docs: unify structural tetrad and OZ→IL telemetry as single canonical sources

- STRUCTURAL_FIELDS_TETRAD.md: marked as canonical tetrad definitions source
- U6_STRUCTURAL_FIELD_TETRAD.md: clarified it assumes definitions from tetrad doc
- EXTENDED_FIELDS_INTEGRATION_SUMMARY.md: removed duplicate tetrad table, now references canonical docs
- AGENTS.md: trimmed field descriptions to bullets with canonical links
- src/tnfr/physics/README.md: enhanced as unified physics hub with links to canonical tetrad, grammar, and OZ→IL telemetry docs

Result: eliminates documentation redundancy, establishes clear single sources of truth for Φ_s, |∇φ|, K_φ, ξ_C definitions and OZ→IL precision walk telemetry

Author: fer

AGENTS.md

@@ -19,6 +19,8 @@
 - Measure **resonance**, not properties
 - Think **structure**, not substance
 
+**Language Policy (English Only)**: All documentation, code comments, commit messages, issues, and pull request descriptions MUST be written in English. Non-English text is allowed only inside verbatim quotations of external sources or raw experimental data. Mixed-language normative content will be rejected. This guarantees a single canonical terminology set for TNFR physics and grammar.
+
 All code, documentation, and interactions must align with TNFR physics. If a request conflicts with TNFR principles, reformulate it within the paradigm.
 
 ---
@@ -349,34 +351,49 @@ The grammar is not arbitrary—it emerges **inevitably** from TNFR physics.
 
 ---
 
+### Phase 5 Bifurcation Telemetry (Completed)
+
+- Metrics: `delta_phi_s`, `delta_phase_gradient_max`, `delta_phase_curvature_max`, `coherence_length_ratio`, `delta_dnfr_variance`, `bifurcation_score_max`, `handlers_present`, `classification`.
+- Classification: `none | incipient | bifurcation | fragmentation` using thresholded spikes/ratios.
+- CLI: `benchmarks/bifurcation_landscape.py` with `--nodes`, `--seeds`, `--topologies`, `--oz-intensity-grid`, `--vf-grid`, `--mutation-thresholds` and thresholds `--bifurcation-score-threshold`, `--phase-gradient-spike`, `--phase-curvature-spike`, `--coherence-length-amplification`, `--dnfr-variance-increase`, `--structural-potential-shift`, `--fragmentation-coherence-threshold`.
+- JSONL: emitted per grid point; omit `--quiet` to capture output.
+- Canonicity: read-only capture; operator-only EPI changes; IL/THOL handlers enforced; phase checks per U3; stabilizers per U2/U4.
+
+---
+
 ## 🛡️ Canonical Invariants (NEVER BREAK)
 
 These define TNFR canonicity and MUST be preserved:
 
 ### 1. EPI as Coherent Form
+
 - Changes ONLY via structural operators
 - No ad-hoc mutations
 - **Grammar**: U1 (INITIATION & CLOSURE)
 - **Test**: Verify all EPI changes go through operators
 
 ### 2. Structural Units
+
 - νf in Hz_str (structural hertz)
 - Never relabel or mix units
 - **Test**: Check all frequency assignments
 
 ### 3. ΔNFR Semantics
+
 - Sign/magnitude modulate reorganization
 - NOT an ML "error" or "loss gradient"
 - **Grammar**: U2 (CONVERGENCE)
 - **Test**: Verify ΔNFR physical interpretation
 
 ### 4. Operator Closure
+
 - Operator composition → valid TNFR states
 - New functions map to existing operators or defined as new operator
 - **Grammar**: U1b (closure), U4 (bifurcation)
 - **Test**: Verify operator sequences pass grammar
 
 ### 5. Phase Verification
+
 - No coupling without explicit phase check
 - |φᵢ - φⱼ| ≤ Δφ_max required
 - **Grammar**: U3 (RESONANT COUPLING)
@@ -385,26 +402,31 @@ These define TNFR canonicity and MUST be preserved:
 - **Test**: Verify phase compatibility before coupling
 
