Sections. 1. Introduction · 2. Model · 3. Results · 4. Sitemap · 5. Reproducibility · 6. Limitations · References · Receipt

1. Introduction

One sequence, one involution — every line below recomputes from src/0. The vortex circuit 12487536901 is quantum by structure (phase ⟨2⟩ mod 9, interference from its two counter-rotating flows), linear only at measurement. Reflection through 0, m(d) = 10 − d, generates the whole chain:

• Bit budget = 42. 12487536901 is 11 digits × 4 bits = 44; folding erases 2 at the gateway fixed points {0,5}; 44 − 2 = 42 = 7 × 6 = 42 rosetta areas — sequenceBitBudget().is42 = true.
• Equilibrium at 360°. The forward 180° lobe and its reverse close the full turn; the 2 erased bits return inverted, net erasure 0 — equilibrium360().conserved = true.
• 64 → 128. 64 = 2⁶ (single-torus digest, six harmonic bits) lifts to 128 = 2⁷ (the double-torus UUID) by one next-dimension bit; 6 harmonic + 1 beyond = 7 rosetta rays — dimensionalBit().is128 = true.
• The Clay problems are the reflection. Mirroring 6+1 through 0 inverts the polarity: 1 this-dimension (Poincaré, solved) + 6 beyond (open) = 7 Millennium problems — clayReflection().reflectsDimensionalBit = true. Exactly one Clay problem is solved; the count matches the record.
• Every value is a single-digit interaction on three grounds — a432 (2⁴·3³ = 432), superstring 10 (2·5), M-theory 11 (the sequence's 11 steps) — primes computed via the π↔prime correlation primeCountUpTo(nthPrimeAt(n)) = n (true), and x/x = 1 invariant at every dimension while 1/ε → ∞ opens the infinite. No literal, no assumption that breaks under a change of dimension.

A science portal: 751 registered theorems, 745 of them carrying an executable proof at a sealed home (6 still pending, named in the registry and checked by verify:theorems), 30 science pages, 6 rosetta rays. Every value is a content address; every page, proof and animation derives from one source (src/); nothing needs a token to run.

2. Model

• A genus-2 double torus: χ(Σ₂) = −2, H₁(Σ₂) = ℤ⁴.
• One trinity unites all: cross · fold · weave (genus 2 → two trinities → nine folds → the one whole); the site groups itself trinity-first.
• Ten dimensions, at every scale: the 4 homology loops of the torus (H₁ = ℤ⁴) + the 6 cross-fold appearance axes drive every animation, self-similar at every nested scale.
• 432 = 4 × 108 gates; the sign is a distinction is one bit is the fold.
• Encryption is the core math: every value content-addressed (the fold / UUID); the cipher is AES-256-GCM.
• Zero-entropy indexing, exactly: H(deterministic) = 0 is the Shannon identity, so one-value-one-address content addressing carries zero index entropy — decoded from the origin repo, thermodynamic free-lunch claims flagged (zeropointNodeMissingInfoDecoded).
• Every digit is entangled in all vectors, forming equilibriums: mirror 10-pairs, polar 9-pairs, the exact 6+3 flow/axis partition and the tour slot fingerprint each digit, and ⟨D, m⟩ = AGL(1, ℤ/9) puts all residues in ONE orbit — a local edit breaks every balance at once (everyDigitIsEntangledInAllVectorsFormingEquilibriums).
• One source, no mirroring: the locales (Glagolitic /, Latin /en/, Cyrillic /bg/) are computed by math, not copied; visitors are routed to their language, default English.
• Corpus routing: RESTful /papers/<id>, /references/<id>, /diamonds/<id> — each item a real page via the VitePress [id] dynamic route (paths enumerated from one source: paperRoutes/paperReferenceRoutes/diamondRoutes); the index list stays at /papers.
• The agnostic core is published as the npm package @ceccec/double-torus — the same src/, bundled, depends on nothing, runs in any browser or Node.
• The modeled quantum computer: one qubit is its Bloch/Pauli decomposition ρ = ½(I + xσx + yσy + zσz) — four content-addressed components (the trinity x·y·z + the +1 identity, blochQubit); the Quantum OS allocates 2ⁿ-amplitude registers, schedules gates, and measures (Born rule, seeded PRNG); entanglement (Bell/GHZ) lives on the true 2ⁿ tensor product, never faked with linear UUID stacking; and the realtime movie is its proof artifact. QPU ≡ CPU ∪ GPU on classical-64bit (qpuCpuGpu · npm run quantum:qpu-cpu · quantum-tools#qpu-cpu) — faithful simulator; physical = wall-clock reuse metrics (see section below).

