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125 lines
3 KiB
Markdown
125 lines
3 KiB
Markdown
# Witness Grammar Specification
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## One-Line Law
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> FNWH decompiles fields into witness grammars; Equation Sniffers compare those grammars; the market filter searches for shared behavioral operators, not shared nouns.
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## What is a Witness Grammar?
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A **Witness Grammar** is the finite symbolic source code recovered from a field.
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It stores the active witnesses, their amplitudes / frequencies / phases, their routing roles, and a residual receipt.
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From the Burgers/FNWH visual verification:
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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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yields the finite witness grammar:
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| Role | ν (frequency) | a (amplitude) | phase |
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|-----------|---------------|---------------|-------|
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| Carrier | 1.0 | 1.0 | 0 |
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| Texture 1 | 2.0 | 0.3 | 0 |
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| Texture 2 | 3.0 | 0.1 | 0 |
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## Pipeline
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```
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Raw field
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→ FNWH peeling
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→ WitnessGrammar
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→ EquationSniffer
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→ route suggestion
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→ MassNumberField
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→ BHOCS / FAMM
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```
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Equation Sniffers do not inspect raw data directly; they **sniff witness grammars**.
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## Equation Sniffer Input (YAML prototype)
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```yaml
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EquationSnifferInput:
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grammar:
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- role: Carrier
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v: 1.0
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a: 1.0
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- role: Texture
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v: 2.0
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a: 0.3
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- role: Texture
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v: 3.0
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a: 0.1
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residual:
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energy: 0
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status: CLOSED
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```
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## Market-Data Bridge
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The market version applies the same pipeline to ontologically unrelated systems:
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```
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price / volume / news / fundamental stream
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→ rolling signal field
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→ witness grammar
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→ behavioral operator class
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→ filter score
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```
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### Asset field example
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```
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S_a(t) = return carrier + volatility texture + liquidity basin + residual stress
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```
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Witness grammar:
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| Component | Role |
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|-----------|--------------------|
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| Carrier | market regime |
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| Texture | volatility shock |
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| Basin | macro drift |
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| Residual | unexplained risk |
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## Market Filter Prototype
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**Behavioral class:** `capacity_constrained_batch_transformer`
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This class unifies:
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- shipping containers
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- DNA sequencing
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- grandmother's cookies
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- semiconductor fabs
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- clinical labs
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- warehouses
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- bakeries
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- ports
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**First test:** Can the manifold cluster ontologically unrelated things by shared operational dynamics?
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**Filter score:**
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```
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S(a, Q) = exp(-d(M_a, Q) / σ) · B(M_a) / (1 + τ(M_a, Q))
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```
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Where:
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| Symbol | Meaning |
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|--------|----------------------------|
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| M_a | witness / manifold point for asset a |
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| Q | query prototype (behavioral class) |
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| d | behavioral distance |
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| B | binding / pattern stability |
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| τ | turbulence / unresolved mismatch |
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| σ | distance temperature |
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High score = asset behaves like the query pattern.
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Low score = asset does not match or is too turbulent.
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## Commit Note
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This spec documents the verified Burgers-harmonic peeling transition from visual proof to executable primitive. The next step is real-data validation, not more theory.
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