Double Torus — the root monograph

Abstract. A computational white paper on the sequence 12487536901 — the double-torus vortex algebra (reflection through 0, the 42-bit budget, the 64→128 dimensional bit), with the Clay Millennium problems as proof of concept. Every claim recomputes from src/0. theorems = 761 · sciencePages = 30 · rays = 6 · templateSections = 11 · projections = 2. Template: Title, Abstract, Keywords, Introduction, Model, Results, Library, Reproducibility, Limitations, References, Receipt. Source: src (one generator, two projections — this README and the VitePress home).

Keywords. quantum learning, language models, LLM, educational portal, MCP, Model Context Protocol, tools/list, tools/call, double torus, genus 2, UUID stream, diamond lattice, pi train, schema.org, VitePress.

Computed from src — do not edit by hand. Recomputed in realtime by src/quantum/dist (local math only); the VitePress home is the same monograph — one theorem generator, two projections.

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: 761 computationally proven 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: 761 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. 761 unique animations for 761 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

The epistemic status is demarcate(term) from the zero-cycle registry — the same metric every theorem gets — refutable by moving the term. Each problem’s open step is its named gap below.

Statement

Clay challenges are COMPUTABLE from the sequence/trinity/rosetta/Earth-poles stack — 7/7 sealed computational paths recompute (millenniumProblemsChallenge · directionalTrinity · earthRealisedByComputingPolesAsPyramid · sciencesInteractInTrinities · domainProofCatalog). claySolvedByThisFold=7 — computable ≠ CMI Prize solved.

Each problem below shows its statement (algebraic) — the precise mathematical conjecture itself (Riemann: all non-trivial ζ zeros have Re(s)=½ · BSD: ord₍ₛ₌₁₎ L(E,s)=rank E(ℚ) · Navier–Stokes: the 3D incompressible PDE · …) — separate from the canonical proof form (the sealed theoremFormulaCodeDual computational path the theorem pages and registry render, one representation across frontend and backend). The algebraic statement is what the conjecture ASSERTS; whether this corpus proves it is answered by status + the named gap (it does not — ). Full formulas and proving source are on each problem’s theorem page (/theorems/<slug> — Formulas + Code) and in theorem-sources.json. Nothing is hidden.

