Research-Stack/6-Documentation/docs/specs/BurgersHarmonicPeelingVerification.md

Burgers Harmonic Peeling — Witness Grammar Verification

Commit title: docs: add witness grammar verification from Burgers harmonic peeling

One-line law:

FNWH decompiles fields into witness grammars; Burgers non-linearity traps the expansion; BEC collapse regularizes the singularity; crystallization bounds the field; phonon draining clears the residual; Brillouin zones forbid the chaos.

1. Burgers Toy → WitnessGrammar Mapping

S(x) = sin(x) + 0.3 sin(2x) + 0.1 sin(3x)

Role	ν	a	Lean Mapping
Carrier	1.0	1.0	WitnessRole.carrier → BHOCS
Texture 1	2.0	0.3	WitnessRole.texture → FAMM
Texture 2	3.0	0.1	WitnessRole.texture → FAMM

Implemented in WitnessGrammar.capacityConstrainedBatchTransformer.

2. Key Mathematical Results

Result	Equation	Role in Stack
Viscosity stiffening	ν_eff = ν_0 (1 + Ω)	Trapping mechanism
Quantum pressure	Q_eff = (1 + κ Ω) Q	Singularity regularization
Stiffening factor	κ = 0.3547 (35.47%)	Global bound safety margin
Solidification	E_eff = E_0 (1 + κ Ω)	Phase transition to crystal
Phonon drain	Γ_drain ∝ Ω²	Residual energy dissipation
Brillouin bound	|∇u| ≤ ℏ k_max / m	Gradient ceiling
Dispersion	ω(k) = c_s k √(1 + κ Ω(k))	Band gap / noise forbidden

3. Module Connections

• WitnessGrammar.lean — stores ν/a/φ/role decomposition
• CoulombComplexity.lean — polarity from amplitude sign (carrier +, texture −)
• SigmaGate — confidence scoring on grammar match quality
• BHOCS — commits carrier-witness nodes
• FAMM — drains texture-witness stress energy

4. What Remains Theoretical

• Full BEC/GPE collapse proof (requires ℏ and m in simulation units)
• Brillouin zone enforcement as explicit lattice constraint
• Phonon drain as time-step dissipative term in NBody state update
• Young's modulus tensor from stiffening in 3D manifold coordinates

Source research log: /home/allaun/Downloads/mathholes.md