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49 lines
2.2 KiB
Markdown
49 lines
2.2 KiB
Markdown
# Burgers Harmonic Peeling — Witness Grammar Verification
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**Commit title:** `docs: add witness grammar verification from Burgers harmonic peeling`
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**One-line law:**
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> 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.
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## 1. Burgers Toy → WitnessGrammar Mapping
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```
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S(x) = sin(x) + 0.3 sin(2x) + 0.1 sin(3x)
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```
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| Role | ν | a | Lean Mapping |
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|-----------|-----|-------|--------------------------------------|
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| Carrier | 1.0 | 1.0 | `WitnessRole.carrier` → BHOCS |
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| Texture 1 | 2.0 | 0.3 | `WitnessRole.texture` → FAMM |
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| Texture 2 | 3.0 | 0.1 | `WitnessRole.texture` → FAMM |
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Implemented in `WitnessGrammar.capacityConstrainedBatchTransformer`.
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## 2. Key Mathematical Results
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| Result | Equation | Role in Stack |
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|--------|----------|---------------|
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| Viscosity stiffening | `ν_eff = ν_0 (1 + Ω)` | Trapping mechanism |
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| Quantum pressure | `Q_eff = (1 + κ Ω) Q` | Singularity regularization |
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| Stiffening factor | `κ = 0.3547` (35.47%) | Global bound safety margin |
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| Solidification | `E_eff = E_0 (1 + κ Ω)` | Phase transition to crystal |
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| Phonon drain | `Γ_drain ∝ Ω²` | Residual energy dissipation |
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| Brillouin bound | `\|∇u\| ≤ ℏ k_max / m` | Gradient ceiling |
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| Dispersion | `ω(k) = c_s k √(1 + κ Ω(k))` | Band gap / noise forbidden |
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## 3. Module Connections
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- `WitnessGrammar.lean` — stores ν/a/φ/role decomposition
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- `CoulombComplexity.lean` — polarity from amplitude sign (carrier +, texture −)
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- `SigmaGate` — confidence scoring on grammar match quality
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- `BHOCS` — commits carrier-witness nodes
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- `FAMM` — drains texture-witness stress energy
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## 4. What Remains Theoretical
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- Full BEC/GPE collapse proof (requires `ℏ` and `m` in simulation units)
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- Brillouin zone enforcement as explicit lattice constraint
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- Phonon drain as time-step dissipative term in NBody state update
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- Young's modulus tensor from stiffening in 3D manifold coordinates
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Source research log: `/home/allaun/Downloads/mathholes.md`
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