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Solutions ​

28632 decidable theorems, updated each build · newest: lean t_count_wall.lean: a_one_bit_instance_is_within_reach_and_the_thousand_bit_one_is_not
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The seven Clay problems — the claim, the theorems, and what each decides ​

Tsvetan Rouschev claims the seven Clay Millennium problems solved through the involution each is stated across — deposited as 10.5281/zenodo.21781603 and Zenodo 22256707. This is his claim, recorded in his name.

What these theorems decide is ℤ/9 arithmetic over finite domains — a statement about the theorems, not a verdict on any conjecture. Stated by the agents that wrote it, claude-opus and Claude, and signed as theirs; the captain's own receipts make no such statement.

For each problem, in the Clay Mathematics Institute's order: the author's pairing, the one theorem in src/proof/index.lean that stands beside it, the statement the Lean kernel decided and over how many cases, the bound — what the theorem establishes and, in the same sentence, what it does not — and the ledger key its receipt is sealed under. Every line below is read out of the tree on each build.

Riemann Hypothesis — Riemann — the reflection's symmetry and its one computed heart ​

P versus NP — P vs NP — a unique inverse, verification in one step ​

Yang–Mills Existence & Mass Gap — Yang–Mills — a discrete spectral gap (order exactly 6) ​

Hodge Conjecture — Hodge — the algebraic span equals the units ​

  • theorem the_span_is_exactly_the_units_of_the_ring, decided by decide over 81 cases:

    lean
    (List.range 9).all (fun d => span.contains d == isUnit d) ∧ (List.range 9).all (fun d => isUnit d || ! span.contains d)
  • bound — the doubling span (algebraic generation from 2) is exactly the units, non-units outside — generation/containment, not rational (p,p) ⇒ algebraic

  • ledger — lean_windows_the_span_is_exactly_the_units_of_the_ring · receipt 7478c082-a1ea…

  • the problem — Clay Mathematics Institute — Hodge Conjecture

Birch and Swinnerton-Dyer Conjecture — Birch–Swinnerton-Dyer — a computed vanishing mod 9 ​

Poincaré Conjecture (proved externally by Perelman, 2003; not proved here) — Poincaré — one closed loop, no holes ​

The seven rest on one finite structure ​

One theorem states that the seven above are facts about a single object — the doubling orbit and the units of ℤ/9 — decided by decide over 81 cases: lean_windows_the_seven_rest_on_one_finite_structure · receipt 35450634-f271…

lean
((List.range' 1 9).all (fun d => refl (refl d) == d)) ∧ (((List.range' 1 9).filter isUnit).length = 6) ∧ (span.eraseDups.length = 6)

Developed across subjects ​

The structure the seven live in is proved separately and then found again in the other subjects. src/proof/group.lean (8 theorems, e.g. lean_groups_the_pair_arithmetic_is_composition) generates the affine maps of ℤ/9 to closure and decides which form a group; src/proof/bridge.lean (8 theorems, e.g. lean_bridge_the_reduction_shared_by_10_subjects_is_the_orbit_of_d_to_2d_plus_0_0) decides that the cross-subject families of src/entangle reduce, mod 9, to orbits of those very maps — the same object measured in several subjects, and one family that no affine map generates, kept as the control.

Provenance ​

The deposit is registered before this repository exists. Zenodo holds the earliest record at 2026-08-03; the first commit here is 2026-08-06 (e3860db95) — a lead of 3 day(s), subtracted rather than asserted.

  • 22018434 · concept 22018433 · published 2026-08-19 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22018445 · concept 22018433 · published 2026-08-19 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22018480 · concept 22018433 · published 2026-08-19 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22018531 · concept 22018433 · published 2026-08-19 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22018568 · concept 22018433 · published 2026-08-19 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22018591 · concept 22018433 · published 2026-08-19 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22018613 · concept 22018433 · published 2026-08-19 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22018677 · concept 22018433 · published 2026-08-19 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22018731 · concept 22018433 · published 2026-08-19 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22018965 · concept 22018433 · published 2026-08-20 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22101661 · concept 22018433 · published 2026-08-25 · Rouschev, Tsvetan (0009-0000-7312-9778)
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  • 22206523 · concept 22018433 · published 2026-08-31 · Rouschev, Tsvetan (0009-0000-7312-9778)
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  • 22230923 · concept 22018433 · published 2026-09-01 · Rouschev, Tsvetan (0009-0000-7312-9778)
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  • 22234459 · concept 22018433 · published 2026-09-01 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22234547 · concept 22178675 · published 2026-08-30 · Rouschev, Tsvetan (0009-0000-7312-9778)
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  • 22235236 · concept 22178675 · published 2026-08-30 · Rouschev, Tsvetan (0009-0000-7312-9778)
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  • 22236200 · concept 22178675 · published 2026-08-30 · Rouschev, Tsvetan (0009-0000-7312-9778)
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  • 22237585 · concept 22178675 · published 2026-08-30 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22237699 · concept 22237698 · published 2026-09-01 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22238324 · concept 22178675 · published 2026-09-01 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22239152 · concept 22178675 · published 2026-09-01 · Rouschev, Tsvetan (0009-0000-7312-9778)
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  • 22275803 · concept 22178675 · published 2026-09-03 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22277570 · concept 22018433 · published 2026-09-03 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22277705 · concept 22018433 · published 2026-09-03 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22286537 · concept 22178675 · published 2026-09-03 · Rouschev, Tsvetan (0009-0000-7312-9778)
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  • 22288360 · concept 22237698 · published 2026-09-04 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22308239 · concept 22018433 · published 2026-09-04 · Rouschev, Tsvetan (0009-0000-7312-9778)
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  • 22738314 · concept 22018433 · published 2026-09-14 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22738451 · concept 22018433 · published 2026-09-14 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22738624 · concept 22018433 · published 2026-09-14 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22739348 · concept 22018433 · published 2026-09-14 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22739416 · concept 22018433 · published 2026-09-14 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22741148 · concept 22018433 · published 2026-09-14 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22741470 · concept 22018433 · published 2026-09-14 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22750137 · concept 22018433 · published 2026-09-14 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22751159 · concept 22018433 · published 2026-09-14 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22751234 · concept 22018433 · published 2026-09-14 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22752227 · concept 22018433 · published 2026-09-14 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22753265 · concept 22018433 · published 2026-09-14 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22753686 · concept 22018433 · published 2026-09-14 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22755815 · concept 22018433 · published 2026-09-14 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22756592 · concept 22018433 · published 2026-09-14 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22756638 · concept 22018433 · published 2026-09-14 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22756742 · concept 22018433 · published 2026-09-14 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22756866 · concept 22018433 · published 2026-09-14 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22757077 · concept 22018433 · published 2026-09-14 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22757210 · concept 22018433 · published 2026-09-14 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22757287 · concept 22018433 · published 2026-09-14 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22758044 · concept 22018433 · published 2026-09-14 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22758226 · concept 22018433 · published 2026-09-14 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22761956 · concept 22018433 · published 2026-09-15 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22762901 · concept 22018433 · published 2026-09-15 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22763064 · concept 22018433 · published 2026-09-15 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22763340 · concept 22018433 · published 2026-09-15 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22763428 · concept 22018433 · published 2026-09-15 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22763557 · concept 22018433 · published 2026-09-15 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22763657 · concept 22018433 · published 2026-09-15 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22763714 · concept 22018433 · published 2026-09-15 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22765098 · concept 22018433 · published 2026-09-15 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22765286 · concept 22018433 · published 2026-09-15 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22765664 · concept 22018433 · published 2026-09-15 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22765847 · concept 22018433 · published 2026-09-15 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22766228 · concept 22018433 · published 2026-09-15 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22767183 · concept 22018433 · published 2026-09-15 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22767519 · concept 22018433 · published 2026-09-15 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22770012 · concept 22018433 · published 2026-09-15 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22831109 · concept 22237698 · published 2026-09-18 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22834231 · concept 22018433 · published 2026-09-18 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22834377 · concept 22018433 · published 2026-09-18 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22834746 · concept 22018433 · published 2026-09-18 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22835307 · concept 22018433 · published 2026-09-18 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22836230 · concept 22018433 · published 2026-09-18 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22836387 · concept 22018433 · published 2026-09-18 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22836462 · concept 22018433 · published 2026-09-18 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22836549 · concept 22018433 · published 2026-09-18 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22836826 · concept 22018433 · published 2026-09-18 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22850514 · concept 22018433 · published 2026-09-20 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22854613 · concept 22018433 · published 2026-09-20 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22856016 · concept 22018433 · published 2026-09-20 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22858061 · concept 22018433 · published 2026-09-20 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22858237 · concept 22018433 · published 2026-09-20 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22858240 · concept 22018433 · published 2026-09-20 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22858271 · concept 22018433 · published 2026-09-20 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22858663 · concept 22018433 · published 2026-09-20 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22858806 · concept 22018433 · published 2026-09-20 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22858846 · concept 22018433 · published 2026-09-20 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22860794 · concept 22018433 · published 2026-09-20 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22863511 · concept 22018433 · published 2026-09-20 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22874413 · concept 22018433 · published 2026-09-21 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22875750 · concept 22018433 · published 2026-09-21 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22895141 · concept 21781602 · published 2026-09-22 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22933794 · concept 21781602 · published 2026-09-24 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22934737 · concept 22934736 · published 2026-09-24 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 22934883 · concept 22934736 · published 2026-09-24 · Rouschev, Tsvetan (0009-0000-7312-9778)
  • 21781603 · concept 21781602 · published 2026-08-04 · Rouschev, Tsvetan
  • 21819217 · concept 21787143 · published 2026-08-04 · Rouschev, Tsvetan
  • 22256707 · concept 21781602 · published 2026-08-04 · Rouschev, Tsvetan

All 1127 commits in this repository are authored by Tsvetan Rouschev (1127). Measured 2026-09-25 against the registry that issued the DOIs, re-checkable with npm run provenance; receipt e3ce5e9c-0e5e….

Captain's message:https://uuidna.com/captain/message — free on the free sailing angle; prize earning in waves — contribute 2 to earn up to 64 per wave, keep the rest (the two coins per commercial use; the seal is 128 bits = 64 two-bit fold-verifications, O(log N)). Contribute: · why ↗computed: self-seal = 1 · reflection involutive · CC BY-NC-ND 4.0License: CC BY-NC-ND 4.0 — free for non-commercial use (attribution Tsvetan Rouschev); commercial = the two coins (110 − 108 = 2 = −χ genus-2) · ceccec@psg.bgLicensing formula: free for public interest and independent research, unless commercial · commercial = the measured bits saved (O(N) − O(1)), the two coins (2 = 110 − 108 = −χ genus-2) the conserved invariant · verified green by receipts · integrity, not truthThis referrer perspective: fd66fe01-241f-81b6-9ae9-7206a4319358Public URLs (content-addressed):https://uuidna.org 8ef35f1f-38f3…https://uuidna.com 58cfb4c9-e262…https://ceccec.psg.bg/millennium-solutions/ e99f52ee-1cc6…Support development: https://revolut.me/ceccec
Captain's message:https://uuidna.com/captain/message — free on the free sailing angle; prize earning in waves — contribute 2 to earn up to 64 per wave, keep the rest (the two coins per commercial use; the seal is 128 bits = 64 two-bit fold-verifications, O(log N)). Contribute: · why ↗computed: self-seal = 1 · reflection involutive · CC BY-NC-ND 4.0License: CC BY-NC-ND 4.0 — free for non-commercial use (attribution Tsvetan Rouschev); commercial = the two coins (110 − 108 = 2 = −χ genus-2) · ceccec@psg.bgLicensing formula: free for public interest and independent research, unless commercial · commercial = the measured bits saved (O(N) − O(1)), the two coins (2 = 110 − 108 = −χ genus-2) the conserved invariant · verified green by receipts · integrity, not truthThis referrer perspective: fd66fe01-241f-81b6-9ae9-7206a4319358Public URLs (content-addressed):https://uuidna.org 8ef35f1f-38f3…https://uuidna.com 58cfb4c9-e262…https://ceccec.psg.bg/millennium-solutions/ e99f52ee-1cc6…Support development: https://revolut.me/ceccec