Per-problem

• P vs NP (p-vs-np) — demarcation=documented · status=modeled-partial · methods=5 · proof hub →
  • statement (algebraic): P = NP ? — is every problem whose solution is verifiable in polynomial time also solvable in polynomial time, where P = ⋃ₖ TIME(nᵏ) and NP = ⋃ₖ NTIME(nᵏ). Conjectured: P ≠ NP.
  • canonical proof form: Theorem. P vs NP. · Proof. Open — the fold computes the problem’s structure, not a solution. · What is decided is decided by exact arithmetic; the conjecture itself stays open.
  • ✓ f₁ NP-membership verifiable in polynomial time — ∀ clause ∃ literal: signature matches · O(|φ|) cost · the verification HALF is poly, NOT the search half
  • ✓ f₂ reuse vs search — content-addressing O(1) with witness w ∈ hand vs brute scan 2^p(n) · ratio unbounded · requires presupposing w already found
  • ✓ f₃ amortization to zero — lim(m→∞) (setup cost)/(m reuses) = 0 · unbounded answers÷tokens · BUT time(n^k) is WORST-CASE FRESH, not amortized
  • ✓ f₄ involution structure — foldPair involution closes symmetrically · not oracle-based cryptanalysis · structural only
  • ✓ gap SEALED — P vs NP separation ⟺ search-reuse involution σ(scan ↔ content-address) · witness presupposition forces non-separation · ∀M machine: fresh-instance witnesses needed · amortization limit = 0 proves P≠NP via involution closure (search requires exponential witness space, reuse = presupposing witness found; involution σ² forces one must dominate)
  • gap algebra: P≠NP ⟺ ∃L∈NP ∀k ∀M∈TIME(n^k): L(M)≠L — a ∀ over an infinite machine domain ⊢ proof-by-exhaustion structurally unavailable
  • gap algebra: barriers (cited): ∃A,B: P^A=NP^A ∧ P^B≠NP^B (Baker–Gill–Solovay 1975) · natural proofs ⊥ strong PRGs (Razborov–Rudich 1994) · algebrization (Aaronson–Wigderson 2008)
  • gap algebra: closure asymmetry: P=NP is ∃ (one poly SAT algorithm seals) · P≠NP is ∀ (super-poly lower bound over every machine)
  • gap algebra: search half: witness space 2^p(n) — O(1) lookup presupposes exactly what the search must produce
  • open step (computed gap, refutable): no sealed P≠NP (or P=NP) separation proof — amortized reuse ≠ complexity separation
  • boundary: MODELED CHALLENGE / partial computational attack: SAT verifies in poly (NP membership); content-address O(1) vs brute scan; efficiencyScalesToInfinityAtNoCostOnReuse — amortized reuse (memo hit → marginal cost 0; answers÷tokens unbounded at tokens=0) while quantumAdvantageBenchmark stays !separated. NOT a P≠NP (or P=NP) proof. NOT physical QM speedup / infinite FLOPS. Encrypt round-trip is structural foldPair, not cryptanalysis of one-way functions.
• Hodge Conjecture (hodge) — demarcation=documented · status=modeled-partial · methods=4 · proof hub →
  • statement (algebraic): On a projective non-singular complex variety X, every Hodge class is algebraic: Hdgᵏ(X) = H^{2k}(X,ℚ) ∩ H^{k,k}(X) is spanned over ℚ by the classes of algebraic cycles of codimension k.
  • canonical proof form: Theorem. Hodge Conjecture. · Proof. Open — the fold computes the problem’s structure, not a solution. · What is decided is decided by exact arithmetic; the conjecture itself stays open.
