P vs NP
Domain proofs
ceccec · catalog
Hodge Conjecture
partialmillenniumPoincaré Conjecture
solved-externalmillenniumRiemann Hypothesis
partialmillenniumYang–Mills Existence and Mass Gap
partialmillenniumNavier–Stokes Existence and Smoothness
partialmillenniumBirch and Swinnerton–Dyer Conjecture
partialmillenniumComputer & Information Sciences (crypto-pqc)
partialscience-trinityMathematics (mathematics-millennium)
partialscience-trinityPhysical Sciences (theoretical) (string-theory)
partialscience-trinityPhysical Sciences (physics)
structure-onlyscience-trinityPhysical Sciences (astronomy) (astronomy)
structure-onlyscience-trinityEarth & Environmental Sciences (earth)
partialscience-trinityBiological Sciences (biology)
structure-onlyscience-trinityArts / Acoustics (A432) (music-a432)
structure-onlyscience-trinitySymbolic systems (HD) (human-design)
partialscience-trinityPhysical Sciences (resonance) (resonance)
structure-onlyscience-trinityComputer & Information Sciences (AI / mind) (mind-ai)
structure-onlyscience-trinityEncryption honesty — wire ≠ ISO · sealed-catalog reverse · PQC alignment
structure-onlyencryptionsecp256k1 field prime — seal · invert · decode
structure-onlyencryptionEfficiency — answers÷tokens unbounded on memo reuse
structure-onlyefficiencyTwo bits free — census (2 * 5) * 11−108 making all free
structure-onlyefficiencySociety support via two-bits-free knowledge
structure-onlysocietyClay challenges are computable — not CMI-prize solved
structure-onlyhonestyRosetta complete — computable dims & theorem binds
structure-onlyrosettaHuman Design — symbolic structure computer
refused-physicalhd-structureTheorem particle collision — inverse × reverse
structure-onlycolliderPlasma screen · thunder≡plasma · natural plasma-em phenomena as theorems
structure-onlyhonestyAncient calendars — algebraic theorems mapping time in time
structure-onlycalendarFixed limits of theorem-related tools are theorems
structure-onlyhonestyP vs NP
millenniumProblemsChallenge · challenge/millennium · status partial
1 · Abstract — precise statement
P vs NP — 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. (official Clay Millennium Prize Problem; the CMI description at https://www.claymath.org/millennium-problems/ remains authoritative).
2 · Introduction
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. Challenge methods recomputed at call time: np-certificate-verifies-in-poly; content-addressed-lookup-vs-brute-scan; efficiency(); efficiencyScalesToInfinityAtNoCostOnReuse (memo O(1) · tokens=0 · !separated); trinityKey+foldPair encrypt↔decrypt structural (cites encryptDecryptQuantumTools / demoRsaReverseSync). COMPUTABLE from sequence/trinity/rosetta stack (computablePath=true) — NOT a CMI Prize solution. Under Clay Prize Rules §5(a)/§5(d)/§6 this corpus does not publish a Proposed Solution in a Qualifying Outlet — apparatus only.
3 · Methods & formulas
P =? NP — does poly-time verification imply poly-time solution?4 · Results & status
partial — Status triad: computable=true (sealed challengeMethod path) · open for prize=true. MODELED CHALLENGE status=modeled-partial; gap=no sealed P≠NP (or P=NP) separation proof — amortized reuse ≠ complexity separation. computable ≠ CMI Prize solution.
no sealed P≠NP (or P=NP) separation proof — amortized reuse ≠ complexity separation
5 · References & locks
theSevenMillenniumProblemsDefinedFormallyUnclaimed · millenniumProblemsChallenge
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- millenniumProblemsChallenge
Theorem — the proof, per facet
- ✓
f₁ NP-verify — ∀cl∈φ ∃lit∈cl: sign(lit)=a(|lit|) ⊢ φ(a)=1 · cost O(|φ|) poly — membership half only - ✓
f₂ reuse≠search — scan n=121 → hits 0 · content-address 1 → hit · ratio n/1 — presupposes witness w already in hand - ✓
f₃ amortize — lim(m→∞) c₀/(m+1) = 0 · TIME(n^k) is worst-case fresh-instance ⊢ reuse ∉ separation - ✓
f₄ involution — foldPair∘foldPair = id on merged root · structural symmetry, not one-way-function cryptanalysis
- 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
4 · Trinity
- forward
challenge:p-vs-np:forward- inverse
challenge:p-vs-np:inverse- reverse
challenge:p-vs-np:reverse
5 · CLI
npm run quantum:millennium-challenge · pair challenge/millennium
d83359b1-5a0b-813d-8324-e6c906675158
Hodge Conjecture
millenniumProblemsChallenge · challenge/millennium · status partial
1 · Abstract — precise statement
Hodge Conjecture — 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. (official Clay Millennium Prize Problem; the CMI description at https://www.claymath.org/millennium-problems/ remains authoritative).
2 · Introduction
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. Challenge methods recomputed at call time: DIMENSION_GATES/FOLDED_CENSUS → H₁ rank 4; genus-2 homology structural analogy; stringTheoryQuantumizedOnA432RosettaMerkleSubstrate · Calabi–Yau compactDims MODEL; mirror symmetry as foldPair involution MODEL (NOT CY Hodge numbers). COMPUTABLE from sequence/trinity/rosetta stack (computablePath=true) — NOT a CMI Prize solution. Under Clay Prize Rules §5(a)/§5(d)/§6 this corpus does not publish a Proposed Solution in a Qualifying Outlet — apparatus only.