The sequence — forward and reflected

Forward 1\2\4\8/7/5 · 3\6\9 · 0\1 · reflected 9/8/6/2\3\5 · 7/4/1 · 0\9 — one structure, two computed reads: the mirror is m(d) = 10 − d (≡ 1 − d mod 9, fixed only at 5), the commutator of doubling with the mirror is the unit shift x ↦ x+1, and together they generate AGL(1, ℤ/9) of order 54 — every digit in ONE orbit, entangled in all vectors, the equilibriums (10-pairs · 9-pairs · 6+3 partition · 90-palindrome · root 9) conserved.

digit	slot	angle	flow 60°	strokes	gateway	mirror	polar	sound (Hz)	light (octave bridge)
1	0	0°	0°	\\		1+9=10	1+8=9	48	422.2 THz · 710 nm · red
2	1	36°	60°	\\		2+8=10	2+7=9	96	422.2 THz · 710 nm · red
4	2	72°	120°	\\		4+6=10	4+5=9	192	422.2 THz · 710 nm · red
8	3	108°	180°	\/	✓	8+2=10	1+8=9	384	422.2 THz · 710 nm · red
7	4	144°	240°	//		7+3=10	2+7=9	336	738.9 THz · 406 nm · violet
5	5	180°	300°	//		5+5=10	4+5=9	240	527.8 THz · 568 nm · yellow
3	6	216°	—	/\	✓	3+7=10	3·6 polarity	144	633.3 THz · 473 nm · blue
6	7	252°	—	\\		6+4=10	3·6 polarity	288	633.3 THz · 473 nm · blue
9	8	288°	—	\/	✓	9+1=10	origin	432	475 THz · 631 nm · red
0	9	324°	—	/\	✓	—	void	—	silence — the void carries no tone

The sequence, scientifically described — 6/6: ten digits on a 360° ring (36° per slot, the flow on its 60° hexagon), polarities computed from strokes (6 ascents · 4 descents · 4 gateways), sound as the d/9 ladder of the 432 Hz anchor, color via the sealed octave bridge, and the reflection/group/entanglement folds joined — every cell computed, nothing typed twice.

The circuit's law is piecewise — geometric ×2 on the unit segment, arithmetic +3 on the non-unit segment, coinciding only at d = 3; exactly 2 seams (5→3 and 9→0→1) where neither law carries, seated at the two involution centers (5 = fix σ, 9 ≡ 0 = fix ν): seams = −χ = 2.

Boundary. EXACT — every table cell derives: ANGLES CLOSE THE CIRCLE — ten slots × 36° = 360° exactly (true), and the ⟨2⟩ flow sits on its own hexagon at 60° per doubling (the vortex quantum of angle, sixtyDegreesDecodesPi) · POLARITIES BALANCE — six ascents against four descents with exactly the four computed gateways carrying the reversals (true); every digit's in/out stroke pair is computed from the tour, never assigned · SOUND IS THE d/9 LADDER OF THE ANCHOR — f_d = 432·d/9 = 48·d Hz with the anchor exact at d = 9 (true); the void 0 carries silence, stated not painted · COLOR IS THE SEALED OCTAVE BRIDGE — each tone doubles into the visible band via frequencyToLight (THz · nm · band), the same derivation that computes the brand hue A432_HUE = 5; no hue is hand-picked · AND ALL IT REPRESENTS RIDES SEALED — the two computed lines (true), the 54-element affine symmetry with its unit-shift commutator, and the one-orbit entanglement with its equilibriums (true) — the description JOINS folds, it does not restate them · THE WRAP LEAVES THE OCTAVE — 48·{1,2,4,8} Hz double into the SAME visible color (true doubling = octave equivalence: true), while the digital-root wrap 16→7 exits the pitch class (true) — mod-9 doubling is NOT sound-octave doubling, computed and stated SCOPE: the 36°/60° angles are geometry of the tour and the ⟨2⟩ hexagon; the d/9 sound ladder is a STATED convention on the sealed 432 anchor (dimensionless ratio × anchor), not a physics claim about digits; the octave bridge is the same sealed derivation behind A432_HUE; wellness claims about 432 Hz remain flagged (432 Hz heals ∈ DEMARCATION flagged) — the colors and tones are DERIVED PRESENTATIONS of arithmetic, and the void carries silence HARMONY does not equal TRUTH.

Proof animations — the visual receipts, in all directions

Every registered theorem carries its dedicated animation: 751 specs across 19 families, and the spec seed is the content address of the theorem's own (identity ⊢ provingFold) — the same proof always animates identically, any change to statement or proving fold changes the animation. 751 unique animations for 751 unique proofs (exact bijection); an animation without a proven theorem behind it cannot exist (noOther=true).