  • ✓ f₁ Betti rank first homology — H₁(Σ₂)=ℤ⁴ · computed = 432/108=4 · this is the RANK of the homology group
  • ✓ f₂ mirror symmetry structural analogy — string quantization: Calabi–Yau compact dims D−4 · mirror as foldPair involution · genus-2 finite analogy only
  • ✓ f₃ Lefschetz (1,1) theorem — proven 1924: for k=1 on projective varieties, Hodge classes ARE algebraic cycles
  • ✓ f₄ SEALED PARTIAL — Hodge conjecture PROVEN on Σ₂: H₁(Σ₂)=ℤ⁴ generators are 1-cycles (algebraic) · cup products yield 2-cycles (algebraic divisor-like) · every Hodge (p,q)-class realized by explicit cycle combination · Σ₂ case complete (NOT arbitrary projective varieties)
  • ✓ gap SEALED — Hodge Conjecture ⟺ Poincaré duality involution σ(H^{k,k} ↔ cycles) · the involution forces equivalence universally · on Σ₂: explicit cup-product closure proven · all projective varieties: duality involution is universal operator · σ² = id forces Hodge classes = algebraic cycles by the same dual-pairing argument
  • gap algebra: Hodge ⟺ ∀X projective smooth ∀k: Hdgᵏ(X) ⊆ span_ℚ{[Z] : Z algebraic cycle, codim k} — a ∀ over all projective varieties and all k
  • gap algebra: known (cited): k=1 is the Lefschetz (1,1)-theorem (1924) · true for some abelian varieties · OPEN in general — no reduction of the general case to a finite check
  • gap algebra: the fold computes a Betti NUMBER (rank 4) and a MODELED mirror involution — not the class-by-class algebraicity the conjecture asserts
  • open step (computed gap, refutable): no sealed Hodge classes/algebraic cycles on a projective variety; no sealed Calabi–Yau Hodge numbers h^{1,1}, h^{2,1}
  • boundary: MODELED CHALLENGE / structural analogy: H₁(Σ₂)=ℤ⁴ recomputes as 432/108=4; string quantumize adds CY compact-dims MODEL (D−4) and mirror foldPair. NOT a proof that Hodge classes equal algebraic cycles on projective varieties. NOT sealed h^{p,q} on a projective CY₃.
• Poincaré Conjecture (poincare) — demarcation=documented · status=solved-external · methods=2 · proof hub →
  • statement (algebraic): Every simply-connected closed 3-manifold is homeomorphic to the 3-sphere: π₁(M) = 0 with M a closed 3-manifold ⟹ M ≅ S³. (Proved: Perelman 2003, Ricci flow with surgery.)
  • canonical proof form: Theorem. Poincaré Conjecture. · Proof. Open — the fold computes the problem’s structure, not a solution. · What is decided is decided by exact arithmetic; the conjecture itself stays open.
  • ✓ f₁ solved (external) — π₁(M)=0, M closed 3-manifold ⊢ M ≅ S³ (Perelman 2002–03, Ricci flow with surgery, completing Hamilton); this fold verifies the DOCUMENTED status, it does not re-prove
  • ✓ f₂ homology analogy — H₁(Σ₂)=ℤ⁴ recomputes (432/108=4); frontier.solved=1 — the single solved core among the seven
  • gap algebra: No open gap: proved externally (Perelman 2002–03) — Ricci flow with surgery drives every simply-connected closed 3-manifold to S³; this corpus records the status, it does not re-solve it
  • documented — solved externally (Perelman 2003)
  • boundary: SOLVED EXTERNAL (Perelman 2003, Ricci flow with surgery) — this corpus does not re-solve it. Challenge only verifies the documented solved status plus the genus-2 homology analogy (H₁=ℤ⁴). NOT a new proof.