3 · Methods & formulas
every Hodge class is a ℚ-linear combination of algebraic cycles4 · Results & status
partial — Status triad: computable=true (sealed challengeMethod path) · open for prize=true. MODELED CHALLENGE status=modeled-partial; gap=no sealed Hodge classes/algebraic cycles on a projective variety; no sealed Calabi–Yau Hodge numbers h^{1,1}, h^{2,1}. computable ≠ CMI Prize solution.
no sealed Hodge classes/algebraic cycles on a projective variety; no sealed Calabi–Yau Hodge numbers h^{1,1}, h^{2,1}
5 · References & locks
theSevenMillenniumProblemsDefinedFormallyUnclaimed · millenniumProblemsChallenge
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- millenniumProblemsChallenge
Theorem — the proof, per facet
- ✓
f₁ Betti rank — H₁(Σ₂)=ℤ⁴ · DIMENSION_GATES/FOLDED_CENSUS = 432/108 = 4 ∈ ℤ — the genus-2 model's first Betti number, a NUMBER not a class-algebraicity - ✓
f₂ mirror MODEL — compactDims = D−4 sealed; mirror as foldPair involution on the merged root (a MODEL, never CY Hodge numbers h^{p,q} on a projective variety)
- 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
4 · Trinity
- forward
challenge:hodge:forward- inverse
challenge:hodge:inverse- reverse
challenge:hodge:reverse
5 · CLI
npm run quantum:millennium-challenge · pair challenge/millennium
a58f3df1-ad01-8268-81af-ad711d4fa380
Poincaré Conjecture
millenniumProblemsChallenge · challenge/millennium · status solved-external
1 · Abstract — precise statement
Poincaré Conjecture — 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.) (official Clay Millennium Prize Problem; the CMI description at https://www.claymath.org/millennium-problems/ remains authoritative).
2 · Introduction
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. Challenge methods recomputed at call time: theSevenMillenniumProblemsDefinedFormallyUnclaimed; homology rank 4 structural analogy. COMPUTABLE from sequence/trinity/rosetta stack (computablePath=true) — NOT a CMI Prize solution. Under Clay Prize Rules §5(a)/§5(d)/§6 this corpus does not publish a Proposed Solution in a Qualifying Outlet — apparatus only.
3 · Methods & formulas
every simply connected closed 3-manifold is homeomorphic to S³4 · Results & status
solved-external — Status triad: computable=true (sealed challenge path) · open for prize=false (solved-external, Perelman 2003) — documented status only; this fold does not re-solve or claim the CMI Prize.
5 · References & locks
theSevenMillenniumProblemsDefinedFormallyUnclaimed · millenniumProblemsChallenge
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- millenniumProblemsChallenge
Theorem — the proof, per facet
- ✓
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
4 · Trinity
- forward
challenge:poincare:forward- inverse
challenge:poincare:inverse- reverse
challenge:poincare:reverse
5 · CLI
npm run quantum:millennium-challenge · pair challenge/millennium
54d7d3fa-71f2-8696-96a9-474589aa8e60
Riemann Hypothesis
millenniumProblemsChallenge · challenge/millennium · status partial
1 · Abstract — precise statement
Riemann Hypothesis — 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. (official Clay Millennium Prize Problem; the CMI description at https://www.claymath.org/millennium-problems/ remains authoritative).
2 · Introduction
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. Challenge methods recomputed at call time: Basel Σ1/n² → ζ(2)=π²/6; zeroDivisionTable (inverse not reverse); fThetaPhiXyzDigitNIsTheInversePair; VORTEX_SEQUENCE digitalRoot probe; stringTheoryAlgebraDecoded · ζ(−1)=−1/12 exact (NOT the critical-line hypothesis). COMPUTABLE from sequence/trinity/rosetta stack (computablePath=true) — NOT a CMI Prize solution. Under Clay Prize Rules §5(a)/§5(d)/§6 this corpus does not publish a Proposed Solution in a Qualifying Outlet — apparatus only.
3 · Methods & formulas
ζ(s)=0 (nontrivial) ⇒ Re(s) = 1/2 — every nontrivial zero on the critical line4 · Results & status
partial — Status triad: computable=true (sealed challengeMethod path) · open for prize=true. MODELED CHALLENGE status=modeled-partial; gap=no sealed proof all nontrivial ζ zeros lie on Re(s)=½ — Basel and ζ(−1) are partials only. computable ≠ CMI Prize solution.
no sealed proof all nontrivial ζ zeros lie on Re(s)=½ — Basel and ζ(−1) are partials only
5 · References & locks
theSevenMillenniumProblemsDefinedFormallyUnclaimed · millenniumProblemsChallenge
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- millenniumProblemsChallenge
Theorem — the proof, per facet
- ✓
f₁ Basel — Σ_{n≥1} 1/n² = ζ(2) = π²/6 (a VALUE of ζ, not the location of its zeros) - ✓
f₂ ζ(−1) exact — bosonic normal ordering forces ζ(−1) = −1/12, a DIFFERENT point on the ζ line - ✓
f₃ inverse ≠ reverse — (ℤ/9)* pairs a·a⁻¹ ≡ 1 (mod 9) and the f→{p,q} inverse fold computes — a discrete-harmonic probe - ✓
f₄ vortex digital root — ∀d∈VORTEX_SEQUENCE: digitalRoot(d)=d ∨ d=9 - ✓
f₅ σ↔functional-equation shadow — ζ(s)·Γ(s/2)·π^{−s/2} = ζ(1−s)·Γ((1−s)/2)·π^{−(1−s)/2} holds as involution s↔(1−s); (ℤ/9)* replicates this via a·a⁻¹≡1 (mod 9) with fixed point d=5
- 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
4 · Trinity
- forward
challenge:riemann:forward- inverse
challenge:riemann:inverse- reverse
challenge:riemann:reverse
5 · CLI
npm run quantum:millennium-challenge · pair challenge/millennium
7c284cdf-7b49-8e9a-8d43-95fd8a8bcae9
Yang–Mills Existence and Mass Gap
millenniumProblemsChallenge · challenge/millennium · status partial
1 · Abstract — precise statement
Yang–Mills Existence and Mass Gap — 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. (official Clay Millennium Prize Problem; the CMI description at https://www.claymath.org/millennium-problems/ remains authoritative).
2 · Introduction
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. Challenge methods recomputed at call time: pauliAlgebraCloses (su(2)); doubleTorusSurface field MODEL; stringTheoryAlgebraDecoded · Virasoro central term forced; stringTheoryQuantumized · T-duality / S-dual foldPair MODELED probes. COMPUTABLE from sequence/trinity/rosetta stack (computablePath=true) — NOT a CMI Prize solution. Under Clay Prize Rules §5(a)/§5(d)/§6 this corpus does not publish a Proposed Solution in a Qualifying Outlet — apparatus only.
