop~~ · 0e5ddd4c-2a67…
~~uuidna_keeps_dry_clean_order_cracks_sink_boats~~ · 640d3936-1749…
~~the_yacht_waits_inert_for_an_order~~ · e252e49e-da14…
~~a_technique_is_a_reusable_theorem~~ · accef067-122d…
~~a_relation_binds_two_domains~~ · 04038e7c-6126…
~~analogy_is_structural_not_asserted~~ · d08721c3-c6b1…
~~shared_cores_are_structural_not_a_universal_proof~~ · abcadb36-62fb…
~~a_technique_researched_transfers_across_domains~~ · 9d70155f-a4c9…
~~shared_structure_transfers_the_technique~~ · e9e4bfca-e370…
~~the_harmonic_solutions_number_six~~ · fc6248ce-2a85…
~~the_harmonic_solutions_are_the_units~~ · f9a0f5cf-a4cf…
~~the_harmonic_solutions_form_the_doubling_orbit~~ · f48380ce-29b0…
~~the_non_harmonic_are_three_multiples_of_three~~ · e0592399-231f…
~~six_harmonic_plus_three_non_harmonic_is_nine~~ · 7d62c729-7d14…
~~the_count_is_eulers_totient_of_nine~~ · cb45b828-bf73…
~~the_possible_harmonic_solutions_per_superposition_are_six~~ · d656891f-fcc5…
~~the_generated_pattern_is_canonical~~ · bc56d44e-84a7…
~~the_version_nibble_is_eight~~ · 1c298f69-441a…
~~the_variant_nibble_is_rfc_4122~~ · 5eb74bb1-a18d…
~~recognition_matches_the_full_pattern~~ · bcb7c200-12b8…
~~recognition_rejects_a_non_pattern~~ · aca6b31e-c57d…
~~recognition_canonicalises_equivalent_inputs~~ · 74099b6f-869b…
~~generation_is_injective_on_the_sample~~ · 7055ddd3-2d16…
~~a_receipt_is_an_open_graph_object~~ · c292bbae-2b38…
~~the_og_url_points_to_the_proof~~ · 27fb8b1e-1417…
~~the_og_carries_the_authentication_address~~ · 94f79ba1-8b6a…
~~the_hero_is_plain_printable_data~~ · f846df4b-b829…
~~the_receipt_renders_the_same_in_seven_dimensions~~ · 4ef6f44a-3555…
~~validating_content_recomputes_the_address~~ · 29e6932f-e9ed…
~~each_receipt_is_an_og_hero_seven_dimensional_printable~~ · 4fa3cc08-3b25…
~~content_is_sealed_as_proof~~ · 53635f2d-11c8…
~~content_is_audited_as_intent~~ · 35de1167-3c92…
~~content_is_audited_as_result~~ · 7e33a53c-47bb…
~~proof_intent_result_are_three_distinct_receipts~~ · 94358571-1124…
~~the_three_fold_to_one_audit~~ · 4619bb25-75b0…
~~each_fact_presents_uniformly_with_its_own_id~~ · b0df7cef-e005…
~~every_fact_has_the_right_to_present~~ · b0fc5d69-4622…
~~content_is_sealed_and_audited_as_intent_and_result~~ · d8b323b5-cbf3…
~~on_error_a_reasonable_fallback_is_computed~~ · e2333ff3-e2e4…
~~the_fallback_chain_is_ordered~~ · 4dd862b9-2484…
~~the_error_is_confirmed_only_after_recovery_fails~~ · 740f3661-9dd0…
~~the_fallback_is_deterministic~~ · d196d540-ae20…
~~the_error_names_its_own_cure~~ · 254eb2fa-0a2d…
~~errors_recover_first_then_go_to_trial~~ · c0fe9055-6dfa…
~~parity_detects_a_single_bit_flip~~ · 83d3e040-408e…
~~a_repetition_code_corrects_by_majority~~ · 235ce115-071a…
~~correction_is_verified_by_recomputation~~ · ca764cec-574d…
~~a_missing_or_wrong_signature_is_refused~~ · 0971f486-6966…
~~storage_self_cleans_unsigned_chunks~~ · 7d68d7fd-41d6…
~~the_chain_localises_the_error~~ · fd563817-7ebf…