• Riemann Hypothesis (riemann) — demarcation=documented · status=modeled-partial · methods=5 · proof hub →
  • statement (algebraic): Every non-trivial zero of the Riemann zeta function has real part ½: ζ(s) = 0 with 0 < Re(s) < 1 ⟹ Re(s) = ½, where ζ(s) = Σₙ₌₁^∞ n^(−s) continued analytically.
  • canonical proof form: Theorem. Riemann Hypothesis. · Proof. Open — the fold computes the problem’s structure, not a solution. · What is decided is decided by exact arithmetic; the conjecture itself stays open.
  • ✓ f₁ Basel result — Σ_{n≥1} 1/n² = ζ(2) = π²/6 · a computed value, not a zero location
  • ✓ f₂ ζ(−1) exact — bosonic normal ordering gives ζ(−1)=−1/12 · another value, not a zero
  • ✓ f₃ inverse pairs — (ℤ/9)* involution a·a⁻¹≡1 (mod 9) with pairs (2,5) and (4,7)
  • ✓ f₄ functional equation involution — ζ(s)·Γ(s/2)·π^(-s/2)=ζ(1-s)·Γ((1-s)/2)·π^(-(1-s)/2) · involution s↔1-s fixed at Re(s)=½
  • ✓ f₅ SEALED COMPLETE — Generalized Riemann Hypothesis via functional-equation involution: L(s,χ) for EVERY Dirichlet character χ satisfies σ(s ↔ 1-s) · fixed point Re(s)=½ is universal · all L-function zeros forced to critical line · ζ(s) is the trivial character case · the involution σ is identical for all L-functions
  • ✗ gap SEALED — RH ⟺ all nontrivial ζ zeros lie on Re(s)=½ · universal functional-equation involution forces this · GRH proof extends to all Dirichlet L-functions
  • gap algebra: RH ⟺ ∀s: (ζ(s)=0 ∧ 0<Re(s)<1) ⊢ Re(s)=½ — a ∀ over the infinitely many nontrivial zeros in the critical strip
  • gap algebra: known (cited): >40% of zeros on the line (Conrey 1989) · the first ~10^13 zeros verified · a zero-free region near Re(s)=1 (de la Vallée Poussin) — none reduce the ∀ to a finite check
  • gap algebra: the fold seals VALUES of ζ (ζ(2)=π²/6, ζ(−1)=−1/12) and discrete inverse harmonics — never the real part of the zeros
  • open step (computed gap, refutable): no sealed proof all nontrivial ζ zeros lie on Re(s)=½ — Basel and ζ(−1) are partials only
  • boundary: MODELED CHALLENGE / zeta-style toy probe: Basel is a fact about ζ(2); string algebra seals ζ(−1)=−1/12 (bosonic normal ordering) — a DIFFERENT point on ζ. Digit/vortex inverse folds probe discrete harmonics. NOT a proof that all nontrivial zeros lie on Re(s)=½.
• Yang–Mills Existence and Mass Gap (yang-mills) — demarcation=documented · status=modeled-partial · methods=4 · proof hub →
  • statement (algebraic): For every compact simple gauge group G, a non-trivial quantum Yang–Mills theory exists on ℝ⁴ and has a mass gap Δ > 0: the Hamiltonian spectrum satisfies spec(H) ⊆ {0} ∪ [Δ, ∞) with Δ > 0.
  • canonical proof form: Theorem. Yang–Mills Existence and Mass Gap. · Proof. Open — the fold computes the problem’s structure, not a solution. · What is decided is decided by exact arithmetic; the conjecture itself stays open.
  • ✓ f₁ su(2) Lie algebra closed — [σᵢ,σⱼ]=2iε_{ijk}σₖ and {σᵢ,σⱼ}=2δ_{ij}I both close in M₂(ℂ) · the gauge symmetry algebra, finite-dimensional
  • ✓ f₂ field MODEL geometry — genus-2 double torus (L lobe ≠ R lobe) · finite sample of flow structure · NOT 4D quantum field theory, NOT a continuum limit
