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SilverSight/6-Documentation/docs/specs/LEAN_BAKER_ANALOGUE_SKELETON.md
allaun 6b26a9bc6e fix: address adversarial review findings 
Architecture fixes:
- Fixed phantom Semantics.* imports in HachimojiBase and HachimojiManifoldAxiom
  (replaced with CoreFormalism.* and SilverSight.* imports)
- RRCLib.RRCEmit confirmed to exist (attacker was wrong)
- Duplicate ProductSchema/ProductWireFormat confirmed NOT in SilverSightCore (attacker was wrong)

Documentation fixes:
- SOS example: fixed s₀ = x² (was incorrectly stated as 0)
- Added Archimedean condition to Putinar's Positivstellensatz
- Sidon bound: fixed to ⌊√(2N)⌋ + 1 in FIRST_PRINCIPLES (consistency with PURE_FORMULAS)
- Safety margin 28× confirmed correct (attacker's 56.7× was wrong — they confused ppm with ×10^-6)

Lean proof status:
- repunit function: documented as 'repunit characteristic' (not mathematical repunit)
- chentsov_50: 7 sorries remain (type bridge + chentsov_theorem internal sorries)
- Fisher metric bridge: cross-term 1/p₀ correctly identified and documented
2026-06-23 08:28:30 -05:00

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FAMM-Sidon-Baker Analogue — Lean Formalization Sketch

File: Semantics.FAMMBaker.SidonVCN.lean

-- Sidon projection and collision structure
def sidonProjection (addr : Fin 8) : Nat := addr.val

structure SidonCollision where
  i j k l : Fin 8
  hneq : {i, j} ≠ {k, l}

-- Collapse functional (linear form in logs)
def collapseFunctional (collisions : List SidonCollision) : Q16_16 :=
  collisions.foldl (· + ·) 0  -- weighted sum

-- Scar energy measure
def scarEnergy (state : BraidState) : Q16_16 :=
  state.ene.scars.foldl (· + ·.pressure.toQ16_16) 0

-- Main theorem skeleton
theorem fammySidonBakerRigidity 
  (state : BraidState) 
  (hcoll : collapseFunctional (findCollisions state) = 0) :
  scarEnergy state > 0 := by
  -- Either collapse is structurally impossible (rigidity)
  -- Or it produces scar energy
  sorry

Next steps:

  1. Add to lakefile.toml under lean_libs
  2. Create SilverSight/0-Core-Formalism/lean/Semantics/FAMMBaker/
  3. Wire into RRC alignment pipeline