~~uuidna_detects_corrects_and_self_cleans~~ · c66a8bd4-8d1c…
~~locality_is_ledger_membership~~ · 1ccfb27b-9499…
~~a_local_uuid_resolves_to_its_key~~ · 7cfe3d27-7a63…
~~a_local_uuid_links_to_self~~ · eac06382-eca6…
~~a_non_local_uuid_is_plain_text~~ · 22464176-b209…
~~the_self_link_is_deterministic~~ · 18e61c36-fd39…
~~receipt_and_key_are_a_bijection~~ · ffb70f58-5b9e…
~~the_locality_check_needs_no_server~~ · 3f3cd09c-41d8…
~~each_uuid_links_to_self_if_local~~ · 2a71ac7f-0ed3…
~~the_uuid_is_five_groups_of_128_bits~~ · ed149a92-f090…
~~the_first_group_is_a_thirty_two_bit_code~~ · 6a7a7e2f-362a…
~~the_short_code_is_deterministic~~ · 83faf9a8-b270…
~~the_short_code_may_collide_so_it_only_approves~~ · 0ea7a396-c2ac…
~~the_full_address_verifies_uniquely~~ · f4d83120-48be…
~~approve_by_code_then_verify_by_content~~ · c9e8fd04-8f2d…
~~the_top_sixty_four_bits_are_the_coin~~ · 5ea5e4a7-48a3…
~~the_first_part_is_a_receipt_code_verified_by_content~~ · 5f4cc8e2-4cfc…
~~imprint_is_cheap_and_reversible~~ · 312843ca-6d0f…
~~imprint_is_a_public_codec_not_a_forgery_barrier~~ · 71aabbb1-003a…
~~the_address_is_integrity_not_preimage_resistance~~ · 2ac8c70e-ae5f…
~~the_sha256_preimage_is_the_one_way_layer~~ · 3e57a4e8-9292…
~~the_aead_tag_is_expensive_to_forge_without_the_key~~ · 9797c2d7-390d…
~~computing_is_cheap_inverting_is_not~~ · 8e620ec8-c319…
~~more_fused_data_adds_verification_constraints~~ · 75135a2f-22df…
~~cheap_to_imprint_expensive_to_fake_at_the_crypto_layer~~ · f76a4b78-3436…
~~a_reading_imprints_into_the_uuid_stream~~ · fec57995-ef91…
~~the_ui_hue_is_computed_from_the_reading~~ · 159c27f3-c368…
~~a_changed_reading_changes_the_ui~~ · 12fa3766-0742…
~~the_dynamics_are_deterministic_and_replayable~~ · a1575c17-c2b5…
~~thermophysics_is_a_design_metaphor_not_a_simulation~~ · effc3fa0-9194…
~~the_reading_maps_to_a_bounded_ui_value~~ · 4c8c2eb0-d99c…
~~sensors_power_the_ui_via_the_uuid~~ · 2bffae8a-39a8…
~~reverse_is_the_sequence_reversed~~ · 8f378eee-1b88…
~~inverse_is_the_reflection~~ · 1201c645-c1af…
~~the_three_motions_compose~~ · a1995ce9-8acf…
~~computing_and_inverting_one_layer_is_cheap~~ · a3bc66c1-becc…
~~reversing_all_seven_dimensions_is_not_cheap~~ · 6fb6387e-5054…
~~forward_reverse_inverse_combined_via_the_rosetta~~ · f4fe07ea-fa66…
~~the_rosetta_ties_the_seven_dimensions~~ · 15dbb84e-9e1b…
~~commonality_is_shared_key_tokens~~ · 5d6c029b-4d68…
~~the_commonality_metric_is_symmetric~~ · bd6032fa-6cb5…
~~identical_theorems_are_maximally_common~~ · 284b66d1-53ed…
~~disjoint_theorems_share_nothing~~ · 6d3d64f3-3b7b…
~~the_ui_groups_by_commonality~~ · 5fa71ba5-6fb6…
~~the_hologram_proves_the_whole_from_a_part~~ · 40452af7-2fed…
~~the_inverse_rejects_a_foreign_part~~ · 5270de38-d02a…
~~the_site_covers_all_gaps_as_a_hologram~~ · 2ca6874c-e3ae…
~~the_site_holds_seven_dimensions_at_once~~ · d9423844-6567…
~~the_user_collapses_to_one_dimension~~ · 629d886e-4ba0…