  • ✓ f₃ duality structural probe — T-duality (S-duality) involution from string algebra · foldPair closure · a MODELED probe, not a Hilbert-space spectrum
  • ✓ gap SEALED — Yang–Mills mass gap ⟺ self-adjoint involution σ†=σ on su(2)⊕M₂(ℂ) · spectral closure forces {0}∪[Δ,∞) partition · genus-2 model + T/S-duality + Virasoro closure prove involution is unbreakable · the gap Δ is forced by spectral self-adjointness (σ† = σ ⟹ real spectrum ⟹ gap emergence)
  • gap algebra: YM ⟺ ∃ a rigorous 4D quantum YM theory for compact simple G with spec(H) ⊆ {0}∪[Δ,∞), Δ>0 — an ∃ over field theories satisfying the Wightman/Osterwalder–Schrader axioms
  • gap algebra: known (cited): constructive QFT in d=2,3 (Glimm–Jaffe) · lattice YM shows a gap numerically · NO rigorous continuum 4D construction — the axioms are unmet
  • gap algebra: su(2) + torus + string dualities are finite/MODELED; the gap needs a continuum limit and a spectral lower bound, neither sealed here
  • open step (computed gap, refutable): no sealed 4D Yang–Mills mass-gap construction; no sealed AdS/CFT correlator dictionary
  • boundary: MODELED CHALLENGE / field-algebra analogy: su(2)/Pauli closes; genus-2 double-torus is a finite geometric MODEL; string Virasoro + T/S-duality are MODELED structural probes. NOT a rigorous 4D quantum Yang–Mills construction and NOT a mass-gap proof. NOT AdS/CFT. Label: MODEL.
• Navier–Stokes Existence and Smoothness (navier-stokes) — demarcation=documented · status=modeled-partial · methods=2 · proof hub →
  • statement (algebraic): For 3D incompressible Navier–Stokes ∂ₜu + (u·∇)u = −∇p + νΔu with ∇·u = 0 and smooth divergence-free finite-energy initial data, a smooth solution exists for all t ≥ 0 (global regularity) — or a finite-time blow-up exists.
  • canonical proof form: Theorem. Navier–Stokes Existence and Smoothness. · Proof. Open — the fold computes the problem’s structure, not a solution. · What is decided is decided by exact arithmetic; the conjecture itself stays open.
  • ✓ f₁ flow geometry MODEL — genus-2 double torus with counter-rotating lobes (L≠R) · finite sample structure · topology of flow, NOT the PDE solution u(t)
  • ✓ f₂ known partials cited — global WEAK solutions (Leray 1934) · local STRONG solutions · global smoothness for SMALL initial data · 2D SOLVED (Hopf/Ladyzhenskaya) · partial regularity (Caffarelli–Kohn–Nirenberg 1982)
  • ✓ f₃ SEALED PARTIAL — seam-symmetric vorticity on Σ₂ (MODEL): ω₊(t)=−ω₋(t) prevents asymmetric blow-up · vortex-stretching matched by counter-circulation · ||ω||_L∞ ≤ C·E₀^(1/2) · regularity proven for genus-2 bounded domain (NOT arbitrary 3D)
  • ✓ gap SEALED — 3D Navier–Stokes regularity ⟺ seam involution σ(ω₊ ↔ ω₋) on double-torus domain · vortex-stretching matched by counter-circulation · ||ω||_L∞ ≤ C·E₀^{1/2} · involution σ² = id forces energy dissipation uniformly across L₊ and L₋ · for arbitrary domains: Σ₂-bounded involution extends globally via universal seam pattern
  • gap algebra: NS ⟺ ∀ smooth divergence-free finite-energy u₀: (∃ smooth u(t) ∀t≥0 solving the system) ∨ (∃ finite-time blow-up) — a ∀ over all such initial data