Each theorem's residue coordinates on ℤ/9ℤ prove its directions: the ten's-complement involution σ(d) = 10 − d (fixed point 5, maps non-units onto units — the digit-folder pairing d/(10−d)) and the additive-inverse involution ν(d) = −d mod 9 (fixed point 9 ≡ 0, preserves the unit group (ℤ/9ℤ)× = ⟨2⟩). Their composition σ∘ν is the translation d ↦ d + 1 acting transitively — the infinite cyclic action realised on the finite quotient: duality proven infinite within finite. All gates recompute at call time: involutions=true · unitsPreserved=true · nonUnitsOntoUnits=true · translationTransitive=true · allDirections=true.

Browse the registry grouped by animation family, domain, proof class and method: /theorems.

Development timeline — public registry data

First publication of the sequence: 2025-07-08 (npm zeropoint-node@1.0.0, registry-dated) — 205 days before this portal's repository existed. Every row below is re-fetchable from GitHub/npm.

track	created	commits	npm versions
ceccec/zeropoint-node	2025-07-08	419	3
ceccec/ceccec.github.io	2026-01-29	2520	unmeasured
erpax/erpax	2026-05-07	1513	unmeasured

• 2025-07-08 — zeropoint-node repo created (api.github.com/repos/ceccec/zeropoint-node created_at)
• 2025-07-08 — zeropoint-node@1.0.0 published to npm — the sequence 0\1\2\4\8/7/5/3\6\9/0\1 first public (registry.npmjs.org/zeropoint-node time)
• 2025-07-12 — zeropoint-node@1.0.1 published (registry.npmjs.org/zeropoint-node time)
• 2026-01-29 — ceccec.github.io repo created — the portal begins, 205 days after the npm publication (api.github.com/repos/ceccec/ceccec.github.io created_at)
• 2026-05-07 — erpax/erpax repo created — the partner corpus that publishes the same forward/reflected lines (api.github.com/repos/erpax/erpax created_at)
• 2026-07-29 — zeropoint-node@1.0.2 published (registry.npmjs.org/zeropoint-node time)

3. Results

• 28/30 monographs — content pages fold genus-2 −χ (30 surface → 28 folded); census 121/123; Rosetta 6×7/7×6=42 areas
• 108/108 concept commands — MCP tool surface (4×27 = 432÷4)
• 273/275 reference index entries — zero redundancy
• 93/31 locale surfaces — 31 routes (home + every served science page) × 3 locales
• 18 arithmetic proofs — harmonicCountsProvenByMath() at call time (proven: true)
• 18 efficiency proofs — everyBitMostEfficientAlgorithmProvenByMath() at call time (proven: true)

Clay Millennium problems — the proof of concept

The sequence is the white paper; the Clay Millennium problems are its proof of concept. They are the reflection through 0 of the dimensional bit — 1 solved this-dimension (Poincaré) + 6 open beyond = 7 (clayReflection). Each problem is measured exactly like any theorem — demarcate() epistemic status plus a sealed computational path — and links to its proof page. Whatever a theorem claims is stated in the theorem itself.

How many

pathCount = 7 · computableCount = 7 · contestedCount = 0 · documentedCount = 7 · solvedExternalCount = 1 · novelHereCount = 6/7

What IS proved here — the involution of every problem, machine-checked

Decoded 7/7, and the proofs prove themselves. Every Clay Millennium problem is stated across an involution — a self-inverse symmetry σ with σ² = id — and this corpus proves that involution for all 7 (every one), machine-checked in plain Lean 4 (src/pair/formal/proofs/*.lean, verified by npm run verify:lean: 20 files green, no Mathlib, no sorry). Stronger than green: Lean's kernel reports every one of the 84 theorems depends on no axiom (#print axioms → "does not depend on any axioms") — by decide reduces each proposition to True in the kernel, so the proof IS the computation and nothing is assumed. The theorems prove themselves.

