TNFR Glossary
Purpose: Operational quick reference for the Resonant Fractal Nature Theory (TNFR) v0.0.1
Status: Complete reference for current implementation
Version: November 29, 2025
Authority: Aligned with AGENTS.md as single source of truth
Scope: This glossary provides API-focused definitions for developers implementing TNFR networks. For complete theoretical foundations, see AGENTS.md and UNIFIED_GRAMMAR_RULES.md.
Core Variables
Primary Information Structure (EPI)
Code: G.nodes[n]['EPI'], ALIAS_EPI
Symbol: (\text{EPI}) or (E)
What: Coherent structural form of a node
Space: (B_{\text{EPI}}) (Banach space)
Rules: Modified only via structural operators, never directly
API: tnfr.structural operators
Math: §2.2 Banach Space B_EPI
Structural Frequency (νf)
Code: G.nodes[n]['vf'], ALIAS_VF
Symbol: (\nu_f)
Units: Hz_str (structural hertz)
Range: (\mathbb{R}^+) (positive reals; node collapse when (\nu_f \to 0))
What: Rate of structural reorganization
API: adapt_vf_by_coherence(), operators
Math: §3.2 Frequency Operator Ĵ
Internal Reorganization Operator (ΔNFR)
Code: G.nodes[n]['dnfr'], ALIAS_DNFR
Symbol: (\Delta\text{NFR})
What: Structural evolution gradient (drives reorganization)
Sign: Positive = expansion, Negative = contraction
Compute: Via default_compute_delta_nfr hook, automatic in step()
Math: §3.3 Reorganization Operator
Phase (φ, θ)
Code: G.nodes[n]['theta'], collect_theta_attr()
Symbol: (\theta) or (\phi)
Range: ([0, 2\pi)) or ([-\pi, \pi)) radians
What: Network synchrony parameter (relative timing)
Phase difference: (\Delta\theta = \theta_i - \theta_j)
API: Phase adaptation in dynamics
Math: §4 Nodal Equation
Total Coherence (C(t))
Code: compute_coherence(G) → float ∈ [0,1]
Symbol: (C(t))
Formula: (C(t) = \text{Tr}(\hat{C}\rho)) where (\hat{C}) is the coherence operator
Range: ([0, 1]) where 1 = perfect coherence, 0 = total fragmentation
What: Global network stability measure
Math: §3.1 Coherence Operator Ĉ
Coherence Operator (Ĉ)
Code: coherence_matrix(G) → (nodes, W)
Symbol: (\hat{C})
Matrix element: (w_{ij} \approx \langle i | \hat{C} | j \rangle)
Properties: Hermitian ((\hat{C}^\dagger = \hat{C})), positive semi-definite
What: Operator measuring structural stability between nodes
Math: §3.1 Theory + §3.1.1 Implementation
Sense Index (Si)
Code: G.nodes[n]['Si'], ALIAS_SI, compute_Si_node()
Symbol: (\text{Si}) (global) or (S_i) (node i)
Formula: (\text{Si} = \alpha \cdot \nu_{f,\text{norm}} + \beta \cdot (1 - \text{disp}\theta) + \gamma \cdot (1 - |\Delta\text{NFR}|{\text{norm}}))
Range: ([0, 1^+]) typically, higher = more stable reorganization
What: Capacity for stable structural reorganization
Weights: (\alpha + \beta + \gamma = 1) (default: 0.4, 0.3, 0.3)
Math: Mathematical Foundations - Metrics
Phase Gradient (|∇φ|) - CANONICAL
Code: compute_phase_gradient(G) → Dict[NodeId, float]
Symbol: (|\nabla\phi|(i))
Formula: (|\nabla\phi|(i) = \text{mean}_{j \in N(i)} |\theta_i - \theta_j|) (circular mean)
What: Local phase desynchronization / stress proxy field
Status: CANONICAL (Nov 2025)
Physics: Captures dynamics C(t) misses due to scaling invariance
Threshold: Classical bound |∇φ| < 0.2904 (harmonic oscillator stability)
API: tnfr.physics.fields.compute_phase_gradient()
Usage: Stress detection, local instability prediction