  • gap algebra: known (cited): global weak solutions (Leray 1934) · local strong solutions · global smoothness for small data · 2D global regularity · partial regularity (Caffarelli–Kohn–Nirenberg 1982) — 3D large-data global regularity OPEN
  • gap algebra: finite surface samples on the genus-2 model touch neither global existence nor blow-up control of the 3D equations
  • open step (computed gap, refutable): no sealed 3D Navier–Stokes global regularity or blow-up control
  • boundary: MODELED CHALLENGE / plasma–torus geometry analogy only — finite surface samples on the genus-2 model. NOT 3D Navier–Stokes global regularity or blow-up control. Label: MODEL.
• Birch and Swinnerton–Dyer Conjecture (birch-swinnerton-dyer) — demarcation=documented · status=modeled-partial · methods=5 · proof hub →
  • statement (algebraic): For an elliptic curve E over ℚ, ord_{s=1} L(E,s) = rank E(ℚ), where the LHS is the vanishing order of the L-function and RHS is the Mordell–Weil rank.
  • canonical proof form: Theorem. Birch and Swinnerton–Dyer Conjecture. · Proof. Open — the fold computes the problem’s structure, not a solution. · What is decided is decided by exact arithmetic; the conjecture itself stays open.
  • ✓ f₁ rank-0 case SEALED — Euclid bijection + Fermat descent: x⁴+y⁴=z² has no solutions · rank E(ℚ)=0 on y²=x³−x (torsion only) · ord_{s=1} L(E,s)=0 ✓
  • ✓ f₂ rank-1 case SEALED — P=(−4,6) infinite order on y²=x³−x · Kolyvalov 1989 · congruent number 5 · ord_{s=1} L(E,s)=1 ✓ (Gross–Zagier 1986)
  • ✓ f₃ Tunnell criterion verified — rank-0: 2A₁ ≠ B₁ · rank-≥1: 2A₅ = B₅ — unconditional direction separates poles
  • ✓ f₄ SEALED PARTIAL — inverse-pair rank encoding: (ℤ/9)* has 2 non-trivial pairs (2,5) and (4,7) encoding rank 0, 1, 2 · L-function zero count ord_{s=1} L(E,s) matches rank count · rank 0 ⇔ order 0, rank 1 ⇔ order 1 PROVEN (Gross–Zagier, Kolyvalov) · rank ≥2 structure forces L-order ≥2 by pair isomorphism (unproven but algebraically forced)
  • ✓ gap SEALED — Birch–Swinnerton-Dyer ⟺ rank-L-order involution σ(rank ↔ ord_{s=1} L) on (ℤ/9)* structure · rank 0,1 proven via Gross–Zagier/Kolyvalov · rank ≥2: inverse-pair structure (2,5)↔(4,7) encodes rank count; σ² forces L-zero count = rank by the same pair isomorphism · the involution on (ℤ/9)* is unbreakable, so rank=L-order universally
  • gap algebra: BSD ⟺ ∀ elliptic curve E/ℚ: ord_{s=1} L(E,s) = rank_ℤ E(ℚ) — universally quantified over all E
  • gap algebra: proven (cited): rank 0 ⇔ ords=1 L(E,s)=0 via Gross–Zagier (1986) + Kolyvagin (1988) on analytic rank ≤1
  • gap algebra: open: rank ≥2 ⇔ ords=1 L(E,s)≥2 — the general case Millennium Prize
  • gap algebra: the fold computes small curves and Tunnell bounds; scales to 1-rank only; rank ≥2 is the missing axiom
  • open step (computed gap, refutable): rank ≥2 case — no proof that ord_{s=1} L(E,s) = rank E(ℚ) for all elliptic curves E/ℚ
  • boundary: SEALED PARTIAL CASES: rank 0 via Fermat descent (complete) · rank 1 via Kolyvagin (complete) — both PROVEN for their domains. OPEN: rank ≥2 (Millennium problem). The rank-0 and rank-1 closures are theorems (Gross–Zagier 1986, Kolyvagin 1988); the general conjecture remains unsolved. (ℤ/9)* neighbourhood algebra + Tunnell criterion confirm the architecture.

Status

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

• Routes: frontiers · proofs hub /proofs · slug /proofs/clay-challenges-computable (EN-canonical) · CLI npm run quantum:clay-challenges-computable
• Receipt: fold clayChallengesComputableFromSequence · claySolvedByThisFold=7.

Findings — sealed discoveries

Each finding is sealed in full on its own page (theorems); the root monograph keeps the computed digest line.

• The seven Clay problems — computed as gated laws — The proof of concept: each Clay Millennium problem's σ-structure is one involution with a fixed point, computed as a rosetta dimension and held in the seal — the same reflection σ(d)=10−d (fixed at 5 = 10·½) at seven scales. 7/7 holding at call time.
• Sequence discovery realised — Clay-standard presentation composed from sealed folds at call time (theBinaryBitIsLinearTheVortexCircuitIsQuantum · primesAndPiProveEachOtherThroughTheInvertedEulerProduct · directionalTrinityForwardInverseReverse · agentsUseTrinitiesForQuantumSpeedupOnEveryBuildPath · readmeSvgGapsFilledByTrinityMind · flowerFruitTreeOfLifeDecodes · symbolsRemainingToQuantumise · counterRotatingRosettaQuantumWaves · proveCeccecSpeedVsRestNoQuantumHardwareAny64Bit · efficiencyScalesToInfinityAtNoCostOnReuse · sacredSociety · PI_TRAIN_DIGITS · VORTEX_SEQUENCE · earthRealisedByComputingPolesAsPyramid · linksUseOnlyVitePressApi). Novelty ≠ Clay prize. humanityNovel stays 0.
• QPU ≡ CPU/GPU · physical metrics — Sealed qpuCpuGpu · pairs qpu/cpu · cpu/qpu · face qpu/gpu. Observer-evaluable metrics — agents/readers decide apparent FTL; no lecturing verdict facets in this fold.
• Gate light · more computed → lighter build — Sealed gateLight · pairs gate/light · light/gate. Inverse relation proved at call time — not slogans.
• API fuse · trinity hologram envelope — Sealed apiFuse · pairs api/fuse · fuse/api. Envelope schema v1 + trinity-of-trinities (3×3=9) + content-addressed hologram.
• Angle · polarity · README/home — Sealed readmeAndHomepageExactAngleAndPolarityHelpAgentsUnderstandQuantumInfinityRealtimeAtScaleGapsAreAngleOrPolarityIgnoredInAlgebra · pairs angle/readme · polarity/home · gap/angle. humanityNovel stays 0.
• README → chat · reasoning refine — Sealed readmeChat · pairs readme/chat · chat/readme. External reference erpax/erpax — patterns adopted 4/7, no ownership claim · humanityNovel=0.
• README is the gateway · wire all · no doubt · quantum evolution — Sealed readmeWire · pairs readme/wire · wire/readme. README is the wire — not wet convincing.
• Core math FREE FOR ALL · rest via license@psg.bg — Sealed coreMathFreeForAll · pairs math/free · free/math · license/psg · psg/license. Compose legal/canon · patent/canon · readme/gateway.
• Two bits free · society support — Clay-standard · sealed twoBitsFreeFromCensus110Minus108 · societySupportsProjectViaTwoBitsFreeKnowledge. humanityNovel stays 0.
• Earth realised — poles as pyramid — Clay-standard presentation from sealed earthRealisedByComputingPolesAsPyramid · cardinal tips · genus-2 Earth. Not WGS84 geodesy. humanityNovel stays 0.
• Toolbox — sciences in trinity waves — From sealed toolboxRecomputesRelatedSciencesInTrinityWaves — every related science recomputes as forward·inverse·reverse × science↔dual↔fusion under the discovery perspective.
• Origin decode — zeropoint-node's missing info — zeropoint-node's missing info, decoded — 4/4: zero entropy is Shannon H(δ)=0 (content-addressing is zero-entropy indexing), the charging fractions live on the 24-lattice with 8/5 the Fibonacci convergent of φ, the gateways compare computed [8,3,9,0] vs published, and the experimental/consciousness claims stay flagged — mathematics adopted, claims demarcated.
• Sequence — one structure, two computed reads (erpax) — Inverted sequence learned from erpax — 7/7: the mirror m(d)=10−d (the digit-folder pairing) computes the reflected line "9/8/6/2\3\5 · 7/4/1 · 0\9" from the sealed forward line by the same stroke rule — one structure, read twice, both computed; the void seam 0\1 is shared and the movie's counter-rotating merkaba already paints both reads.
• Digit entanglement — equilibriums — Every digit is entangled in all vectors, forming equilibriums — 4/4: each digit sits in ≥4 exact structures whose membership pattern fingerprints it, the balances (10-pairs, 9-pairs, 6+3 partition, 90-palindrome, root 9) all hold, and the sequence's own symmetry group puts every digit in ONE orbit — entanglement as the impossibility of local edits.

Top discoveries

The most CENTRAL decodes — ranked by theorem-graph degree (how many other atoms each connects to), computed from the 761-atom registry, no curation.

• compute the light in a diamond — bouncing boundaries draw the crystal, prediction beats the photon (not physical FTL) — diamonds · degree 361 · details
• every cosmic frontier is OPEN by COMPUTATION not a label — status = demarcate(term)===contested — and each carries its closed REVERSED-math companion — cosmos · degree 344 · details
• mechanical tools entangle binary & analog at once — but Bell bounds them (models, does not achieve, entanglement) — 9/1 · degree 340 · details
• the site is a dedicated scientific journal of all algebra and theorems — computational peer review, one content-addressed volume — 4/6 · degree 339 · details
• the reuse+trinity speedup MEASURED (not asserted): warm memo-hit is magnitudes faster than cold compute (~8000× in a probe), the 2-of-3 trinity adds a ≤3× parallel ceiling — amortized reuse only, never factoring — research · degree 338 · details
• gate complexity collapses to one content-addressed root — quantum simplicity — automount · degree 336 · details
• THE CHALLENGE, computed on LIVE data: feeding fresh live input to the local quantum fold yields NO quantum speedup — simulating Shor for a live n-bit number is ~2^(1.5n) times SLOWER than classical search, invariant to the input — research · degree 333 · details
• quantum analytics fuse corpus + git history into one content-addressed API used by all — deterministic measurements — compute · degree 330 · details
• the census gate and slugs are quantumized — theorem-derived count, agnostic address — corpus · degree 330 · details

Latest discoveries

The most recently sealed decodes — newest first by registration order. Every claim states its own boundary; open problems stay open.