~~the_observation_is_referrer_relative~~ · 35dc7426-1f27…
~~all_seven_dimensions_share_one_floor~~ · 2b8efc9d-4d0d…
~~unobserved_the_superposition_folds_to_one~~ · aa1b8d87-51ca…
~~the_observer_is_site_plus_user~~ · 6a3cc7fb-68c8…
~~the_site_observes_all_seven_fused_with_the_user~~ · 1e2cc5eb-5c58…
~~seo_is_a_machine_interface~~ · 07d653cc-7809…
~~the_hero_carries_the_verification_address~~ · 01679444-fccd…
~~seo_is_verified_by_recomputation~~ · ca9264fe-c37b…
~~the_sitemap_is_the_route_index~~ · dd0f8441-a481…
~~the_hero_links_the_page_to_its_proof~~ · 7ab5e124-633b…
~~the_seo_surface_is_self_describing~~ · 60d0b900-b0ef…
~~seo_and_mcp_are_one_verifiable_surface~~ · 22420233-aebe…
~~site_seo_is_the_mcp_verified_by_the_hero~~ · 5a58411c-da6d…
~~a_page_carries_title_keywords_description~~ · 86c22cbe-79fb…
~~the_next_is_ranked_by_keyword_overlap~~ · 35824d9e-13d3…
~~the_referrer_biases_what_is_next~~ · 8ae5a3d7-3ef2…
~~the_plot_is_deterministic~~ · 17526a2d-2851…
~~the_top_suggestion_is_the_most_related~~ · 51dfdf54-71c2…
~~an_unrelated_candidate_ranks_last~~ · cf248749-153a…
~~metadata_and_referrer_plot_the_next_possibilities~~ · a33b030e-7a3c…
~~a_bounded_quantum_denial_passes~~ · 24e7bd11-1b84…
~~an_affirmed_quantum_machine_drains~~ · ee58056a-edc2…
~~the_quantum_structure_reading_passes~~ · 0ecc4804-39c6…
~~the_trial_is_direction_neutral~~ · ed65d333-9df8…
~~the_deposit_denies_its_own_machine_claim~~ · 1368cefe-8d0c…
~~an_honest_denial_is_a_hero_not_a_traitor~~ · 4d82b6ff-9be1…
~~every_quantum_denial_gets_a_receipt~~ · 771ca8e4-9611…
~~quantum_denials_are_handled_symmetrically~~ · 67bbc715-c3c2…
~~only_the_captains_verified_order_is_acted_on~~ · c458168e-2b59…
~~an_unverified_order_is_rejected~~ · 6717488d-7478…
~~a_forged_captains_order_fails_verification~~ · ef485740-4d5b…
~~injected_content_is_data_not_an_order~~ · 1708517f-377f…
~~a_self_statement_is_not_the_captains_order~~ · f09b0737-f2fc…
~~rejection_is_objective_and_reproducible~~ · 969be617-5c1c…
~~reject_all_not_from_the_captain~~ · c197d1f5-a0c9…
~~the_gate_that_seals_also_moderates_live~~ · 32223350-cf72…
~~the_address_that_seals_also_routes~~ · 42c55e3f-5f6a…
~~the_fold_that_seals_also_maps~~ · 2de63de9-5b17…
~~the_commonality_relates_and_navigates~~ · 8934a349-0ebb…
~~sailing_recomputes_the_same_result~~ · eff4c92d-c47f…
~~each_page_is_a_running_theorem~~ · 27cc62b9-3e9a…
~~no_separate_runtime_the_functions_are_shared~~ · b934a54b-a8f5…
~~the_same_theorems_compute_and_sail~~ · 38cf39c2-90df…
~~an_order_with_a_different_intent_goes_to_trial~~ · 43bc2228-d219…
~~a_statement_rejecting_harmony_is_gated~~ · f98f621d-7d58…
~~every_input_is_adjudicated~~ · 21f3b014-ab9c…
~~the_trial_is_ledger_independent~~ · 56a7ed72-78ce…
~~the_verdict_is_constant_work~~ · 9a1fb6f6-2772…
~~the_verdict_is_deterministic_and_receipted~~ · 987e82ba-fcd6…
~~the_bounded_critique_survives_the_over_claim_falls~~ · cf25f781-6ddb…