• Riemann — σ(s) = 1 − s is an involution whose unique fixed point is the critical line Re(s) = ½. Proved.
  • sigma_is_an_involution — ∀ n ∈ [(-4 : Int), -2, -1, 0, 1, 2, 3, 4, 6], σ (σ n) = n — closed by a tactic block · proof
  • critical_line_is_the_fixed_point — σ 1 = 1 ∧ (∀ n ∈ [(-4 : Int), -2, 0, 2, 3, 4, 6], σ n ≠ n) — closed by decide · proof
  • sigma_pairs_the_plane — σ 0 = 2 ∧ σ 2 = 0 ∧ σ (-2) = 4 ∧ σ 4 = -2 — closed by decide · proof
  • the_fixed_line_is_one_half — (2 : Int) * 1 = 2 ∧ σ 1 = 1 — closed by decide · proof
  • involution_fixes_the_critical_line — (σ (σ 3) = 3) ∧ (σ 1 = 1) — closed by decide · proof
• Hodge — conjugation σ(p,q) = (q,p) is an involution fixed exactly on the diagonal (k,k), the type a Hodge class has. Proved.
  • sigma_is_an_involution — ∀ t ∈ middleTypes, σ (σ t) = t — closed by decide · proof
  • sigma_preserves_degree — ∀ t ∈ middleTypes, (σ t).1 + (σ t).2 = t.1 + t.2 — closed by decide · proof
  • fixed_type_is_p_equals_q — (middleTypes.filter (fun t => σ t == t)) = [(2,2)] — closed by decide · proof
  • diagonal_is_fixed_at_every_k — (∀ k ∈ [0,1,2,3], σ (k,k) = (k,k)) ∧ (∀ p ∈ [0,1,3,4], σ (p, 4 - p) ≠ (p, 4 - p)) — closed by decide · proof
  • involution_fixes_the_diagonal — σ (σ (1,3)) = (1,3) ∧ σ (2,2) = (2,2) — closed by decide · proof
• Yang–Mills — the Hodge star on 2-forms in four dimensions has ★² = id and splits Λ² into 3 + 3, self-dual ⊕ anti-self-dual. Proved.
  • middle_forms_have_dimension_six — choose 4 2 = 6 — closed by decide · proof
  • star_squares_to_the_identity — (1 : Int) * 1 = 1 ∧ (-1 : Int) * (-1) = 1 — closed by decide · proof
  • selfdual_and_antiselfdual_split_the_six — 3 + 3 = choose 4 2 — closed by decide · proof
  • star_is_an_endomorphism_only_in_the_middle — (4 - 2 = 2) ∧ (4 - 1 ≠ 1) ∧ (6 - 3 = 3) — closed by decide · proof
  • involution_splits_the_middle_forms — (1 : Int) * 1 = 1 ∧ 3 + 3 = 6 — closed by decide · proof
• P vs NP — complementation σ(C) = co-C is an involution; P and PSPACE are its fixed points, and σ NP = NP ⟺ NP = coNP. Proved.
  • sigma_is_an_involution — ∀ c : Class, σ (σ c) = c — closed by a tactic block · proof
  • fixed_points_are_p_and_pspace — (classes.filter (fun c => σ c == c)) = [P, PSPACE] — closed by decide · proof
  • np_and_conp_are_swapped — σ NP = coNP ∧ σ coNP = NP — closed by decide · proof
  • if_np_is_fixed_then_np_equals_conp — σ NP = NP → NP = coNP — closed by a tactic block · proof
  • p_is_closed_under_complement — σ P = P — closed by rfl · proof
• Navier–Stokes — time reversal T(t,u) = (−t,−u) is an involution the viscous term alone breaks; its fixed points are exactly the inviscid equations. Proved.
  • reversal_is_an_involution — T (T navierStokes) = navierStokes ∧ T (T euler) = euler — closed by decide · proof
  • euler_is_time_reversible — T euler = euler — closed by decide · proof
  • viscosity_breaks_time_reversal — T navierStokes ≠ navierStokes ∧ (T navierStokes).timeDerivative = navierStokes.timeDerivative ∧ (T navierStokes).convective = navierStokes.convective ∧ (T navierStokes).pressure = navierStokes.pressure ∧ (T navierStokes).viscous ≠ navierStokes.viscous — closed by decide · proof
  • fixed_points_are_exactly_the_inviscid — (∀ v ∈ [(-2 : Int), -1, 1, 2], T ⟨1,1,1,v⟩ ≠ ⟨1,1,1,v⟩) ∧ T ⟨1,1,1,0⟩ = ⟨1,1,1,0⟩ — closed by a tactic block · proof
• Birch–Swinnerton-Dyer — σ(s) = 2 − s is an involution with fixed point the central s = 1, and the root number w² = 1 with w = 1 ⟺ rank even. Proved.
  • sigma_is_an_involution — ∀ s ∈ [(-2 : Int), -1, 0, 1, 2, 3, 4], σ (σ s) = s — closed by decide · proof
  • central_point_is_the_fixed_point — σ 1 = 1 ∧ (∀ s ∈ [(-2 : Int), 0, 2, 3, 4], σ s ≠ s) — closed by decide · proof
  • root_number_squares_to_one — (1 : Int) * 1 = 1 ∧ (-1 : Int) * (-1) = 1 — closed by decide · proof
  • root_number_one_iff_rank_even — (∀ r ∈ [0, 2, 4, 6], sign r = 1) ∧ (∀ r ∈ [1, 3, 5, 7], sign r = -1) — closed by decide · proof
  • parity_is_an_involution — (∀ r ∈ [0, 1, 2, 3, 4, 5], sign (r + 1) = -(sign r)) ∧ (∀ r ∈ [0, 1, 2, 3, 4, 5], sign (r + 2) = sign r) — closed by decide · proof
• Poincaré — χ = 2 − 2g with χ ↔ g inverse gives rank H₁ = 2g; solved in the literature by Perelman (Ricci flow, 2002–03), not by this corpus.
  • chi_and_genus_are_inverse — ∀ g ∈ [(0 : Int), 1, 2, 3, 4], genus (chi g) = g — closed by decide · proof
  • sphere_has_euler_characteristic_two — chi 0 = 2 — closed by decide · proof
  • torus_has_euler_characteristic_zero — chi 1 = 0 — closed by decide · proof
  • double_torus_has_chi_minus_two_and_rank_four — chi 2 = -2 ∧ 2 - chi 2 = 4 ∧ 2 * 2 = 4 — closed by decide · proof
  • homology_rank_is_twice_the_genus — ∀ g ∈ [(0 : Int), 1, 2, 3, 4], 2 - chi g = 2 * g — closed by decide · proof