Documentation: docs/STRUCTURAL_FIELDS_TETRAD.md
Phase Curvature (K_φ) - CANONICAL
Code: compute_phase_curvature(G) → Dict[NodeId, float]
Symbol: (K_\phi(i))
Formula: (K_\phi = \text{wrap_angle}(\phi_i - \text{circular_mean}(\text{neighbors})))
What: Phase torsion and geometric confinement field
Status: CANONICAL (Nov 2025)
Physics: Flags mutation-prone loci via geometric constraints
Threshold: Classical bound |K_φ| < 2.8274 (90% of π theoretical maximum)
API: tnfr.physics.fields.compute_phase_curvature()
Usage: Geometric confinement monitoring, bifurcation prediction
Documentation: docs/STRUCTURAL_FIELDS_TETRAD.md
Coherence Length (ξ_C) - CANONICAL
Code: estimate_coherence_length(G) → float
Symbol: (\xi_C)
Formula: Spatial correlation function (C(r) = A \exp(-r/\xi_C))
What: Spatial correlation scale of local coherence
Status: CANONICAL (Nov 2025)
Physics: Critical phenomena and finite-size scaling analysis
Thresholds:
- Critical: ξ_C > 1.0 × diameter (finite-size scaling dominates)
- Watch: ξ_C > π ≈ 3.14 × mean_distance (RG scaling)
- Stable: ξ_C < mean_distance (bulk behavior)
API: tnfr.physics.fields.estimate_coherence_length()
Usage: Critical point detection, correlation analysis
Documentation: docs/STRUCTURAL_FIELDS_TETRAD.md
Structural Potential (Φ_s) - CANONICAL
Code: compute_structural_potential(G, alpha=2.0) → Dict[NodeId, float]
Symbol: (\Phi_s(i))
Formula: (\Phi_s(i) = \sum_{j \neq i} \frac{\Delta\text{NFR}_j}{d(i,j)^\alpha}) where (\alpha = 2)
What: Global structural potential field from ΔNFR distribution
Status: CANONICAL (Nov 2025)
Validation: 2,400+ experiments across 5 topologies
Physics: Passive equilibrium confinement landscape
Grammar: U6 STRUCTURAL POTENTIAL CONFINEMENT (Δ Φ_s < 2.0 escape threshold)
API: tnfr.physics.fields.compute_structural_potential()
Threshold: Classical bound |Φ_s| < 0.771 (von Koch fractal theory)
Documentation: docs/STRUCTURAL_FIELDS_TETRAD.md
- src/tnfr/physics/fields.py - Implementation
Interpretation: - Φ_s minima = passive equilibrium states - Δ Φ_s < 2.0 = system confined (safe regime) - Δ Φ_s ≥ 2.0 = escape threshold (fragmentation risk) - Valid sequences: Δ Φ_s ≈ 0.6 (30% of threshold) - Violations: Δ Φ_s ≈ 3.9 (195% of threshold)
Mechanism: Grammar U1-U5 acts as passive confinement (NOT active attractor). Reduces escape drift by 85%.
The Nodal Equation
The fundamental equation of TNFR governs structural evolution:
[ \frac{\partial \text{EPI}}{\partial t} = \nu_f \cdot \Delta\text{NFR}(t) ]
Where: - (\frac{\partial \text{EPI}}{\partial t}): Rate of change of structure - (\nu_f): Structural frequency (reorganization rate) in Hz_str - (\Delta\text{NFR}(t)): Reorganization gradient (driving pressure)
Interpretation: - Structure changes only when both (\nu_f > 0) (capacity) and (\Delta\text{NFR} \neq 0) (pressure) exist - Rate of change is proportional to both frequency and gradient - When (\nu_f \to 0), evolution freezes (node collapse) - When (\Delta\text{NFR} = 0), structure reaches equilibrium
Implementation: See src/tnfr/dynamics/ for numerical integration
Theory: §4 The Nodal Equation
Structural Operators
The 13 canonical operators are the only way to modify nodes in TNFR. They're not arbitrary functions—they're resonant transformations with rigorous physics.