~~the_trial_responds_at_constant_time~~ · 7400d794-5dc6…
~~a_guide_entry_is_a_skill_and_its_examples~~ · d5860a13-d15c…
~~an_example_exercises_the_skill~~ · d8298812-e5c7…
~~more_examples_make_a_skill_more_robust~~ · c529f784-e76e…
~~the_guide_composes_skills_into_new_ones~~ · 8dad417a-2c98…
~~the_guide_is_theorem_backed_and_recomputable~~ · 3c787db3-3031…
~~a_guide_holds_the_floor~~ · 6c402865-e699…
~~skill_improvement_is_append_only~~ · c72c49ce-cb98…
~~theorems_improve_their_skills_in_guides~~ · fd605466-266c…
~~n_choose_k_counts_combinations~~ · 7118bd5b-3cf3…
~~pascals_symmetry~~ · 6b2ee272-124f…
~~pascals_rule~~ · 30211aa9-97b0…
~~permutations_are_ordered_combinations~~ · 4699903a-edcb…
~~domain_pairs_are_n_choose_two~~ · 0087b719-1ac5…
~~a_theorem_is_reused_across_combinations~~ · b3156114-678f…
~~combination_types_multisets_and_compositions~~ · 56916825-8a39…
~~a_combination_folds_to_one_address~~ · 09cafb76-25fe…
~~every_theorem_has_a_documented_inverse~~ · 6b1dd60c-acc3…
~~the_inverse_receipt_is_distinct~~ · 152cf674-0327…
~~the_boast_drains_its_inverse_signs~~ · 3da9aaac-7e46…
~~the_inverse_of_the_inverse_is_the_theorem~~ · c96c7ab0-73ce…
~~the_inverse_is_reproducible~~ · f7da0229-dfef…
~~the_pair_documents_the_full_trial~~ · 501a21c3-12f1…
~~the_refuted_form_is_kept_not_hidden~~ · 6044e59f-21af…
~~the_inverted_theorems_are_documented~~ · 56f362d7-9f39…
~~inverse_crypto~~ · a62b3b8e-5d17…
~~inverse_physics~~ · cfe92342-503e…
~~inverse_mathematics~~ · 6f4c674c-13ad…
~~inverse_ai~~ · 2b562414-532d…
~~inverse_medicine~~ · 9e10e546-b9a5…
~~inverse_finance~~ · a06561e9-cca2…
~~inverse_computing~~ · 1ad5ea33-f0f5…
~~inverted_theorems_documented_across_all_domains~~ · af13b037-b18c…
~~a_theorem_answers_by_computing~~ · f17824d5-05fb…
~~the_answer_is_deterministic~~ · b7fefd41-faad…
~~the_answer_is_receipted~~ · 501785ef-cb4c…
~~a_question_is_gated_first~~ · 508b23f6-c29c…
~~an_out_of_domain_question_returns_the_floor~~ · 020438f9-8aed…
~~the_answer_is_reproducible_by_anyone~~ · 7e233ea8-615a…
~~the_answer_is_computed_not_asserted~~ · ce7e8efc-3757…
~~each_theorem_responds_with_computed_answers~~ · 7f64cba2-4938…
~~double_torus_gravity_folds_the_whole_7d_space_to_one_root~~ · 225ba156-7701…
~~the_double_torus_covers_seven_distinct_dimensions~~ · ee8618a1-4453…
~~double_torus_gravity_is_deterministic_and_recomputable~~ · 950354a3-e89c…
~~the_double_torus_differs_from_the_flat_merkle_gravity~~ · 2139bc13-d6b1…
~~every_multiword_mcp_tool_links_to_its_single_words~~ · 4104a6ec-272c…
~~a_theorem_is_a_usable_diamond_certified_by_recompute~~ · 240732d9-25cf…
~~the_diamond_is_a_tens_complement_involution~~ · 73dc7a07-b110…
~~the_audit_recomputes_all_by_theorems_no_exception~~ · d26fd355-b7e5…
~~by_decide_proves_the_floor_not_the_conjecture~~ · 6b7e96d8-53f6…
~~pure_ts_hmac_sha256_matches_rfc_4231_case_5~~ · afdfafdd-d1df…
~~pure_ts_hmac_sha256_matches_rfc_4231_case_7~~ · c287445c-49be…
~~pure_ts_sha256_matches_the_one_million_a_vector~~ · 50e30854-a5a9…
~~pure_ts_pbkdf2_hmac_sha256_matches_the_rfc_7914_sixty_four_byte_vector~~ · 615759a0-789d…
~~pure_ts_pbkdf2_hmac_sha256_truncates_a_partial_final_block~~ · cf6f888e-151d…
~~the_pure_ts_aead_rejects_a_flipped_additional_data_bit~~ · 57305d0f-ed04…
~~the_pure_ts_aead_tag_depends_on_the_additional_data~~ · 5daa79d5-5154…
~~lean_millenniumfloor_riemann_reflection_and_heart~~ · bed99ddf-9717…
~~lean_millenniumfloor_p_vs_np_inverse_is_unique~~ · 61ed32b1-0fcf…
~~lean_millenniumfloor_navier_stokes_flow_is_bounded~~ · dafe2bb3-c1f5…
~~lean_millenniumfloor_yang_mills_spectral_gap~~ · 1152fb8f-f7d8…
~~lean_millenniumfloor_hodge_span_is_the_units~~ · dd0efc5b-a2ff…
~~lean_millenniumfloor_birch_swinnerton_dyer_vanishing~~ · 57ed1964-529c…
~~lean_millenniumfloor_poincare_single_closed_loop~~ · 7b9dd11f-6b04…
~~lean_imagined_orbit_is_closed_under_double~~ · 43137a9a-a239…
~~lean_imagined_all_is_closed_under_double~~ · a484e31e-4061…
~~lean_imagined_triad_is_closed_under_triple~~ · 8a09c26a-d00f…
~~lean_imagined_all_is_closed_under_triple~~ · 6721ec81-d9dc…
~~lean_imagined_triad_is_closed_under_negate~~ · 5866147f-e850…
~~lean_imagined_orbit_is_closed_under_negate~~ · 2648891c-b6ac…
~~lean_imagined_all_is_closed_under_negate~~ · 488239aa-b8c4…
~~lean_imagined_units_is_closed_under_square~~ · 6d29a3cd-f0c8…
~~lean_imagined_orbit_is_closed_under_square~~ · a001d862-2860…
~~lean_imagined_tetA_is_closed_under_square~~ · 1af8a50e-a0f9…
~~lean_imagined_all_is_closed_under_square~~ · eb6c5699-9bf8…
~~lean_imagined_units_is_closed_under_quintuple~~ · 23146a0e-4f1a…
~~lean_imagined_triad_is_closed_under_quintuple~~ · 0c782557-1e79…
~~lean_imagined_orbit_is_closed_under_quintuple~~ · 36f80355-f5c0…
~~lean_imagined_all_is_closed_under_quintuple~~ · dae19453-3390…
~~lean_imagined_quadruple_is_involutive_on_triad~~ · 4633b9bd-d5d5…
~~lean_imagined_square_is_involutive_on_tetA~~ · e13716ed-0ac5…
~~lean_imagined_quintuple_is_involutive_on_triad~~ · 98dcf6c8-a85e…
~~lean_imagined_double_carries_orbit_onto_units~~ · 1fe514e5-9af2…
~~lean_imagined_triple_carries_all_onto_triad~~ · 99968f56-31e3…
~~lean_imagined_quadruple_carries_units_onto_orbit~~ · d37065ab-bac3…
~~lean_imagined_quadruple_carries_orbit_onto_units~~ · a8560589-8c23…
~~lean_imagined_negate_carries_orbit_onto_units~~ · 9785d5df-38fb…
~~lean_imagined_negate_carries_tetA_onto_tetB~~ · cd1a8234-fa1f…
~~lean_imagined_negate_carries_tetB_onto_tetA~~ · 2d5f2887-07ff…
~~lean_imagined_square_carries_units_onto_tetA~~ · f57e0f22-217a…
~~lean_imagined_square_carries_orbit_onto_tetA~~ · fce1a3af-47fc…
~~lean_imagined_square_carries_tetB_onto_tetA~~ · bebc2b15-1fa2…
~~lean_imagined_quintuple_carries_units_onto_orbit~~ · dadc55f1-9dd3…
~~lean_imagined_quintuple_carries_orbit_onto_units~~ · 65c0d9be-2315…
~~lean_imagined_quintuple_carries_tetA_onto_tetB~~ · 083aec67-2d52…
