mirror of https://github.com/allaunthefox/SilverSight.git synced 2026-07-31 01:25:21 +00:00

allaun 78f211a611 docs: reorganize claim status, separate proven from hypothetical

CLAIMS_STATUS.md:
- §1: PROVEN (Lean theorems + exact identities)
- §2: COMPUTATIONAL WITNESS (#eval, axioms with receipts)
- §3: STRUCTURAL (proven for n=8, general pending)
- §4: UNPROVEN / EXPLORATORY (not claimed as established)
- §5: ROUTES UNDER INVESTIGATION (Noether, Rossby, E8, Ingest)
- §6: NAMING CONVENTION (theorem/axiom/conjecture/route)

noether_route.md:
- Explicitly framed as 'route under investigation'
- What's proven: Cartan arithmetic (independent of Noether)
- What's proposed: Lagrangian on S⁷ → Noether charges → same integers
- Plausibility arguments: for and against
- Prerequisites: 4-step proof chain
- Risk assessment: high difficulty but nothing reliant on it breaks

The Cartan proof stands independently. Noether is a possible
deepening, not a retroactive justification.

2026-06-30 19:58:17 -05:00

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SilverSight Formal Claims — Status Map

Date: June 30, 2026 Principle: Every claim is tracked to its proof status. Nothing claimed without provenance.

§1 — PROVEN (Lean theorem or exact identity)

Claim	Source	Method
σ = 39/256 (8-strand Cartan spectral radius)	`PIST/CartanConnection.lean:66-81`	`simp` + integer arithmetic
τ = 1/7 (Sidon doubling threshold)	`CoreFormalism/BraidStateN.lean`	structural from n=8
D = lcm(256, 7) = 1792	`PIST/CartanConnection.lean:66`	`lcm(256,7) = 1792`
∆ = σ − τ = 17/1792 > 0	`PIST/UnifiedCovariant.lean:100`	`13×7 − 256 = 17`
π₀(Diff⁺(S⁶)) ≅ ℤ₂₈	Kervaire-Milnor (1963)	external reference
28 = 7 × 4 = (n−1) × c	`HopfFibration.lean:112`	`Finset.card` on `Fin 28`
Rossby step count increase	`BraidStateN.lean:278`	`rfl` (crossStep always +1)
Rossby drift active for chiral labels	`BraidStateN.lean:288`	`rfl` (unfold)
Kelvin drift inactive for achiral	`BraidStateN.lean:292`	`rfl` (unfold)
AVM ISA arithmetic (12 ports)	`docs/avm_ports_audit.md`	cross-port test harness
Wolfram-verified AVM constants	`signatures/avm_verification_receipt.json`	4/4 verified

§2 — COMPUTATIONAL WITNESS (specific instances proven by evaluation)

Claim	Source	Method
Rossby energy ≤ initial energy (n=8 test state)	`BraidStateN.lean:296`	`#eval` via `crossingEnergy`
E8 level sets N=8,16,32,64 are Sidon	`E8Sidon.lean:44-56`	axiom (computational receipt)
Rossby energy dissipation rate (step bound)	`BraidStateN.lean:278`	proven (step count increment)
8-strand corkscrew-Durán correspondence	`HopfFibration.lean:120`	axiom

§3 — STRUCTURAL (proven for n=8, general n pending)

Claim	Status	Blocker
Hopf Portability Criterion (6 conditions)	Conditions documented, classification verified for n=8	Σ_general needs σ derivation for other Lie types
Spectral gap factorization 28 = 4×7	Proven for n=8	For n≠8: c varies, π₀ varies
15 domain templates classified	3 via strong structural match; 12 via analogical	Formal proofs only for n=8 braid domain

§4 — UNPROVEN / EXPLORATORY (not claimed as established)

Claim	Status	Notes
Noether's theorem maps S⁷ Lagrangian → conserved currents	Unproven	Possible route. Requires explicit Lagrangian on total space of Hopf fibration, Noether charge computation. Not yet formalized.
"Unified field theory of computation"	Not claimed	Premature framing. The Hopf portability criterion classifies structural analogs; does not prove computational equivalence.
Rossby wave ↔ chiral braid correspondence	Conjecture	Documented in `docs/rotational_wave_braid_correspondence.md`. Structural analogy only.
28 regimes bound all Hopf-portable problems	Conditional	Follows IF a problem satisfies all 6 portability conditions. The "all" quantifier is unproven.
Exotic diffeomorphism = braid crossing identity	Axiom	`duran_is_braid_crossing` in HopfFibration.lean is an axiom, not a theorem.
ε ≥ 1/4 for Erdős 30	Conditional	Depends on `e8_levelset_sidon` for general N (currently axiomatic for N≤64).

§5 — ROUTES UNDER INVESTIGATION (possible next proofs)

Route 1: Noether on S⁷ Lagrangian

Prerequisites:
  □ Define Lagrangian density ℒ on S⁷ (qua total space of Hopf fibration)
  □ Identify continuous symmetry group SU(2) × SU(2)
  □ Apply Noether's first theorem → conserved currents
  □ Map conserved charge spectrum → Cartan integer a = 39
  □ Verify that broken generators count = 17 (the gap numerator)
Status: Not started. Plausible but requires new formalization.

Route 2: Rossby Energy Monotonicity (general n)

Prerequisites:
  □ Prove crossingEnergy(s') ≤ crossingEnergy(s) for crossStep
  □ Prove strict inequality under Rossby drift
  □ Bound decrease rate by chiral asymmetry
Status: Stub exists (rossby_energy_monotone axiom).
  Computational witness for n=8 only.

Route 3: E8 Sidon (structural, not computational)

Prerequisites:
  □ Unblock sigma3_multiplicative (needs Mathlib Nat.divisors_mul)
  □ Prove e8_levelset_sidon for general N (smooth number theory)
  □ Derive ε ≥ 1/4 unconditionally
Status: Computational (N≤64) witnessed. Structural blocked.

Route 4: Ingest Bridge Implementation

Prerequisites:
  □ Python classifier accepting problem metadata
  □ 6-condition checker
  □ Receipt emission in AVM-compatible format
Status: Spec written (docs/hopf_ingest_bridge.md). Not implemented.

§6 — NAMING CONVENTION

Theorem: Proven in Lean with explicit proof
Lemma: Auxiliary proven statement
Axiom: Accepted without Lean proof (annotated with TODO)
#eval witness: Computational receipt for specific values
Conjecture: Claimed but not proven (annotated with TODO)
Route: Plausible investigation path (not yet claimed)

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