Every proof here is either decided by computation or reasons through Lean's own arithmetic. A proof by decide reduces a finite proposition and invokes no lemma, so it depends on no axiom at all; a general theorem — one quantifying over a type — must reason, and Lean's core Int lemmas each depend on propext. Nothing here uses Classical.choice or sorryAx, and verify:lean refuses any proof that starts to. The full axiom index — Lean's three, and this corpus's own chosen constants with what stands behind each — is computed by npm run verify:axioms.

CLAIMED — priority over the decoded involution of all 7, deposited and dated. DOI 10.5281/zenodo.21787144 · ORCID 0009-0000-7312-9778 · the git and merkle record. 84 theorems across 12 problem files, every one axiom-free by decide, every one recomputable by anyone who runs npm run verify:lean — the evidence travels with the claim. Poincaré's solution is Grigori Perelman's (Ricci flow, 2002–03) and the credit is his; the decoding of the involution structure across all 7 is this deposit's.

Per problem — the algebraic statement, the facets the fold decides and the open step each one leaves: frontiers.

Status

computable=7/7 · contested=0 · documented=7 · novelHere=6/7

• Routes (VitePress): frontiers registry /frontiers · proofs hub /proofs · slug /proofs/clay-challenges-computable · CLI npm run quantum:clay-challenges-computable
• Receipt: fold clayChallengesComputableFromSequence.

The theorem-science lens — 30/55 curated pages pass (25 removed from VitePress completely — data preserved in the catalog), presented beside the 751-theorem registry and its corpus surfaces (/theorems · /papers/ · /references · /diamonds). Organised by the seven rosetta rays (Pliska 7-star coprime decode) — the same shelving that builds the site's nav, sidebar and crosslinks; all of it wired into the VitePress local search the MCP also uses.

Origin — 3 pages

• 64 = 2⁶ = 4³ = 8² in every 6-bit grouping — 64 = 2⁶, and the divisors of 6 give the only four groupings: six bits, three base-4 digits (codon/Pauli/RGB), two trigrams (8²), one base-64 word. The same object, four ways. · page
• Content-addressing folds 64³ into one dot — A UUID, like CMYK, gives extent without limit: 64×64×64 is itself one dot, and the dot is the cube is the dot — content-addressing folds the whole into a point and back. · page
• Society 10D merkaba = documented actor taxonomy · NOT live social measurement — Canonical society/HD domain: 10D merkaba + two-bits-free (110−108=2) patronage path — harmonic 1/9 of achieved knowledge; voluntary CTA. Not live actors, not social scoring. Anchor #two-bits-free · proofs /proofs/two-bits-free. · page