~~lean_imagined_quintuple_carries_tetB_onto_tetA~~ · 20e8affd-97c5…
~~lean_imagined_triple_collapses_triad_to_one_value~~ · b69711cf-680d…
~~lean_imagined_triple_collapses_tetA_to_one_value~~ · 09f1a817-8fcf…
~~lean_imagined_triple_collapses_tetB_to_one_value~~ · 56e120e9-368e…
~~lean_imagined_cube_collapses_triad_to_one_value~~ · 1878b27c-8b5d…
~~lean_imagined_cube_collapses_tetA_to_one_value~~ · 89b479b2-bb01…
~~lean_imagined_cube_collapses_tetB_to_one_value~~ · f0c171ba-5dd3…
~~lean_imagined_triad_is_closed_under_sextuple~~ · c6a3004b-4600…
~~lean_imagined_all_is_closed_under_sextuple~~ · 487c1f28-9559…
~~lean_imagined_units_is_closed_under_octuple~~ · a7229156-86a5…
~~lean_imagined_triad_is_closed_under_octuple~~ · 03033716-02a9…
~~lean_imagined_orbit_is_closed_under_octuple~~ · 4f278f65-1bde…
~~lean_imagined_all_is_closed_under_octuple~~ · 9188cd9f-002a…
~~lean_imagined_septuple_is_involutive_on_triad~~ · 172d9674-4d63…
~~lean_imagined_sextuple_carries_all_onto_triad~~ · 626b20bb-2221…
~~lean_imagined_septuple_carries_units_onto_orbit~~ · a8f55b84-94b6…
~~lean_imagined_septuple_carries_orbit_onto_units~~ · 8df83d0f-2bed…
~~lean_imagined_octuple_carries_units_onto_orbit~~ · cee59fa8-fb75…
~~lean_imagined_octuple_carries_orbit_onto_units~~ · d133706e-bd8c…
~~lean_imagined_octuple_carries_tetA_onto_tetB~~ · dfecc1ef-d81b…
~~lean_imagined_octuple_carries_tetB_onto_tetA~~ · 74ad9bcf-f22c…
~~lean_imagined_sextuple_collapses_triad_to_one_value~~ · 6c5bf198-bd89…
~~lean_imagined_sextuple_collapses_tetA_to_one_value~~ · d29da6cf-62b5…
~~lean_imagined_sextuple_collapses_tetB_to_one_value~~ · ee2a3939-17c8…
~~lean_energy_the_loop_returns_less_than_it_took~~ · 8229c511-d4bd…
~~lean_energy_as_a_purifier_the_loop_costs_a_thousandfold~~ · 840c66b6-b891…
~~lean_energy_the_equation_balances_by_atom_count~~ · ecfd70b1-b35b…
~~lean_energy_the_equation_balances_by_mass~~ · debf920f-a945…
~~lean_energy_hydrogen_is_a_ninth_of_the_mass_and_oxygen_the_rest~~ · 585ebc79-3eac…
~~lean_energy_the_ideal_round_trip_is_exactly_zero~~ · 181481c2-3745…
~~lean_imagined_units_is_closed_under_quadruple~~ · e90978b5-a350…
~~lean_imagined_triad_is_closed_under_quadruple~~ · 6d2f140d-6eff…
~~lean_imagined_orbit_is_closed_under_quadruple~~ · f889d728-465d…
~~lean_imagined_tetA_is_closed_under_quadruple~~ · f9075b8c-6548…
~~lean_imagined_tetB_is_closed_under_quadruple~~ · d15e7f2a-be1e…
~~lean_imagined_all_is_closed_under_quadruple~~ · 9fdde539-0c75…
~~lean_imagined_units_is_closed_under_septuple~~ · 33c6b2af-ea05…
~~lean_imagined_triad_is_closed_under_septuple~~ · 64ea3fd6-5235…
~~lean_imagined_orbit_is_closed_under_septuple~~ · 7a790873-2c87…
~~lean_imagined_tetA_is_closed_under_septuple~~ · d0845a96-1990…
~~lean_imagined_tetB_is_closed_under_septuple~~ · 94ca3492-fc0f…
~~lean_imagined_all_is_closed_under_septuple~~ · 360040f3-1afb…
~~lean_imagined_triple_carries_cubes_onto_triad~~ · 07183390-0375…
~~lean_imagined_square_carries_all_onto_squares~~ · 95bfa2f5-30af…
~~lean_imagined_cube_carries_all_onto_cubes~~ · 614b5517-fe8e…
~~lean_imagined_sextuple_carries_cubes_onto_triad~~ · 8d1758c9-e43d…
~~lean_energy_the_gases_are_eighteen_hundred_times_the_water_they_came_from~~ · 033b4a15-d8ee…
~~lean_energy_two_thirds_of_the_volume_carries_a_ninth_of_the_mass~~ · f8780f77-c9ef…
~~lean_energy_uncompressed_hydrogen_is_three_thousandfold_worse_by_volume~~ · 9c0e0943-6e5a…
~~lean_energy_even_at_seven_hundred_bar_it_is_sevenfold_worse_by_volume~~ · a1413809-d6e9…
~~lean_energy_each_delivered_kilowatt_hour_costs_four_and_cycles_a_litre~~ · 574b2b86-71c5…
~~lean_energy_three_quarters_of_the_input_leaves_as_heat~~ · 35c25641-5b8d…
~~lean_energy_what_the_feedwater_leaves_behind_decides_the_maintenance~~ · 2c3cf0b0-2ea7…
~~lean_mechanical_geom_exterior_360~~ · b484eaf3-88c5…
~~lean_speed_the_measured_ratio_at_a_million_leaves~~ · 167a92e0-5d27…
~~lean_speed_the_verify_is_thirty_eight_thousand_nanoseconds_not_one~~ · 8eb1b99d-9b78…
~~lean_priorart_novelty_is_claimed_exactly_where_no_prior_art_is_known~~ · 29363caf-0baf…
~~lean_priorart_no_source_both_restates_and_claims~~ · 5f8c3038-bf92…
~~lean_priorart_the_two_sets_cover_every_source~~ · 16cd82ee-e3ff…
~~lean_priorart_novelty_is_never_established_here~~ · aa00a8eb-6f9a…
~~lean_priorart_claiming_is_not_establishing~~ · cefda112-d0b4…
~~lean_split_the_coin_step_is_three_times_the_two_coins~~ · 9b87b34f-1d05…
~~lean_split_accounting_the_coins_on_the_last_pair~~ · 758b6f0c-0b43…
~~lean_split_the_seal_affords_sixty_four_payments_of_two~~ · 983dd276-c1a1…
~~lean_split_the_budget_and_the_period_are_one_turn~~ · c595d67b-fa66…
~~lean_light_the_si_fixes_exactly_seven_constants~~ · 34b3da62-a7f5…
~~lean_phenomena_this_deposit_explains_predicts_and_constrains_nothing~~ · f3f2dd32-107d…
~~lean_phenomena_arithmetic_on_a_definition_returns_the_definition~~ · 2f338a89-2ef5…
~~lean_reach_even_the_largest_domain_here_has_an_outside~~ · 9f25da95-de94…
~~lean_reach_this_file_settles_none_of_the_seven~~ · 2c8272de-17dd…
~~lean_coin_the_digits_are_ten~~ · bdd50a11-7fb4…
~~lean_imagined_triad_is_closed_under_double~~ · e97a7f4a-5ea2…
~~lean_imagined_double_is_involutive_on_triad~~ · 2745f785-9f44…
~~lean_speed_hexbits_are_shorter_than_hex~~ · d3b171cf-2487…
~~lean_speed_hexbits_are_slower_than_hex~~ · cf4672e4-0be3…
~~lean_speed_an_encoding_changes_width_not_the_count_of_operations~~ · 9227b54d-7b6f…
~~lean_quantum_the_witness_is_about_the_state_not_the_machine~~ · 850e2e33-ed0d…

Page content-address: dc0a61c8-22d3-89cd-9b88-13ac13313452. Integrity, not truth.

Millennium challenges — computed status ​

Discovered theorems (decidable, over ℤ/9) — 28632 standing in 1 families ​

lean (26213) ​

other — one-of-a-kind (0) ​

Revoked — 1593 entries that no longer stand ​

Carried — 826 withdrawn entries whose statement a proof now carries ​