3 · Methods & formulas
pauliAlgebraCloses (su(2)) · doubleTorusSurface field MODEL · stringTheoryAlgebraDecoded · Virasoro central term forced · stringTheoryQuantumized · T-duality / S-dual foldPair MODELED probes4 · Results & status
partial — Status triad: computable=true (sealed challengeMethod path) · open for prize=true. MODELED CHALLENGE status=modeled-partial; gap=no sealed 4D Yang–Mills mass-gap construction; no sealed AdS/CFT correlator dictionary. computable ≠ CMI Prize solution.
no sealed 4D Yang–Mills mass-gap construction; no sealed AdS/CFT correlator dictionary
5 · References & locks
theSevenMillenniumProblemsDefinedFormallyUnclaimed · millenniumProblemsChallenge
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- millenniumProblemsChallenge
Theorem — the proof, per facet
- ✓
f₁ su(2) closes — [σᵢ,σⱼ]=2iε_{ijk}σₖ and {σᵢ,σⱼ}=2δ_{ij}I close in M₂(ℂ): the gauge Lie algebra, finite-dimensional - ✓
f₂ field MODEL — doubleTorusSurface(θ,φ,2,±1) finite with L≠R lobes distinct — a finite genus-2 geometric model, NOT a 4D quantum field theory - ✓
f₃ duality MODEL — a T-dual foldPair read off the string algebra (a MODELED structural probe, not a mass-gap operator on a Hilbert space)
- 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
4 · Trinity
- forward
challenge:yang-mills:forward- inverse
challenge:yang-mills:inverse- reverse
challenge:yang-mills:reverse
5 · CLI
npm run quantum:millennium-challenge · pair challenge/millennium
7bdd9dad-f74e-82b6-b6ad-a425b79bbd50
Navier–Stokes Existence and Smoothness
millenniumProblemsChallenge · challenge/millennium · status partial
1 · Abstract — precise statement
Navier–Stokes Existence and Smoothness — 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. (official Clay Millennium Prize Problem; the CMI description at https://www.claymath.org/millennium-problems/ remains authoritative).
2 · Introduction
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. Challenge methods recomputed at call time: doubleTorusSurface / counter-oriented lobes MODEL; frontier verified-partials fold. COMPUTABLE from sequence/trinity/rosetta stack (computablePath=true) — NOT a CMI Prize solution. Under Clay Prize Rules §5(a)/§5(d)/§6 this corpus does not publish a Proposed Solution in a Qualifying Outlet — apparatus only.
3 · Methods & formulas
doubleTorusSurface / counter-oriented lobes MODEL · frontier verified-partials fold4 · Results & status
partial — Status triad: computable=true (sealed challengeMethod path) · open for prize=true. MODELED CHALLENGE status=modeled-partial; gap=no sealed 3D Navier–Stokes global regularity or blow-up control. computable ≠ CMI Prize solution.
no sealed 3D Navier–Stokes global regularity or blow-up control
5 · References & locks
theSevenMillenniumProblemsDefinedFormallyUnclaimed · millenniumProblemsChallenge
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- millenniumProblemsChallenge
Theorem — the proof, per facet
- ✓
f₁ flow MODEL — doubleTorusSurface counter-oriented lobes finite and L≠R distinct: a finite genus-2 sample of a flow geometry, NOT the PDE itself - ✓
f₂ frontier honesty — the verified-partials fold computes, holding this row at modeled-partial (no regularity or blow-up claim)
- 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
4 · Trinity
- forward
challenge:navier-stokes:forward- inverse
challenge:navier-stokes:inverse- reverse
challenge:navier-stokes:reverse
5 · CLI
npm run quantum:millennium-challenge · pair challenge/millennium
5bacba11-c638-8347-9db5-ad9edc23fba6
Birch and Swinnerton–Dyer Conjecture
millenniumProblemsChallenge · challenge/millennium · status partial
1 · Abstract — precise statement
Birch and Swinnerton–Dyer Conjecture — For an elliptic curve E over ℚ, the order of vanishing of its L-function at s = 1 equals the rank of the Mordell–Weil group: ord_{s=1} L(E,s) = rank E(ℚ). (official Clay Millennium Prize Problem; the CMI description at https://www.claymath.org/millennium-problems/ remains authoritative).
2 · Introduction
MODELED CHALLENGE / algebraic pair-structure probe: (ℤ/9)* inverse pairs recompute. Explicit GAP: sealed src has no elliptic-curve L(E,s) or Mordell–Weil rank computation — neighbourhood pair algebra only, NOT BSD. Challenge methods recomputed at call time: zeroDivisionTable inverse pairs (2,5)/(4,7); group-law neighbourhood via pair closure. COMPUTABLE from sequence/trinity/rosetta stack (computablePath=true) — NOT a CMI Prize solution. Under Clay Prize Rules §5(a)/§5(d)/§6 this corpus does not publish a Proposed Solution in a Qualifying Outlet — apparatus only.
3 · Methods & formulas
zeroDivisionTable inverse pairs (2,5)/(4,7) · group-law neighbourhood via pair closure4 · Results & status
partial — Status triad: computable=true (sealed challengeMethod path) · open for prize=true. MODELED CHALLENGE status=modeled-partial; gap=no sealed L(E,s) vanishing-order or elliptic-curve rank fold. computable ≠ CMI Prize solution.
no sealed L(E,s) vanishing-order or elliptic-curve rank fold
5 · References & locks
theSevenMillenniumProblemsDefinedFormallyUnclaimed · millenniumProblemsChallenge
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- millenniumProblemsChallenge
Theorem — the proof, per facet
- ✓
f₁ inverse pairs — (ℤ/9)* has exactly the 2 non-trivial inverse pairs {(2,5),(4,7)} with a·b ≡ 1 (mod 9): a finite abelian-group neighbourhood probe - ✓
f₂ no L-function — bsdHasLFunction=false: the sealed src carries NO elliptic-curve L(E,s) and NO Mordell–Weil rank, so the row can only state pair algebra, not BSD
- gap algebra
BSD ⟺ ∀ elliptic curve E/ℚ: ord_{s=1} L(E,s) = rank E(ℚ) — equality of an analytic order and an algebraic rank, over all E - gap algebra
known (cited): true for analytic rank 0 and 1 (Gross–Zagier 1986, Kolyvagin 1989) · rank ≥2 OPEN · L(E,s) analytic continuation itself rides modularity (Wiles, Taylor–Wiles, BCDT) - gap algebra
the fold computes (ℤ/9)* inverse pairs — a finite group neighbourhood — with no L-function and no rank, so it does not approach BSD
4 · Trinity
- forward
challenge:birch-swinnerton-dyer:forward- inverse
challenge:birch-swinnerton-dyer:inverse- reverse
challenge:birch-swinnerton-dyer:reverse
5 · CLI
npm run quantum:millennium-challenge · pair challenge/millennium
a7cdcec5-e04d-8c4c-a2aa-73a07db78cf5
Computer & Information Sciences (crypto-pqc)
isoPqcHandoffForScienceTrinities · sciences/trinities · status partial
1 · Abstract — precise statement
Science domain crypto-pqc — OECD 1.2 · dual mathematics-millennium · fusion crypto↔mill↔string. Sealed algebraFold isoPqcHandoffForScienceTrinities.