For complete specifications with physics derivations, contracts, and usage examples, see AGENTS.md § The 13 Canonical Operators.
Quick Reference
| Symbol | Name | Physics | Grammar Sets | When to Use |
|---|---|---|---|---|
| AL | Emission | Creates EPI from vacuum via resonant emission | Generator (U1a) | Starting new patterns, initializing from EPI=0 |
| EN | Reception | Captures and integrates incoming resonance | - | Information gathering, listening phase |
| IL | Coherence | Stabilizes form through negative feedback | Stabilizer (U2) | After changes, consolidation |
| OZ | Dissonance | Introduces controlled instability | Destabilizer (U2), Bifurcation trigger (U4a), Closure (U1b) | Breaking local optima, exploration |
| UM | Coupling | Creates structural links via phase synchronization | Requires phase verification (U3) | Network formation, connecting nodes |
| RA | Resonance | Amplifies and propagates patterns coherently | Requires phase verification (U3) | Pattern reinforcement, spreading coherence |
| SHA | Silence | Freezes evolution temporarily (νf → 0) | Closure (U1b) | Observation windows, pause for synchronization |
| VAL | Expansion | Increases structural complexity (dim ↑) | Destabilizer (U2) | Adding degrees of freedom |
| NUL | Contraction | Reduces structural complexity (dim ↓) | - | Simplification, dimensionality reduction |
| THOL | Self-organization | Spontaneous autopoietic pattern formation | Stabilizer (U2), Handler (U4a), Transformer (U4b) | Emergent organization, fractal structuring |
| ZHIR | Mutation | Phase transformation at threshold | Bifurcation trigger (U4a), Transformer (U4b) | Qualitative state changes |
| NAV | Transition | Regime shift, activates latent EPI | Generator (U1a), Closure (U1b) | Switching between attractor states |
| REMESH | Recursivity | Echoes structure across scales | Generator (U1a), Closure (U1b) | Multi-scale operations, memory |
Operator Composition
Operators combine into sequences that implement complex behaviors:
- Bootstrap = [Emission, Coupling, Coherence]
- Stabilize = [Coherence, Silence]
- Explore = [Dissonance, Mutation, Coherence]
- Propagate = [Resonance, Coupling]
Critical: All sequences must satisfy unified grammar (U1-U6).
API:
- tnfr.structural.<OperatorName>() - Individual operators
- run_sequence(G, node, ops) - Execute operator sequences
- validate_sequence(ops) - Check grammar compliance
Grammar: See UNIFIED_GRAMMAR_RULES.md for complete rules
Detailed Specs: See AGENTS.md § The 13 Canonical Operators
Math: Mathematical Foundations §5
Canonical Invariants (Optimized Set)
From AGENTS.md - Optimized from 10 to 6 invariants based on mathematical derivation:
- Nodal Equation Integrity: EPI evolution only via ∂EPI/∂t = νf · ΔNFR(t)
- Phase-Coherent Coupling: |φᵢ - φⱼ| ≤ Δφ_max required for resonant operations
- Multi-Scale Fractality: Operational fractality and nested EPIs maintained
- Grammar Compliance: All operator sequences must satisfy U1-U6 validation
- Structural Metrology: Units consistency (νf in Hz_str) and telemetry exposure
- Reproducible Dynamics: Deterministic evolution with seed-based control
Quick Reference Tables
Variable Summary
| Symbol | Mathematical | Code Attribute | Units | Range | Type |
|---|---|---|---|---|---|