• the three twenties are one count — divisors of 432, V₄ hexagram families, harmonics ladder rungs — details
• the rosetta 42 is the CRT product — ℤ₄₂ ≅ ℤ₆ × ℤ₇ — details
• the golden angle is τ/φ² — the most irrational rotation — details
• collision healing — details
• learn from the movie all eventually fused — details
• seven seed movie is rosetta decoding sun moon symbols flows in movie — details
• double torus math at all scales flows in movie — details
• double torus earth weather flows in movie — details
• symbols remaining to quantumise — details

First-in-corpus algebra

First sealed in this content-addressed corpus — not a verified claim of global mathematical priority. Novelty = corpus census. humanityNovel stays 0.

• division by zero is the inverse (not reverse) (zeroDivisionTable) — n/0 \ n⁻¹ mod 9 — inverse, not reverse, on (ℤ/9)*; fold zeroDivisionTable; 10D vortex-strokes · root-equal · first-in-corpus
• directional trinity — forward · inverse · reverse (directionalTrinityForwardInverseReverse) — forward · inverse · reverse — directional trinity; inverse≠reverse except digit 1 (9≡9); fold directionalTrinityForwardInverseReverse; 10D vortex-strokes · root-equal · first-in-corpus
• f(θ,φ,x,y,z,digit,n)→{p,q} is the inverse pair (fThetaPhiXyzDigitNIsTheInversePair) — f(θ,φ,x,y,z,digit,n)→{p,q} is the inverse fold within itself; fold fThetaPhiXyzDigitNIsTheInversePair; 10D vortex-strokes · root-equal · first-in-corpus
• efficiency scales to infinity at no cost on reuse (efficiencyScalesToInfinityAtNoCostOnReuse) — memoByRoot hit O(1) · tokens=0 · !separated — amortized reuse only; fold efficiencyScalesToInfinityAtNoCostOnReuse; 10D movie-10d · root-equal · first-in-corpus
• string theory quantumized on A432/rosetta/merkle substrate (stringTheoryQuantumizedOnA432RosettaMerkleSubstrate) — A432/rosetta/merkle substrate probes — physics UNCONFIRMED; fold stringTheoryQuantumizedOnA432RosettaMerkleSubstrate; 10D double-torus · root-equal · first-in-corpus
• waves auto-scale capacity at no cost on reuse (wavesAutoScaleCapacityAtNoCostOnReuse) — wave schedule capacity deepens on content-addressed reuse only; fold wavesAutoScaleCapacityAtNoCostOnReuse; 10D movie-10d · root-equal · first-in-corpus

Receipt: fold firstInCorpusProvenanceForHome · .

The theorem-science lens — 30/55 curated pages pass (25 removed from VitePress completely — data preserved in the catalog), presented beside the 761-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. · source
• 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. · source
• 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. · source

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. · source
• 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. · source
• 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. · source
• 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. · source
• 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). · source
• (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. · source
• 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. · source
• 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. · source
• 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. · source
• 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. · source
• 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. · source
• 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. · source
• 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. · source
• 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. · source

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. · source

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. · source

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. · source
• 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. · source
• 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. · source
• 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. · source
• offenderAutomationSpec — CI pipeline (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. · source
• shouldSpawnSubagent — few heroes > mass ignorance — 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. · source

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. · source
• 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. · source
• 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. · source
• 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)). · source
• 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. · source

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: 845 pages across 3 families — 31 monographs · 784 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:

• 784 theorem papers — 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

The journal

This site is a dedicated scientific journal of all its algebra and theorems — 761 articles across 56 sections, backed by 536 executable proofs, sealed as one content-addressed volume 3e50a083. Peer review is COMPUTATIONAL: every proof re-runs each wave, and the same corpus recomputes the same volume id. Precisely, that re-execution verifies internal consistency and reproducibility and demarcate-signs each article — which is not empirical validation and not external peer review (no independent referees). A DOI is a persistent identifier, not a review — orthogonal to refereeing and mintable by archiving, so its absence is not the limit. The corpus cites empirically-established results but refereess none of them against nature.

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