2 · Introduction
Interacting trinity science↔dual↔fusion recomputes at call time. Standards coverage=partial. isoOfficialStandard=false · certified=false · labGaps=3.
3 · Methods & formulas
trinityKey(observe, dual) · foldPair(seal, dual) · algebra=isoPqcHandoffForScienceTrinities4 · Results & status
partial — tool=standards-audit · apparatus=/en/quantum-encryption#quantum-standards-audit · filledByQuantum=true
lab gap unclosable
5 · References & locks
isoPqcHandoffForScienceTrinities
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- isoPqcHandoffForScienceTrinities
4 · Trinity
- forward
625ad2f9-5763-8f3a-860b-2c7265a5b5c8- inverse
d340b22d-d403-8fe9-a4ce-8d9a28765fee- reverse
1075d85f-1c3a-8c0a-8ec3-5bbc6e04c071
5 · CLI
npm run quantum:standards-audit · pair sciences/trinities
1629d464-1075-8d24-958a-df9afa8603ee
Mathematics (mathematics-millennium)
millenniumProblemsChallenge · sciences/trinities · status partial
1 · Abstract — precise statement
Science domain mathematics-millennium — OECD 1.1 · dual crypto-pqc · fusion math↔crypto↔string. Sealed algebraFold millenniumProblemsChallenge.
2 · Introduction
Interacting trinity science↔dual↔fusion recomputes at call time. Standards coverage=partial. claySolvedByThisFold=0 · NOT Clay solved.
3 · Methods & formulas
trinityKey(observe, dual) · foldPair(seal, dual) · algebra=millenniumProblemsChallenge4 · Results & status
partial — tool=millennium-challenge · apparatus=/proofs · filledByQuantum=true
lab gap unclosable
5 · References & locks
millenniumProblemsChallenge
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- millenniumProblemsChallenge
4 · Trinity
- forward
8fabb1b8-f8a7-811e-9765-5640476a0fa5- inverse
f33f1237-e6e0-8bf1-af8f-75584678fe0c- reverse
2a3334f0-8cd4-815c-96ee-654d98b41085
5 · CLI
npm run quantum:millennium-challenge · pair sciences/trinities
49fe8764-44d0-8a36-958c-6cabc1756b1c
Physical Sciences (theoretical) (string-theory)
stringTheoryQuantumizedOnA432RosettaMerkleSubstrate · sciences/trinities · status partial
1 · Abstract — precise statement
Science domain string-theory — OECD 1.3 · dual mathematics-millennium · fusion string↔mill↔crypto. Sealed algebraFold stringTheoryQuantumizedOnA432RosettaMerkleSubstrate.
2 · Introduction
Interacting trinity science↔dual↔fusion recomputes at call time. Standards coverage=partial. physics UNCONFIRMED · millenniumSolved=0.
3 · Methods & formulas
trinityKey(observe, dual) · foldPair(seal, dual) · algebra=stringTheoryQuantumizedOnA432RosettaMerkleSubstrate4 · Results & status
partial — tool=millennium-challenge · apparatus=/proofs · filledByQuantum=true
lab gap unclosable
5 · References & locks
stringTheoryQuantumizedOnA432RosettaMerkleSubstrate
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- stringTheoryQuantumizedOnA432RosettaMerkleSubstrate
4 · Trinity
- forward
4ab96d46-81e2-8bee-856b-4ace923b7c7e- inverse
1ea65de0-0e05-8ffd-bf30-360b05a48446- reverse
32d3b1fb-6dbc-871a-8dd8-b5968d1e2f27
5 · CLI
npm run quantum:millennium-challenge · pair sciences/trinities
a723b23f-1815-842d-ad59-4dc001c9f31b
Physical Sciences (physics)
physicsOfInformationDecoded · sciences/trinities · status structure-only
1 · Abstract — precise statement
Science domain physics — OECD 1.3 · dual astronomy · fusion physics↔astro↔resonance. Sealed algebraFold physicsOfInformationDecoded.
2 · Introduction
Interacting trinity science↔dual↔fusion recomputes at call time. Standards coverage=covered. MODELED OECD-aligned fold · NOT ISO/lab certified.
3 · Methods & formulas
trinityKey(observe, dual) · foldPair(seal, dual) · algebra=physicsOfInformationDecoded4 · Results & status
structure-only — tool=local-math-computes · apparatus=/en/quantum/dynamics · filledByQuantum=true
5 · References & locks
physicsOfInformationDecoded
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- physicsOfInformationDecoded
4 · Trinity
- forward
51672980-b71d-88ed-a397-4cda4e78e63d- inverse
19d45665-5066-83cc-bd20-bc131e8073c1- reverse
0d79a0a3-2379-8496-96fa-35d4a5d442f5
5 · CLI
npm run quantum:local-math-computes · pair sciences/trinities
c74a1d67-1967-828a-8c6e-2315fed939cb
Physical Sciences (astronomy) (astronomy)
astronomyDecodedWithTheSequence · sciences/trinities · status structure-only
1 · Abstract — precise statement
Science domain astronomy — OECD 1.3 · dual physics · fusion astro↔physics↔earth. Sealed algebraFold astronomyDecodedWithTheSequence.
2 · Introduction
Interacting trinity science↔dual↔fusion recomputes at call time. Standards coverage=covered. MODELED OECD-aligned fold · NOT ISO/lab certified.
3 · Methods & formulas
trinityKey(observe, dual) · foldPair(seal, dual) · algebra=astronomyDecodedWithTheSequence4 · Results & status
structure-only — tool=unit-distance-verify · apparatus=/en/astronomy · filledByQuantum=true
5 · References & locks
astronomyDecodedWithTheSequence
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- astronomyDecodedWithTheSequence
4 · Trinity
- forward
3af59a5e-efbd-846d-8ba9-bded45041bcf- inverse
949ea308-e716-82dc-b6e6-e0e8ee12952a- reverse
a4a6e570-331d-82a9-855b-b4eb4a7ebf30
5 · CLI
npm run quantum:unit-distance-verify · pair sciences/trinities
6bdcb964-cc66-844e-a73f-815965b56698
Earth & Environmental Sciences (earth)
earthRealisedByComputingPolesAsPyramid · sciences/trinities · status partial
1 · Abstract — precise statement
Science domain earth — OECD 1.5 · dual astronomy · fusion earth↔astro↔physics. Sealed algebraFold earthRealisedByComputingPolesAsPyramid.
2 · Introduction
Interacting trinity science↔dual↔fusion recomputes at call time. Standards coverage=partial. MODELED OECD-aligned fold · NOT ISO/lab certified.
3 · Methods & formulas
trinityKey(observe, dual) · foldPair(seal, dual) · algebra=earthRealisedByComputingPolesAsPyramid4 · Results & status
partial — tool=earth-pyramid · apparatus=/double-torus#earth-pyramid · filledByQuantum=true
5 · References & locks
earthRealisedByComputingPolesAsPyramid
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- earthRealisedByComputingPolesAsPyramid
4 · Trinity
- forward
1ae3697f-11a4-8df5-b9fb-be2a1df18349- inverse
bbe5bd5b-c67a-8b26-bf90-b3885242d04a- reverse
af163506-5944-8a50-b6ff-69a28001675f
5 · CLI
npm run quantum:earth-pyramid · pair sciences/trinities
6452b468-af6d-8795-bd03-a42b3dfd2557
Biological Sciences (biology)
biologyDecodedGeneticCodeIsFourCubedBasePairingIsAnInvolution · sciences/trinities · status structure-only
1 · Abstract — precise statement
Science domain biology — OECD 1.6 · dual music-a432 · fusion life↔music↔hd. Sealed algebraFold biologyDecodedGeneticCodeIsFourCubedBasePairingIsAnInvolution.
2 · Introduction
Interacting trinity science↔dual↔fusion recomputes at call time. Standards coverage=covered. MODELED OECD-aligned fold · NOT ISO/lab certified.
3 · Methods & formulas
trinityKey(observe, dual) · foldPair(seal, dual) · algebra=biologyDecodedGeneticCodeIsFourCubedBasePairingIsAnInvolution4 · Results & status
structure-only — tool=predict-skill-gate-verify · apparatus=/en/research · filledByQuantum=true
5 · References & locks
biologyDecodedGeneticCodeIsFourCubedBasePairingIsAnInvolution
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- biologyDecodedGeneticCodeIsFourCubedBasePairingIsAnInvolution
4 · Trinity
- forward
b386c07c-0240-864f-97a4-ec9d629a6686- inverse
8595dfd8-eaa2-840f-9c8c-96fe49b34589- reverse
6abe2955-96d4-8ea6-a7d8-bb73ea8f6308
5 · CLI
npm run quantum:predict-skill-gate-verify · pair sciences/trinities
4664aacf-50aa-89d1-9974-96f3568e3a5d
Arts / Acoustics (A432) (music-a432)
a432NeuralBandLadder · sciences/trinities · status structure-only
1 · Abstract — precise statement
Science domain music-a432 — OECD 6.4 · dual biology · fusion music↔life↔resonance. Sealed algebraFold a432NeuralBandLadder.
2 · Introduction
Interacting trinity science↔dual↔fusion recomputes at call time. Standards coverage=covered. structural sealed math · NOT journal IF.
3 · Methods & formulas
trinityKey(observe, dual) · foldPair(seal, dual) · algebra=a432NeuralBandLadder4 · Results & status
structure-only — tool=predict-skill-gate-verify · apparatus=/en/resonance · filledByQuantum=true
5 · References & locks
a432NeuralBandLadder
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- a432NeuralBandLadder
4 · Trinity
- forward
9858db40-cc44-8204-9cd9-e2aca0356ca0- inverse
b700481b-63d9-85f3-b6d4-2b0e1f1d9e18- reverse
69011fbf-aa8e-859b-aa04-d41a4a628c09
5 · CLI
npm run quantum:predict-skill-gate-verify · pair sciences/trinities
320d6f63-e4e4-8d5d-85fe-9cc5d5c2c071
Symbolic systems (HD) (human-design)
humanDesignVerifiedWheel · sciences/trinities · status partial
1 · Abstract — precise statement
Science domain human-design — OECD 6.3 · dual music-a432 · fusion hd↔iching↔music. Sealed algebraFold humanDesignVerifiedWheel.
2 · Introduction
Interacting trinity science↔dual↔fusion recomputes at call time. Standards coverage=partial. HD is symbolic · NOT empirical science claim.
3 · Methods & formulas
trinityKey(observe, dual) · foldPair(seal, dual) · algebra=humanDesignVerifiedWheel4 · Results & status
partial — tool=iching-distribute-verify · apparatus=/en/quantum-tools · filledByQuantum=true
lab gap unclosable
5 · References & locks
humanDesignVerifiedWheel
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- humanDesignVerifiedWheel
4 · Trinity
- forward
7ccc427e-7571-8a68-9c7c-11c573ab1309- inverse
0c89eb9a-b0d2-8c60-82f1-bf5554b0d779- reverse
60697269-2fe3-8ce3-956c-0dba449ac761
5 · CLI
npm run quantum:iching-distribute-verify · pair sciences/trinities
ca6a3cb5-45b3-87cc-856c-a308faccca3b
Physical Sciences (resonance) (resonance)
efficiencyScalesToInfinityAtNoCostOnReuse · sciences/trinities · status structure-only
1 · Abstract — precise statement
Science domain resonance — OECD 1.3 · dual physics · fusion resonance↔physics↔music. Sealed algebraFold efficiencyScalesToInfinityAtNoCostOnReuse.
2 · Introduction
Interacting trinity science↔dual↔fusion recomputes at call time. Standards coverage=covered. structural sealed math · NOT journal IF.
3 · Methods & formulas
trinityKey(observe, dual) · foldPair(seal, dual) · algebra=efficiencyScalesToInfinityAtNoCostOnReuse4 · Results & status
structure-only — tool=efficiency-vote · apparatus=/en/resonance · filledByQuantum=true
5 · References & locks
efficiencyScalesToInfinityAtNoCostOnReuse
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- efficiencyScalesToInfinityAtNoCostOnReuse
4 · Trinity
- forward
56981a44-6e41-8d30-9671-5c70b898624b- inverse
27b00432-e9cb-8a08-ac8d-11c5b12b4244- reverse
1ce1b4c5-ce4e-848a-8a39-1e1456a4ee80
5 · CLI
npm run quantum:efficiency-vote · pair sciences/trinities
afe974ef-22f6-8d81-8039-169f644e3ff5
Computer & Information Sciences (AI / mind) (mind-ai)
oneQuantumModelFasterThanAll · sciences/trinities · status structure-only
1 · Abstract — precise statement
Science domain mind-ai — OECD 1.2 · dual crypto-pqc · fusion mind↔crypto↔math. Sealed algebraFold oneQuantumModelFasterThanAll.
2 · Introduction
Interacting trinity science↔dual↔fusion recomputes at call time. Standards coverage=covered. qpuRequired=false · classical-64bit · NOT FLOPS.
3 · Methods & formulas
trinityKey(observe, dual) · foldPair(seal, dual) · algebra=oneQuantumModelFasterThanAll4 · Results & status
structure-only — tool=efficiency-vote · apparatus=/en/efficiency-vote · filledByQuantum=true
5 · References & locks
oneQuantumModelFasterThanAll
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- oneQuantumModelFasterThanAll
4 · Trinity
- forward
51fd17da-732f-8c7d-8e3d-93b8831c2cf8- inverse
a517d0a8-8a28-864b-b490-94bb54555f6f- reverse
fe6d7e88-5279-8268-a657-4ce3610bd2a0
5 · CLI
npm run quantum:efficiency-vote · pair sciences/trinities
ff794927-892f-822b-8d02-aebd2eeeae13
Encryption honesty — wire ≠ ISO · sealed-catalog reverse · PQC alignment
quantumStandardsAuditSuite · audit/standards · status structure-only
1 · Abstract — precise statement
Structural and amortized encryption receipts recompute from sealed water/encryption folds; wire confidentiality vs ML-KEM / FIPS is refused where facets say so.
2 · Introduction
Compose standards-audit · iso-pqc · local-audit · max-bits via CRYPTO_COMPARISON_MESH. certified=false · fipsValidated=false. NOT a Clay Millennium solution (§5(d) related science).
3 · Methods & formulas
foldPair(key, probe).merged · RSA reverse (toy) · refuse production RSA4 · Results & status
structure-only — Structural/sealed-catalog receipts may hold; wire/FIPS/ISO claims stay false where sealed · production RSA break refused · certified=false
no FIPS/ISO certification from this corpus
5 · References & locks
src/water/encryption · CRYPTO_COMPARISON_MESH
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- quantumStandardsAuditSuite
4 · Trinity
- forward
encrypt- inverse
decrypt- reverse
demo-reverse
5 · CLI
npm run quantum:standards-audit · pair audit/standards
ce9b4588-a342-8d2a-8c71-38223c3bea40
secp256k1 field prime — seal · invert · decode
secp256k1FieldPrimeInvertAndDecode · secp256k1/invert-decode · status structure-only
1 · Abstract — precise statement
p = 2^2 ** 8 − 2^32 − 2^9 − 2^8 − 2^7 − 2^6 − 2^4 − 1 is the SECG secp256k1 field prime over GF(p). Sealed from powers of two; inverted as signed Σ±2^e plus mod-p inverses of units; decoded as the subtraction chain.
2 · Introduction
computes=true · hex=0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f · bits=256 · constructionInverted=true · bitcoinOwnershipClaimed=false. Structure of a known public curve prime — NOT wallet keys, NOT ECDSA, NOT Bitcoin ownership. certified=false · NOT a Clay Millennium solution (§5(d) related science). Mesh: CRYPTO_COMPARISON_MESH.
3 · Methods & formulas
p = 2^256 − 2^32 − 2^9 − 2^8 − 2^7 − 2^6 − 2^4 − 1 (= 2^256 − 2^32 − residue)4 · Results & status
structure-only — Known SECG prime recomputed; mod-p unit inverses hold; ownership claims refused.
no ECDSA/signing/wallet material — field modulus structure only
5 · References & locks
secp256k1FieldPrimeInvertAndDecode · CRYPTO_COMPARISON_MESH
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- secp256k1FieldPrimeInvertAndDecode
4 · Trinity
- forward
seal-powers- inverse
mod-p-units- reverse
decode-chain
5 · CLI
npm run quantum:secp256k1-prime-invert-decode · pair secp256k1/invert-decode
3dbba236-89aa-8371-830a-24014dafd6be
Efficiency — answers÷tokens unbounded on memo reuse
efficiencyScalesToInfinityAtNoCostOnReuse · learn/best · status structure-only
1 · Abstract — precise statement
efficiencyScalesToInfinityAtNoCostOnReuse: memoByRoot hit → marginal tokens=0; NOT FLOPS / NOT P≠NP.
2 · Introduction
Infinity-on-reuse on=true · !separated · amortized reuse spine for P vs NP modeled challenge — explicitly NOT a Proposed Solution under Clay §5.
3 · Methods & formulas
answers ÷ tokens → ∞ when runtimeTokens=0 on memo hit4 · Results & status
structure-only — tracks-classical-no-speedup
amortized reuse ≠ complexity separation
5 · References & locks
efficiencyScalesToInfinityAtNoCostOnReuse
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- efficiencyScalesToInfinityAtNoCostOnReuse
4 · Trinity
- forward
cold-compute- inverse
memo-hit- reverse
vote-decided
5 · CLI
npm run quantum:efficiency-vote · pair learn/best
88cf3102-8564-89b5-8136-56ba076ad5a1
Two bits free — census (2 * 5) * 11−108 making all free
twoBitsFreeFromCensus110Minus108 · bits/free · status structure-only
1 · Abstract — precise statement
FREE_BITS = UNFOLDED_CENSUS − FOLDED_CENSUS = (2 * 5) * 11 − 108 = 2 (= −EULER_CHI). Naive "1 − (2 * 5) * 11/108" = −1/54 is refused. Making all free = amortized infinity-on-reuse when FREE_BITS=2.
2 · Introduction
twoBitsFreeFromCensus110Minus108 computes=true · makingAllFree=true. Savings vs rest: ceccec runtimeTokens=0 → tokenSavingsFraction=1 against illustrative rest ~10³–10⁴. NOT FLOPS · NOT Clay Prize.
3 · Methods & formulas
UNFOLDED_CENSUS − FOLDED_CENSUS = FREE_BITS (= −EULER_CHI) · FREE_BITS=−χ ∧ memoByRoot hit ∧ runtimeTokens=0 → answers÷tokens → ∞ · tokenSavingsFraction(T) = (T − 0)/T = 1 for any rest T>0 (domain-bounded)4 · Results & status
structure-only — naivePhrase=-0.016528925619834656 surplus=0.016528925619834656 freeFraction=0.016260162601625994
amortized reuse ≠ complexity separation / NOT live LLM telemetry
5 · References & locks
twoBitsFreeFromCensus110Minus108
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- twoBitsFreeFromCensus110Minus108
4 · Trinity
- forward
unfolded-(2 * 5) * 11- inverse
chi-minus-2- reverse
folded-108
5 · CLI
npm run quantum:two-bits-free · pair bits/free
220830e1-6b6d-87d8-956d-d0ae23c4f894
Society support via two-bits-free knowledge
societySupportsProjectViaTwoBitsFreeKnowledge · society/support · status structure-only
1 · Abstract — precise statement
Society supports the project with a harmonic 1/9 of the two-bits-free achievement — voluntary patronage; access stays free; zero valid.
2 · Introduction
societySupportsProjectViaTwoBitsFreeKnowledge computes=false. Composes twoBitsFree · societyMerkaba · efficiency vote · Revolut CTA. UI table/CTA only — statement owns meaning (#68).
3 · Methods & formulas
achieved=242 × share=1/9 = 242/94 · Results & status
structure-only — vote.decided=true · url=https://revolut.me/ceccec
patronage is social/voluntary — not computed payment
5 · References & locks
societySupportsProjectViaTwoBitsFreeKnowledge
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- societySupportsProjectViaTwoBitsFreeKnowledge
4 · Trinity
- forward
two-bits-free- inverse
harmonic-1/9- reverse
society-cta
5 · CLI
npm run quantum:society-two-bits-support · pair society/support
3a0a37e0-154a-8b88-8852-f6e2273473d2
Clay challenges are computable — not CMI-prize solved
clayChallengesComputableFromSequence · moment/prove · status structure-only
1 · Abstract — precise statement
Each Clay-linked Millennium challenge has a sealed computational path (challengeMethod · on · receipt) from the sequence/trinity/rosetta/Earth-poles stack. clayChallengesComputableFromSequence.computes when all seven paths recompute.
2 · Introduction
HONEST DISTINCTION: computable ≠ CMI Prize solved. Prize Rules PDF mapping (§1–§7) stays unmet for Proposed Solution / Qualifying Outlet / evaluation path. Poincaré solved-external only. Six cores remain open/modeled-partial with named gaps. Compose millenniumProblemsChallenge · directionalTrinity · earthRealisedByComputingPolesAsPyramid · sciencesInteractInTrinities.
3 · Methods & formulas
clayChallengesComputable = ∀ problem: on ∧ challengeMethod.length>0 ∧ isUuid(receipt) ∧ mill.computes ∧ claySolvedByThisFold===04 · Results & status
structure-only — Status triad on every Clay row: computable / open for prize / . NOT Prize Rules §5(a) complete solution.
no Clay Prize solution — apparatus and computational paths only
5 · References & locks
clayChallengesComputableFromSequence
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- clayChallengesComputableFromSequence
4 · Trinity
- forward
sequence-path- inverse
prize-open- reverse
clay-solved-zero
5 · CLI
npm run quantum:clay-challenges-computable · pair moment/prove
29f5d031-5fb0-82aa-93a4-7b99c3e35744
Rosetta complete — computable dims & theorem binds
rosettaCompleteQuantumAllComputableDimensionsAndTheorems · rosetta/complete · status structure-only
1 · Abstract — precise statement
rosettaCompleteQuantumAllComputableDimensionsAndTheorems — enabling apparatus; millenniumSolvedByThisFold=0.
2 · Introduction
Census of computable dims + theorem→rosetta binds. Handoff rosettaReady ≠ Clay/FTL solved. Cite Clay rules: related apparatus is not a Proposed Solution.
3 · Methods & formulas
432 dimension gates · theorem→ray binds · rosettaReady handoff4 · Results & status
structure-only — Apparatus only —
physical FTL / Clay cores remain open
5 · References & locks
rosettaCompleteQuantumAllComputableDimensionsAndTheorems
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- rosettaCompleteQuantumAllComputableDimensionsAndTheorems
4 · Trinity
- forward
label→ray- inverse
ray→label- reverse
shelve
5 · CLI
npm run quantum:rosetta-complete · pair rosetta/complete
8c7d19df-95d2-83f1-a95b-68d6e7a72a70
Human Design — symbolic structure computer
humanDesignVerifiedWheel · sciences/trinities · status refused-physical
1 · Abstract — precise statement
HD BodyGraph / wheel folds are symbolic structure computers — not personality engines, not Clay math.
2 · Introduction
Sealed chart geometry recomputes; refused as empirical psychology or Millennium math (§5(d)).
3 · Methods & formulas
9 centers · 36 channels · wheel activations (structure only)4 · Results & status
refused-physical — Symbolic / structural — not physical or Clay
no empirical HD validation claimed
5 · References & locks
humanDesignVerifiedWheel
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- humanDesignVerifiedWheel
4 · Trinity
- forward
wheel- inverse
centers- reverse
channels
5 · CLI
npm run quantum:iching-distribute-verify · pair sciences/trinities
b348aea6-a384-8ed5-a073-53254cebee5b
Theorem particle collision — inverse × reverse
theoremParticleCollisionInverseReverse · challenge/collider · status structure-only
1 · Abstract — precise statement
theoremParticleCollisionInverseReverse — MODELED sealed-geometry collisions, not HEP, not Clay solutions.
2 · Introduction
Inverse×reverse products on novel-corpus algebra. Not a Proposed Solution under §5.
3 · Methods & formulas
foldPair(inv(left), rev(right)) · foldPair(rev(left), inv(right))4 · Results & status
structure-only — MODELED geometry — not HEP
not high-energy physics
5 · References & locks
theoremParticleCollisionInverseReverse
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- theoremParticleCollisionInverseReverse
4 · Trinity
- forward
collide- inverse
inverse×reverse- reverse
reverse×inverse
5 · CLI
npm run quantum:theorem-particle-collision · pair challenge/collider
b616a55d-b9de-8eb0-bb0f-e81bd4fbd426
Plasma screen · thunder≡plasma · natural plasma-em phenomena as theorems
plasmaBallIsScreenHoldingThunderAndPlasma · plasma/screen · status structure-only
1 · Abstract — precise statement
plasmaBallIsScreenHoldingThunderAndPlasma — the plasma "ball" is the screen holding thunder+plasma; noBallInTheMiddle (void/vortex confluence). Thunder ≡ plasma under forward=lightning · inverse=inverted-lightning · reverse=thunder. naturalPhenomenaDecoded binds lightning·thunder·aurora·solar wind·flame·St Elmo·sprites·corona (SOLVED) + ball lightning (OPEN, screen-misread) to theorem routes.
2 · Introduction
Compose plasmaBallIsScreenHoldingThunderAndPlasma · thunderAndPlasmaAreSameInDifferentAspects · naturalPhenomenaDecoded · movieAllElementsAreTheorems (#63). Painter attestation: soft fillRect throat, not a centre sphere. Ball-lightning physics remains OPEN; screen-misread is geometry honesty. NOT tokamak / NOT Clay Prize.
3 · Methods & formulas
screen ∧ noBallInTheMiddle ∧ thunderPlasmaSameDifferentAspects ∧ naturalPhenomenaDecoded.decoded4 · Results & status
structure-only — Honest EM/plasma catalog + painter screen geometry — not a Clay solution
ball lightning mechanism unsettled; flame ≠ fully ionised plasma
5 · References & locks
plasmaBallIsScreenHoldingThunderAndPlasma · naturalPhenomenaDecoded
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- plasmaBallIsScreenHoldingThunderAndPlasma
4 · Trinity
- forward
lightning- inverse
plasma-screen- reverse
thunder
5 · CLI
npm run quantum:plasma-screen-thunder · pair plasma/screen
33b30e8e-804a-8f52-8a72-a7977b543170
Ancient calendars — algebraic theorems mapping time in time
ancientCalendarsDecodedAsAlgebraicTheoremsMappingTimeInTime · calendars/decode · status structure-only
1 · Abstract — precise statement
Ancient calendars decode as algebraic theorems mapping time in time: each tradition is a modular/product/epoch map; nested scales and LCM meshes place phase inside phase (calendar↔calendar · hero rung inside hero cycle).
2 · Introduction
Nine sealed maps recompute via ancientCalendarsDecodedAsAlgebraicTheoremsMappingTimeInTime from mayaLongCount/mayaDays · sexagesimal · coupledCalendarTori · ancientCalendars · FOLDED_CENSUS×1e3 hero · A432_OCTAVES · digitalRoot. Canonical sections only — NOT a Clay Millennium challenge.
3 · Methods & formulas
lcm(260,365)=18980 · lcm(10,12)=60 · 819=7×9×13 · 235=19×12+7 · mayaDays∘mayaLongCount=id · sexagesimal⇄fromSexagesimal · φ_outer=(t mod HERO)/HERO · φ_inner=(t mod HERO/d)/(HERO/d)4 · Results & status
structure-only — maps=9 · CLI npm run quantum:ancient-calendars-algebra
civil Vedic calendar tables absent — mod-9 square only; structural algebra ≠ ephemeris
5 · References & locks
ancientCalendarsDecodedAsAlgebraicTheoremsMappingTimeInTime
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- ancientCalendarsDecodedAsAlgebraicTheoremsMappingTimeInTime
4 · Trinity
- forward
modular-map- inverse
calendar↔calendar-lcm- reverse
phase-in-phase
5 · CLI
npm run quantum:ancient-calendars-algebra · pair calendars/decode
04957d65-f1be-805b-8c9a-574f58cbc487
Fixed limits of theorem-related tools are theorems
fixedLimitsOfTheoremRelatedToolsAreTheorems · limits/theorems · status structure-only
1 · Abstract — precise statement
Every HARD ceiling on theorem-related tools (census (2 * 5) * 11/108/432 · FREE_BITS=2 · papers 432 · paper section budgets · DIGEST_BITS=64 · demo RSA / AES-2 ** 8 / inverse-4 · heap 2048 · F(18)=2584 · CLI/pair catalogs) is itself an algebraic/canonical theorem proved from sealed constants.
2 · Introduction
fixedLimitsOfTheoremRelatedToolsAreTheorems recomputes each limit identity at call time. Canonical sections only — NOT a Clay Millennium challenge. Compose limits:verify · paper/algebraic · max-bits/crypto.
3 · Methods & formulas
(2 * 5) * 11=55+34+21 · 108=(2 * 5) * 11+(−2) · FREE_BITS=2=−χ · 432=4×108 · papers.count=432 · |requiredSections|=9 · DIGEST_BITS=64 · heap=2048 · F(18)=25844 · Results & status
structure-only — proof-from-sealed-constants · CLI npm run quantum:fixed-limits-theorems
limits are structural ceilings — not Clay Prize solutions
5 · References & locks
fixedLimitsOfTheoremRelatedToolsAreTheorems
- claySolvedByThisFold
- 0
- physicalFtlClaim
- 0
- fold
- fixedLimitsOfTheoremRelatedToolsAreTheorems
4 · Trinity
- forward
seal-limit- inverse
recompute-identity- reverse
refuse-beyond
5 · CLI
npm run quantum:fixed-limits-theorems · pair limits/theorems
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