| (\text{EPI}) | Primary Information Structure | 'EPI' |
dimensionless | (B_{\text{EPI}}) | Coherent form |
| (\nu_f) | Structural frequency | 'vf' |
Hz_str | (\mathbb{R}^+) | Reorganization rate |
| (\Delta\text{NFR}) | Reorganization operator | 'dnfr' |
dimensionless | (\mathbb{R}) | Evolution gradient |
| (\theta), (\phi) | Phase angle | 'theta' |
radians | ([0, 2\pi)) | Network synchrony |
| (C(t)) | Total coherence | compute_coherence() |
dimensionless | ([0, 1]) | Global stability |
| (\text{Si}) | Sense Index | 'Si' |
dimensionless | ([0, 1^+]) | Reorganization stability |
Common API Patterns
# Access node attributes
epi = G.nodes[node_id]['EPI']
vf = G.nodes[node_id]['vf']
theta = G.nodes[node_id]['theta']
# Compute metrics
C_t = compute_coherence(G)
nodes, W = coherence_matrix(G)
Si = compute_Si_node(G, node_id)
# Apply operators
from tnfr.structural import Emission, Coherence, Resonance
run_sequence(G, node_id, [Emission(), Coherence(), Resonance()])
# Evolution step
from tnfr.dynamics import step
step(G, use_Si=True, apply_glyphs=True)
Telemetry & Traces
Expose in telemetry:
- C(t) - Total coherence
- νf per node - Structural frequency
- phase per node - Synchrony state
- Si per node/network - Sense index
- ΔNFR per node - Reorganization gradient
- Operator history - Applied transformations
- Events - Birth, bifurcation, collapse
API: tnfr.utils.callback_manager, history tracking in G.graph['_hist']
Domain Neutrality
TNFR is trans-scale and trans-domain: - Works from quantum to social systems - No built-in assumptions about specific domains - Structural operators apply universally
Guideline: Avoid domain-specific hard-coding in core engine
Reproducibility
All simulations must be: 1. Seeded: Explicit RNG seeds 2. Traceable: Log operators, parameters, states 3. Deterministic: Same seed → same trajectory
Tools: RNG scaffolding, structural history, telemetry caches
Unified Grammar Terms
Unified Grammar
The consolidated TNFR grammar system (U1-U6) that replaces the old C1-C3 and RC1-RC4 systems.
Source of Truth: UNIFIED_GRAMMAR_RULES.md
Quick Reference: AGENTS.md § Unified Grammar (U1-U6)
Implementation: src/tnfr/operators/grammar.py
Grammar Completeness: The canonical TNFR grammar consists of exactly six rules (U1-U6) and is COMPLETE. No additional rules (U7, U8, etc.) are required or planned. Extended dynamics (flux fields) add telemetry, not prescriptive constraints.
Six Canonical Constraints:
| Rule | Name | Physics Basis | Requirement | Canonicity |
|---|---|---|---|---|
| U1 | STRUCTURAL INITIATION & CLOSURE | ∂EPI/∂t undefined at EPI=0 | Start with generator {AL, NAV, REMESH}, End with closure {SHA, NAV, REMESH, OZ} | ABSOLUTE |
| U2 | CONVERGENCE & BOUNDEDNESS | ∫νf·ΔNFR dt must converge | If destabilizer {OZ, ZHIR, VAL}, then include stabilizer {IL, THOL} | ABSOLUTE |
| U3 | RESONANT COUPLING | Phase compatibility required for resonance | If coupling {UM, RA}, verify |φᵢ - φⱼ| ≤ Δφ_max | ABSOLUTE |
| U4 | BIFURCATION DYNAMICS | ∂²EPI/∂t² > τ requires control | Triggers {OZ, ZHIR} need handlers {THOL, IL}; Transformers need context | STRONG |
| U5 | MULTI-SCALE COHERENCE | Hierarchical coupling + chain rule | Nested EPIs require stabilizers {IL, THOL} at each level | ABSOLUTE |
| U6 | STRUCTURAL POTENTIAL CONFINEMENT | Emergent Φ_s field: Φ_s(i) = Σ ΔNFR_j/d(i,j)² | Monitor Δ Φ_s < 2.0 (telemetry-based safety) | STRONG |
Canonicity Levels: - ABSOLUTE: Mathematical necessity (direct consequence of nodal equation) - STRONG: Strong empirical/theoretical support (2,400+ experiments for U6)
Recent Updates: - U5 added 2025-11-10 (hierarchical REMESH stabilization) - U6 promoted to canonical 2025-11-11 (Φ_s field validation complete) - Replaces experimental "Temporal Ordering" research proposal - Validated across 5 topologies: ring, scale_free, small-world, tree, grid - Correlation: corr(Δ Φ_s, ΔC) = -0.822 (R² ≈ 0.68) - 2025-11-15: Grammar declared COMPLETE (U1-U6) - no U7/U8 required
Not Part of Grammar (telemetry/dynamics, NOT rules): - Structural Field Hexad: Tetrad (Φ_s, |∇φ|, K_φ, ξ_C) + Flux Pair (J_φ, ∇·J_ΔNFR) - "Proposed U7": Historical research direction (Temporal Ordering) - NOT canonical, NOT implemented
See Also: - UNIFIED_GRAMMAR_RULES.md - Complete derivations from physics - AGENTS.md § Unified Grammar - Quick reference - docs/grammar/U6_STRUCTURAL_POTENTIAL_CONFINEMENT.md - U6 complete specification - docs/grammar/U6_STRUCTURAL_FIELD_TETRAD.md - Why no U7/U8 - TNFR_FORCES_EMERGENCE.md § 14-15 - U6 validation details - src/tnfr/physics/fields.py - Φ_s implementation
Generator Operator
Operator that can create EPI from null/dormant states.
Set: GENERATORS = {emission, transition, recursivity}
Physics: Only these operators can initialize when EPI=0
Grammar Rule: U1a (STRUCTURAL INITIATION)
See: UNIFIED_GRAMMAR_RULES.md § U1a
Closure Operator
Operator that leaves system in coherent attractor state.
Set: CLOSURES = {silence, transition, recursivity, dissonance}
Physics: Terminal states preserving coherence
Grammar Rule: U1b (STRUCTURAL CLOSURE)
See: UNIFIED_GRAMMAR_RULES.md § U1b
Stabilizer Operator
Operator that provides negative feedback for convergence.
Set: STABILIZERS = {coherence, self_organization}
Physics: Ensures ∫νf·ΔNFR dt converges (bounded evolution)
Grammar Rule: U2 (CONVERGENCE & BOUNDEDNESS)
See: UNIFIED_GRAMMAR_RULES.md § U2
Destabilizer Operator
Operator that increases |ΔNFR| through positive feedback.
Set: DESTABILIZERS = {dissonance, mutation, expansion}
Physics: Without stabilizers, leads to divergence
Grammar Rule: U2 (CONVERGENCE & BOUNDEDNESS)
See: UNIFIED_GRAMMAR_RULES.md § U2
Coupling/Resonance Operator
Operators that require phase verification for valid coupling.
Set: COUPLING_RESONANCE = {coupling, resonance}
Physics: Resonance requires |φᵢ - φⱼ| ≤ Δφ_max
Grammar Rule: U3 (RESONANT COUPLING)
See: UNIFIED_GRAMMAR_RULES.md § U3
Universal Tetrahedral Correspondence
Theory: Central TNFR discovery establishing exact correspondence between four universal mathematical constants and four structural fields.
Mathematical Constants
| Constant | Value | Role | Domain |
|---|---|---|---|
| φ (Golden Ratio) | 1.618034... | Harmonic proportion | Global/Harmonic |
| γ (Euler Constant) | 0.577216... | Harmonic growth rate | Local/Dynamic |
| π (Pi) | 3.141593... | Geometric relations | Geometric/Spatial |
| e (Euler Number) | 2.718282... | Exponential base | Correlational/Temporal |
Structural Field Correspondences
- φ ↔ Φ_s: Global harmonic confinement (Δ Φ_s < φ ≈ 1.618)
- γ ