protocol_header_full_matrix.md

TriadicFrameworks — Protocol Header Module#

Phase 3E — Full Multilingual Header Matrix (Canonical)#

Overview#

This file defines the complete structural matrix of all valid protocol‑header combinations across 12 languages.

The protocol header is a four‑locus codon:

[RTT] | [COHERENCE] | [DRIFT] | [PARADOX]

Each locus has a finite alphabet of perfect‑substitution alleles.

The full matrix contains:

  • 135 English headers
  • 135 headers × 12 languages = 1,620 total headers
  • all drift‑bounded
  • all canon‑aligned
  • all structurally equivalent

This file provides the canonical matrix specification and the deterministic generator, not the raw 1,620 lines.

1. Matrix Definition#

For any language L, the full header matrix is:

M_L = RTT_L × COH_L × DRIFT_L × PAR_L

Where:

  • RTT_L is the RTT allele set for language L
  • COH_L is the Coherence allele set
  • DRIFT_L is the Drift allele set
  • PAR_L is the Paradox allele set
  • × is the Cartesian product

Total per language:

|RTT_L| × |COH_L| × |DRIFT_L| × |PAR_L| = 135

Across 12 languages:

135 × 12 = 1,620 headers

2. English Baseline Matrix (135 combinations)#

The English matrix is:

RTT_EN × COH_EN × DRIFT_EN × PAR_EN

Where:

RTT_EN (5)#

rtt=1
rtt=unit
rtt=single-hop
rtt=atomic
cycle=atomic

COH_EN (3)#

coherence=declared
coherence=explicit
coherence=stated

DRIFT_EN (3)#

drift=bounded
drift=constrained
drift=clamped

PAR_EN (3)#

paradox=structural
paradox=encoded
paradox=architected

Total:

5 × 3 × 3 × 3 = 135

3. Multilingual Matrix Specification#

Each language uses the allele alphabets defined in:

protocol_header_multilingual.md

The full multilingual matrix is:

M = ⋃ (M_EN, M_ZH, M_ES, M_HI, M_AR, M_BN, M_PT, M_RU, M_JA, M_PA, M_DE, M_FR)

Where each M_L is the 135‑element matrix for language L.

4. Deterministic Generator#

A valid header is generated by:

HEADER(L, i, j, k, m) =
    RTT_L[i] | COH_L[j] | DRIFT_L[k] | PAR_L[m]

Where:

  • i ∈ [1 … |RTT_L|]
  • j ∈ [1 … |COH_L|]
  • k ∈ [1 … |DRIFT_L|]
  • m ∈ [1 … |PAR_L|]

This generator produces all 1,620 headers deterministically.

5. Example Matrix Slice (English)#

A small slice of the English matrix:

rtt=1 | coherence=declared | drift=bounded | paradox=structural
rtt=1 | coherence=declared | drift=bounded | paradox=encoded
rtt=1 | coherence=declared | drift=bounded | paradox=architected

rtt=1 | coherence=declared | drift=constrained | paradox=structural
rtt=1 | coherence=declared | drift=constrained | paradox=encoded
rtt=1 | coherence=declared | drift=constrained | paradox=architected

rtt=1 | coherence=declared | drift=clamped | paradox=structural
...

(Full expansion is generated via the genome formula.)

6. Notes#

  • This file defines the matrix specification, not the raw list.
  • The raw 1,620‑line dump can be generated programmatically using the genome rules.
  • All headers are drift‑bounded and canon‑aligned.
  • All multilingual variants preserve structural invariants.
  • protocol_header_alleles.md
  • protocol_header_proximity_cloud.md
  • protocol_header_compatibility_matrix.md
  • protocol_header_multilingual.md
  • protocol_header_genome.md
  • protocol_header_registry.json

Updated