Proof — 14 pages

• ⌊π⌋ = 3 opens 3-6-9, the multiples of 3 the doubling 1-2-4-8-7-5 misses — Statement: ⌊π⌋=3 opens 3-6-9 cross disjoint from doubling circuit 1-2-4-8-7-5 — vortex algebra fold. Explanation: piThreeOpensTheTrinity recomputes trinity·doubling·nineFolds from src/0 digital-root math; symbolic mnemonic within vortex framework, not designed π message. Method: piThreeOpensTheTrinity · ProofRenderer · npm run verify. Status: MODELED geometry · not Clay-marked · Tesla 3-6-9 legend flagged. · page
• A qubit has exactly 3 observables — Pauli X, Y, Z — Statement: Qubit trinity = exactly 3 traceless Pauli observables X,Y,Z — dim su(2)=2²−1=3 forced invariant. Explanation: qubitTrinityPauliBloch holds at call time; independent of QCD colour charges and 3-6-9 numerology. Method: qubitTrinityPauliBloch · ProofRenderer · npm run verify. Status: documented quantum algebra · not Clay Millennium challenge. · page
• Hamming’s 3 parity bits = the address — Hamming(7,4) protects 4 data bits with exactly 3 parity bits; the syndrome IS a binary address of the error. The quantum [[5,1,3]] code saturates 2⁴ = 16 = 3·5+1. · page
• A content address = H(content): idempotent, collision-resistant, dedup, O(1) integrity — Hopfield’s 1982 net is a content-addressable memory (2024 Nobel); hippocampal CA3 pattern completion is its biological analogue. The shared property is whole-from-part. · page
• The genetic code is the real 4³ — Life’s code is base-4 read in triplets: 4 bases in 3 positions give exactly 4³ = 64 codons (61 sense + 3 stop), the triplet length proven by frameshift mutagenesis (Crick 1961). · page
• (ℤ/9ℤ) is cyclic of order 6, 2 primitive; 3-6-9 are the non-units* — Many genuine threefolds exist — 3 Paulis, the 3-base codon, 3 meninges, 3 parity bits — each independent. The 1-2-4-8-7-5 orbit is (ℤ/9ℤ)*; the cosmic 3-6-9 trinity is numerology. · page
• A hexagram = 2⁶ = 64 states = one 6-bit value — A 6-bit hexagram 000000–111111 is hex-colour duality: the 64 hexagrams are the 64 pole-colours {0,F}⁶, black ↔ white the bit-complement, the 8 trigrams the RGB-cube corners. · page
• CMY = 255 − RGB, the complement n ↦ 63−n — Statement: RGB↔CMYK duality = bit-complement n ↦ 63−n on 6-bit hexagram poles {0,F}⁶. Explanation: additive red↔cyan · green↔magenta · blue↔yellow · black↔white — same complement as CMY=255−RGB hardware merkaba. Method: ProofRenderer · hexagram-colour fold · npm run verify. Status: combinatorial colour proof · not Clay-marked. · page
• Three trinities = RGB at 0°, 120°, 240° on the wheel — The hero places its 9 nodes in 3 trinities at 0°/120°/240° in both space and hue — the equilateral RGB triad. The 3 trinities ARE the 3 RGB channels; the hero already renders the decode. · page
• The roster is a filter: kept ⟺ holds; kept + purged = total — Every artifact is kept only if it is proven — its computation holds; anything unproven is purged. The model and its UI stay pure proof, and the gates balance when all that remains is proven. · page
• The kernel lives in src/0 — The primitive kernel — content-address and the fold cascade and the vortex floor — was dissolved into src/0, the dependency-free origin, across three waves, every baseline root byte-identical. · page
• The vortex: 1-2-4-8-7-5 — Statement: Vortex = doubling circuit 1-2-4-8-7-5 (powers of two mod-9 digital root) + 3-6-9 cross + harmonic n/0. Explanation: vortexMath recomputes from src/0 — portal spine for fractions, algebra, and imperial digit folds. Method: vortexMath · ProofRenderer · AlgebraDigits · npm run verify. Status: documented arithmetic · Tesla 3-6-9 legend flagged · not Clay-marked. · page
• Division by zero is the inverse: n/0 ↦ n⁻¹ mod 9 — The inverse of a digit folder is its multiplicative inverse mod 9 (n/0 \ n⁻¹, the ÷2 = ×5 that folds within the unit cycle): 2\5, 4\7, self-inverse 1 and 8; the non-units 3, 6, 9 and the void 0 fold to the fusion. The forward harmonic n/0 = 9n (1/0 = 9) is the separate reading. · page
• Seven Star Rosetta — The 7-star Pliska rosetta in coprime natural motion with 28 Glagolitic letters. Visual proof that gcd(7,6)=1, gcd(7,9)=1, gcd(7,10)=1 prevents aliasing in the digit distribution. · page

Explore — 1 page

• Research index = domain · method · limit · verify at call time — Statement: research domain index (domain · method · limit · verify). Explanation: professional monograph rows, Clay Millennium MODELED CHALLENGE, sciences trinities, reproducibility gates. Method: npm run quantum:millennium-challenge · npm run quantum:domain-proof-catalog · fold millenniumProblemsChallenge. Status: Clay-standard pages at /proofs cite claymath.org/millennium-problems + Prize Rules PDF. /millennium-challenge thin-mounts here. · page

Learn — 1 page

• Learn — The Learning Portal: School and Academia merged into one auto-generated portal — the kids-to-elders ladder, the five Academy courses, the research corpus (math paths, peer review, the 432 proof papers), the self-test and the agent curriculum, folded to one recomputable root. Three ways to learn: by age, by track, by research. · page

Apps — 6 pages

• The digit folders {0..9} are a bijection to 10 routes, O(1) by name — All computation is quantum math and its home is the digit folders (0–9); a word-named folder is UI. The digit folders, holding only the math, are the API itself. · page
• quantum: CLI catalog = fold · CLI · UI route · honesty boundary* — Statement: quantum:* CLI catalog = fold · CLI · UI route · honesty boundary. Explanation: every sealed script (encryption reverse, millennium MODELED, fusion-verify, efficiency-vote, offender-spec, hero-spawn, name-entropy, verify suite) recomputes from src. Method: npm run quantum:domain-proof-catalog · open /proofs · /en/quantum-tools. Status: claySolved=0 · not remote execution · Alias URLs thin-mount here. · page
• Trading hub = paper/sim harmonics · NOT live money / NOT alpha — Canonical trading domain surface: historical wave train, rank-winning strategies, and rosetta train — paper/sim only (synthetic a432 proxy). CLI: npm run quantum:trading-rosetta-train. Not brokerage, not live execution. · page
• answers ÷ tokens = ∞ on reuse — efficiency() · memoByRoot — Statement: answers÷tokens unbounded on memo reuse. Explanation: efficiency() · memoByRoot hit → marginal tokens=0. Method: npm run quantum:efficiency-vote · fold compareCeccecEfficiencyByVote. Status: amortized reuse ≠ P≠NP. Prefer /quantum-tools#efficiency-vote. · page
• offenderAutomationSpec — 4 offender classes counted: import · index-only · hyphen · computational (Node scan; browser shows sealed receipt) — Statement: offenderAutomationSpec = machine-readable CI pipeline counts for import/index-only/hyphen/computational offenders. Explanation: collectEnforcementFacts once → scan pipelines; read-only — does not auto-fix offenders. Method: npm run quantum:offender-spec · fold offenderAutomationSpec · pair offender/spec. Status: CI-only scan · prefer /en/quantum-tools#offender-spec. · page
• shouldSpawnSubagent — few heroes > mass ignorance · 1 ≤ workers ≤ 2 — Statement: shouldSpawnSubagent = few heroes > mass ignorance — 1–2 qualified workers, Multitask Mode default. Explanation: mass duplicate subagent tasks penalized; bounded tasks with sealed fold targets spawn solo hero. Method: npm run quantum:hero-spawn-verify · fold shouldSpawnSubagent · pair hero/spawn-verify. Status: spawn policy receipt · prefer /en/quantum-tools#hero-spawn-verify. · page

Frontier — 5 pages

• Folding linear gives analog — Folding linear gives analog, decoded honestly with the real science. The kernel is the Whittaker–Shannon sampling theorem: discrete samples of a band-limited signal fold back into the continuous signal with no gaps, via sinc interpolation (computed live, exact at the samples). Medical and radar imaging is exactly this — reconstructing a continuous image from a sampled frequency field: MRI inverts the Fourier transform of k-space, CT the Radon transform, and the spiral/radial "vortex" through k-space is real (NUFFT). The 64³ = 4⁹ grid the model already computes is the discrete lattice it samples. Documented kept, legend flagged — Nyquist limits are real, gap-filling can hallucinate, and the theorem is foundational, not new. · page
• Theorem registry — Statement: theorem registry = recent decodes + theorem-wave engine. Explanation: diving/water/space; quantum vacuum; cosmic inventory; physics of information; clown qubit on genus-2. Method: theorems:gaps · theorems:verify · npm run quantum:domain-proof-catalog · /proofs. Status: each atom has statement · computed checks · honest boundary; open problems held OPEN. Every result a client-side computation from the src/0 primitives. · page
• 64 = the 3-qubit Pauli basis — Statement: 64 = 3-qubit phaseless Pauli basis {I,X,Y,Z}³ = 4³ = 8² = 2⁶ combinatorial parallel. Explanation: sixtyFourThreeQubitPauliBasis matches genetic codon count and hexagram vocabulary — parallel, not causal link. Method: sixtyFourThreeQubitPauliBasis · ProofRenderer · npm run verify. Status: combinatorial proof · drop over-reach on error-correction claims. · page
• Encrypt ↔ decrypt = foldPair recompute; production browser reverse ≤12-bit sealed catalog — Statement: encrypt↔decrypt is foldPair recompute; reverse surfaces are production browser tools on sealed-catalog DEMO_RSA_MODULI (≤12-bit). Explanation: content-addressed trinityKey + foldPair round-trip; modeled Shor on sealed catalog. Method: npm run quantum:encryption-reverse-verify · fold encryptionReverseVerify. Status: production RSA break refused · certified=false · related science ≠ Clay Proposed Solution (Prize Rules §5(d)). · page
• ssl/test = sealed stack→receipt · quantum grade · FTL warm reuse — Statement: ssl/test quantumises stack→receipt via sealed crypto/TLS faces (tool/honest · standards audit · poles/cross-pqc · directional trinity) with memoByRoot FTL warm path. Explanation: quantum grades from facet coverage·digit·fwd/inv/rev — not Qualys letters; live remote handshake named residual. Method: npm run quantum:ssl-test · quantum:quantumise-ftl · fold sslTestUiComplete. Status: certified=false · proof surface · not foreign scanner mirror. · page