 ### 6. Node Birth/Collapse
+
 - Birth: sufficient νf, coupling, reduced ΔNFR
 - Collapse: extreme dissonance, decoupling, νf → 0
 - **Test**: Verify lifecycle conditions
 
 ### 7. Operational Fractality
+
 - EPIs can nest without losing identity
 - No flattening that breaks recursivity
 - **Test**: Multi-scale tests with nested EPIs
 
 ### 8. Controlled Determinism
+
 - Stochastic allowed BUT reproducible (seeds)
 - Traceable (structural logs)
 - **Test**: Same seed → same trajectory
 
 ### 9. Structural Metrics
+
 - Expose C(t), Si, phase, νf in telemetry
 - No alien metrics that dilute TNFR semantics
 - **Test**: Verify metric availability
 
 ### 10. Domain Neutrality
+
 - Trans-scale, trans-domain
 - No hard-wired field-specific assumptions in core
 - **Test**: Cross-domain examples work
@@ -832,33 +854,17 @@ A TNFR expert:
 
 #### **Structural Potential (Φ_s)** - CANONICAL (First promotion 2025)
 
-```python
-Φ_s(i) = Σ_{j≠i} ΔNFR_j / d(i,j)^α  (α=2)
-```
-
-**Validation Evidence** (2,400+ experiments):
-- ✅ **Predictive power**: corr(Δ Φ_s, ΔC) = -0.822 (R² ≈ 0.68)
-- ✅ **Universality**: CV < 1% across 5 topology families
-- ✅ **Safety criterion**: Δ Φ_s < 2.0 (escape threshold)
-
-**Physical Role**: Global structural potential, passive equilibrium states
+- Global structural potential, passive equilibrium states
+- Safety criterion (U6 telemetry): Δ Φ_s < 2.0 (escape threshold)
+- For full physics, equations, and validation, see `docs/STRUCTURAL_FIELDS_TETRAD.md` and `docs/grammar/U6_STRUCTURAL_FIELD_TETRAD.md`.
 
 ---
 
 #### **Phase Gradient (|∇φ|)** - CANONICAL ⭐ **NEWLY PROMOTED (Nov 2025)**
 
-```python
-|∇φ|(i) = mean_{j ∈ neighbors(i)} |θ_i - θ_j|
-```
-
-**Validation Evidence** (450 experiments):
-- ✅ **Predictive power**: corr(Δ|∇φ|, Δmax_ΔNFR) = +0.6554 (31% above 0.5 threshold)
-- ✅ **Universality**: All topologies achieve |corr| > 0.5 (Tree: 0.74, Scale-free: 0.71)
-- ✅ **Superior performance**: 12% better than Φ_s as predictor of peak stress
-- ✅ **Safety criterion**: |∇φ| < 0.38 for stable operation
-- ✅ **Grammar compliance**: U1-U5 compatible, read-only telemetry
-
-**Physical Role**: Local phase desynchronization, early warning for fragmentation
+- Local phase desynchronization / stress proxy
+- Safety criterion: |∇φ| < 0.38 for stable operation
+- For formal definition and evidence, see `docs/STRUCTURAL_FIELDS_TETRAD.md` and `docs/grammar/U6_STRUCTURAL_FIELD_TETRAD.md`.
 
 **Critical Discovery**: C(t) = 1-(σ_ΔNFR/ΔNFR_max) is invariant to proportional scaling. 
 |∇φ| correlation validated against alternative metrics (max_ΔNFR, mean_ΔNFR, Si) that 
@@ -875,23 +881,9 @@ capture dynamics C(t) misses.
 
 #### **Phase Curvature (K_φ)** - CANONICAL ⭐ **NEWLY PROMOTED (Nov 2025)**
 
-```python
-K_φ(i) = φ_i - (1/deg(i)) Σ_{j∈N(i)} φ_j
-```
-
-**Validation Evidence** (2025 research battery):
-- ✅ Threshold revision: literature value 4.88 disproven (55% accuracy);
-    new threshold |K_φ| ≥ 3.0 achieved 100% accuracy in aggressive
-    fragmentation tests
-- ✅ Asymptotic freedom: multiscale decay var(K_φ) ~ 1/r^α with
-    α ≈ 2.76; excellent fits (R² ≥ 0.8) on scale-free/WS, good elsewhere
-- ✅ Cross-domain universality: neural (R² > 0.8), AI scale-free
-    (R² ≈ 0.998), social (high-variance |K_φ| pinpoints conflict zones)
-- ✅ Safety integration: complements Φ_s (global) and |∇φ| (local)
-    by adding geometric curvature; forms the safety triad
-
-**Physical Role**: Phase torsion and confinement; identifies mutation-
-prone loci and confinement pockets not visible to Φ_s or |∇φ| alone
+- Phase torsion and geometric confinement; flags mutation-prone loci
+- Safety criteria: |K_φ| ≥ 3.0 (local fault zones); multiscale safety via `k_phi_multiscale_safety`
+- See `docs/STRUCTURAL_FIELDS_TETRAD.md` and `docs/grammar/U6_STRUCTURAL_FIELD_TETRAD.md` for definitions, asymptotic freedom evidence, and thresholds.
 
 **Safety criteria (telemetry-based)**:
 - Local: |K_φ| ≥ 3.0 flags confinement/fault zones
@@ -910,60 +902,9 @@ prone loci and confinement pockets not visible to Φ_s or |∇φ| alone
 
 #### **Coherence Length (ξ_C)** - CANONICAL ⭐ **NEWLY PROMOTED (Nov 2025)**
 
-```python
-# Per-node local coherence
-c_i = 1.0 / (1.0 + |ΔNFR_i|)
-
-# Spatial autocorrelation at distance r
-C(r) = ⟨c_i · c_j⟩ where d(i,j) ≈ r
-
-# Coherence length from exponential decay fit
-C(r) ~ exp(-r/ξ_C)
-```
-
-**Validation Evidence** (Nov 2025 multi-topology experiment):
-- ✅ **1,170 measurements** across 3 topology families (WS, scale-free, grid)
-- ✅ **100% success rate**: All measurements valid (no systematic failures)
-- ✅ **Critical point prediction**: Theoretical I_c = 2.015 matches observed 
-    peaks at I ≈ 2.010 (WS/Grid) with deviation ±0.005
-- ✅ **Power law scaling**: ξ_C ~ |I - I_c|^(-ν) confirmed experimentally
-- ✅ **Multi-scale behavior**: ξ_C spans 271 - 46,262 (2-3 orders of magnitude)
-- ✅ **Critical exponents**: ν ≈ 0.61 (WS, mean-field), 0.95 (Grid, 3D-like)
-- ✅ **Phase transitions**: Clear second-order critical behavior observed
-
-**Physical Role**: Spatial scale over which local coherence correlations 
-persist; quantifies transition from local to global structural stability
-
-**Critical Point Behavior**:
-- Below I_c: ξ_C finite, coherence localized
-- At I_c: ξ_C diverges, system-wide correlations emerge
-- Above I_c: ξ_C decreases, coherence fragments
-
-**Safety criteria (telemetry-based)**:
-- Critical approach: ξ_C > system_diameter (system-wide reorganization imminent)
-- Long-range correlations: ξ_C > 3 × mean_node_distance (monitor closely)
-- Localized: ξ_C < mean_node_distance (stable regime)
-
-**Complements existing CANONICAL fields**:
-- Φ_s: Global potential (field theory) → ξ_C adds spatial correlation scale
-- |∇φ|: Local stress (gradient) → ξ_C adds correlation length
-- K_φ: Geometric confinement (curvature) → ξ_C adds critical phenomena
-
-**Usage**:
-- Import from [src/tnfr/physics/fields.py](src/tnfr/physics/fields.py)
-- Compute via `estimate_coherence_length(G)` [CANONICAL]
-- Monitor for phase transitions and critical point detection
-- **Grammar compliance**: Read-only telemetry, no operator sequence modification
-
-**Critical Discovery**: ξ_C provides unique **spatial correlation dimension** 
-not captured by Φ_s, |∇φ|, or K_φ. Enables detection of genuine phase 
-transitions through divergence near critical points. Topology-dependent 
-critical exponents suggest rich universality class structure in TNFR networks.
-
-**Documentation**: See [docs/XI_C_CANONICAL_PROMOTION.md](docs/XI_C_CANONICAL_PROMOTION.md) for complete 
-experimental validation, [docs/XI_C_BREAKTHROUGH_REPORT.txt](docs/XI_C_BREAKTHROUGH_REPORT.txt) for detailed 
-analysis, and [benchmarks/results/xi_c_critical_behavior_analysis.png](benchmarks/results/xi_c_critical_behavior_analysis.png) for 
-visualization of critical behavior across topologies.
+- Spatial correlation scale of local coherence; quantifies approach to critical points
+- Safety cues: ξ_C > system diameter (critical), ξ_C > 3 × mean distance (watch), ξ_C < mean distance (stable)
+- For full derivation and experimental validation, see `docs/STRUCTURAL_FIELDS_TETRAD.md` and `docs/XI_C_CANONICAL_PROMOTION.md` (plus `docs/XI_C_BREAKTHROUGH_REPORT.txt` and the benchmark visuals).
 
 ---
 

docs/EXTENDED_FIELDS_INTEGRATION_SUMMARY.md

@@ -12,14 +12,21 @@ We have successfully **completed the full pipeline** from extended fields resear
 
 ### **Extended Canonical Hexad** (Previously Tetrad)
 
-| Field | Status | Physics | Validation |
-|-------|--------|---------|------------|
-| **Φ_s** | CANONICAL | Global structural potential | r(Δ Φ_s, ΔC) = -0.822 |
-| **\|∇φ\|** | CANONICAL | Phase gradient/desynchronization | r(Δ\|∇φ\|, Δmax_ΔNFR) = +0.655 |
-| **K_φ** | CANONICAL | Phase curvature/confinement | \|K_φ\| ≥ 3.0 threshold (100% accuracy) |
-| **ξ_C** | CANONICAL | Coherence length/spatial correlations | Critical point I_c = 2.015 |
-| **J_φ** | 🆕 CANONICAL | Phase current/directed transport | r(J_φ, K_φ) = +0.592 ± 0.092 |
-| **J_ΔNFR** | 🆕 CANONICAL | ΔNFR flux/reorganization transport | r(J_ΔNFR, Φ_s) = -0.471 ± 0.159 |
+The **formal definitions, safety criteria, and physics** of the structural tetrad (Φ_s, \|∇φ\|, K_φ, ξ_C) are centralized in:
+
+- `docs/STRUCTURAL_FIELDS_TETRAD.md` – canonical field definitions and thresholds
+- `docs/grammar/U6_STRUCTURAL_FIELD_TETRAD.md` – U6 umbrella, safety roles, and Hexad taxonomy
+
+This summary only tracks **integration status** and implementation surfaces:
+
+| Field | Status | Role |
+|-------|--------|------|
+| **Φ_s** | CANONICAL | Global structural potential (see canonical tetrad docs) |
+| **\|∇φ\|** | CANONICAL | Phase gradient/desynchronization (see canonical tetrad docs) |
+| **K_φ** | CANONICAL | Phase curvature/confinement (see canonical tetrad docs) |
+| **ξ_C** | CANONICAL | Coherence length/spatial correlations (see canonical tetrad docs) |
+| **J_φ** | 🆕 CANONICAL | Phase current/directed transport (flux pair, dynamics) |
+| **J_ΔNFR** | 🆕 CANONICAL | ΔNFR flux/reorganization transport (flux pair, dynamics) |
 
 ---
 

docs/STRUCTURAL_FIELDS_TETRAD.md

@@ -2,7 +2,7 @@
 
 Status: CANONICAL (Updated 2025-11-12)
 
-This guide centralizes the physics, math, implementation, telemetry, and usage of the four structural fields that characterize TNFR networks across scales. It avoids duplication by pointing to definitive sources where appropriate and gives a single operational entry point for engineers and researchers.
+This guide centralizes the physics, math, implementation, telemetry, and usage of the four structural fields that characterize TNFR networks across scales. It is the **single canonical source** for formal definitions of Φ_s, \|∇φ\|, K_φ, and ξ_C; other documents SHOULD reference this file instead of restating the equations.
 
 - Structural Potential (Φ_s): Global potential from ΔNFR distribution (inverse-square law analog)
 - Phase Gradient (|∇φ|): Local phase desynchronization (stress proxy)

docs/grammar/U6_STRUCTURAL_FIELD_TETRAD.md

@@ -8,7 +8,7 @@ Scope: Extends U6 (Structural Potential Confinement) into a multi-field safety s
 
 ## Summary
 
-We formalize the Structural Field Hexad as two complementary groups with distinct roles:
+We formalize the Structural Field Hexad as two complementary groups with distinct roles. This document **assumes the field definitions from `docs/STRUCTURAL_FIELDS_TETRAD.md`** and focuses on their role within the grammar (U6 umbrella), safety criteria, and Hexad taxonomy rather than re-deriving their physics.
 
 - Telemetry Tetrad (read-only, U6 umbrella):
   - Φ_s: Global structural potential (field-theoretic aggregate of ΔNFR)

src/tnfr/physics/README.md

@@ -28,17 +28,26 @@ TNFR dynamics begins with a fundamental equation governing each node:
 
 ## 📐 Structural Fields: System Telemetry
 
-From the nodal equation emerge **four canonical fields** that characterize the system state:
+From the nodal equation emerge **four canonical fields** that characterize the system state.
 
-### **Structural Tetrad** → [`docs/STRUCTURAL_FIELDS_TETRAD.md`](../../../docs/STRUCTURAL_FIELDS_TETRAD.md)
+### **Structural Tetrad (Canonical Definitions)**
 
-1. **Φs (Structural Potential)**: Global field from ΔNFR distribution
-2. **|∇φ| (Phase Gradient)**: Local desynchronization 
-3. **Kφ (Phase Curvature)**: Geometric confinement
-4. **ξC (Coherence Length)**: Spatial correlation scale
+- Physics, equations, and thresholds → [`docs/STRUCTURAL_FIELDS_TETRAD.md`](../../../docs/STRUCTURAL_FIELDS_TETRAD.md)
+- Grammar / U6 safety roles and Hexad taxonomy → [`docs/grammar/U6_STRUCTURAL_FIELD_TETRAD.md`](../../../docs/grammar/U6_STRUCTURAL_FIELD_TETRAD.md)
+
+Brief overview (see docs above for full details):
+
+1. **Φ_s (Structural Potential)**: Global field from ΔNFR distribution (U6 confinement)
+2. **|∇φ| (Phase Gradient)**: Local desynchronization / stress proxy
+3. **K_φ (Phase Curvature)**: Geometric confinement / torsion
+4. **ξ_C (Coherence Length)**: Spatial correlation scale / critical behavior
 
 **Implementation**: [`src/tnfr/physics/fields.py`](fields.py)  
-**Safety thresholds**: ΔΦs < 2.0, |∇φ| < 0.38, |Kφ| ≥ 3.0, ξC divergent near Ic
+**Extended canonical fields (flux pair & spectra)**: see [`docs/EXTENDED_FIELDS_INTEGRATION_SUMMARY.md`](../../../docs/EXTENDED_FIELDS_INTEGRATION_SUMMARY.md)
+
+**OZ→IL precision walks & telemetry behavior** (Φ_s, |∇φ|, K_φ, ξ_C under dissonance/coherence sequences):
+- Canonical correlation narrative → [`benchmarks/results/ozil_hi_correlation_summary.md`](../../../benchmarks/results/ozil_hi_correlation_summary.md)
+- Aggregated snapshots / dashboards → [`benchmarks/results/precision_walk_dashboard.md`](../../../benchmarks/results/precision_walk_dashboard.md)
 
 ---