Witness Grammar Specification

One-Line Law

FNWH decompiles fields into witness grammars; Equation Sniffers compare those grammars; the market filter searches for shared behavioral operators, not shared nouns.

What is a Witness Grammar?

A Witness Grammar is the finite symbolic source code recovered from a field. It stores the active witnesses, their amplitudes / frequencies / phases, their routing roles, and a residual receipt.

From the Burgers/FNWH visual verification:

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

yields the finite witness grammar:

Role	ν (frequency)	a (amplitude)
Carrier	1.0	1.0
Texture 1	2.0	0.3
Texture 2	3.0	0.1

Pipeline

Raw field
  → FNWH peeling
  → WitnessGrammar
  → EquationSniffer
  → route suggestion
  → MassNumberField
  → BHOCS / FAMM

Equation Sniffers do not inspect raw data directly; they sniff witness grammars.

Equation Sniffer Input (YAML prototype)

EquationSnifferInput:
  grammar:
    - role: Carrier
      v: 1.0
      a: 1.0
    - role: Texture
      v: 2.0
      a: 0.3
    - role: Texture
      v: 3.0
      a: 0.1
  residual:
    energy: 0
    status: CLOSED

Market-Data Bridge

The market version applies the same pipeline to ontologically unrelated systems:

price / volume / news / fundamental stream
  → rolling signal field
  → witness grammar
  → behavioral operator class
  → filter score

Asset field example

S_a(t) = return carrier + volatility texture + liquidity basin + residual stress

Witness grammar:

Component	Role
Carrier	market regime
Texture	volatility shock
Basin	macro drift
Residual	unexplained risk

Market Filter Prototype

Behavioral class: capacity_constrained_batch_transformer

This class unifies:

shipping containers
DNA sequencing
grandmother's cookies
semiconductor fabs
clinical labs
warehouses
bakeries
ports

First test: Can the manifold cluster ontologically unrelated things by shared operational dynamics?

Filter score:

S(a, Q) = exp(-d(M_a, Q) / σ) · B(M_a) / (1 + τ(M_a, Q))

Where:

Symbol	Meaning
M_a	witness / manifold point for asset a
Q	query prototype (behavioral class)
d	behavioral distance
B	binding / pattern stability
τ	turbulence / unresolved mismatch
σ	distance temperature

High score = asset behaves like the query pattern.
Low score = asset does not match or is too turbulent.

Commit Note

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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