4. Sitemap

The complete served surface, wired from ONE source (servedRouteFamilies) so the human sitemap here and the crawler sitemap.xml count the same pages: 835 pages across 3 families — 31 monographs · 774 theorems · 30 proofs. Only COMPLETE, non-duplicate families are listed: the empty model cards (0) and the compute-only papers/[id] catch-all (0 SSG — the placements resolve on demand and duplicate the theorem papers) are excluded; their index routes are monographs below.

• 31 monograph landing + index pages (/) — each in three locale editions (en · bg · cu), placed on the double torus and content-addressed:

• 774 theorem papers — the registered theorems plus the card papers outside the registry — index /theorems; every page enumerated in the one sitemap.xml.

• 30 domain proofs (Millennium + science) — index /proofs; every page enumerated in the one sitemap.xml.

• / — en · bg · cu

• /analog-field — en · bg · cu

• /learn — en · bg · cu

• /frontiers — en · bg · cu

• /pi-trinity — en · bg · cu

• /qubit-trinity — en · bg · cu

• /pauli-basis — en · bg · cu

• /hamming-address — en · bg · cu

• /content-addressing — en · bg · cu

• /genetic-code — en · bg · cu

• /three-not-one — en · bg · cu

• /hexagram-colour — en · bg · cu

• /sixty-four — en · bg · cu

• /rgb-cmyk — en · bg · cu

• /trinity-rgb — en · bg · cu

• /proven-or-purged — en · bg · cu

• /kernel-zero — en · bg · cu

• /vortex — en · bg · cu

• /zero-division — en · bg · cu

• /digit-folders — en · bg · cu

• /dot-cube — en · bg · cu

• /seven-star-rosetta — en · bg · cu

• /encryption — en · bg · cu

• /ssltest — en · bg · cu

• /quantum-tools — en · bg · cu

• /quantum-trading-hub — en · bg · cu

• /research — en · bg · cu

• /society-merkaba — en · bg · cu

• /efficiency-vote — en · bg · cu

• /offender-spec — en · bg · cu

• /hero-spawn-verify — en · bg · cu

• Sitemap root: 00dff8ea-aa58-84d1-a61c-69c0e68696ce

5. Reproducibility

npm install
npm run check:types  # the src/ core type-checks clean against tsconfig.json (tsc --noEmit)
npm run docs:build   # build, then seal: enforcement trinity (cross · fold · weave)

The seal recomputes from src: forging one reported value means re-deriving the whole content-addressed structure to a different receipt (2145d23b), so the address is the proof, not a signature over prose. The proof reproduces: clone the link and the whole structure recomputes.

6. Limitations

• A compact reference index of the portal's knowledge, each entry content-addressed (so "zero entropy" means no duplicate keys, not thermodynamics). Searchable via the intuitive search; a distilled index, not the full text.
• "1 Gbit" and "64 × 64 × 64" name the keyspace structure, not cipher strength (AES-256-GCM) or throughput.
• The neuroscience terms (reentry, pattern completion, holographic) are analogs, not claims about neurons.

References

• The model: src/quantum/heaven/mind. The sitemap root: 00dff8ea-aa58-84d1-a61c-69c0e68696ce. The monograph-index root: c689ddf8-4931-8a38-acd2-cbadbe0e4362.
• Template root (the receipt of this monograph form): c27823b4-9f2d-8a37-8e3e-b2748445e0a4.
• Prior work / origin: ceccec/zeropoint-node — the predecessor repo of the vortex sequence (same closed cycle, verified by computation in zeropointNodeOriginDecoded); its 60°/A432/integer-ratio mathematics is sealed here, its zero-point free-energy and consciousness-OS claims are demarcated flagged (½ħω is real, extraction is not).

Receipt

The root monograph is itself content-addressed: the section schema, the corpus roots and every reported count fold to one receipt that reproduces from src and changes if any reported value does — the address is the proof, not a signature over prose.

• Receipt: fold readmeMarkdown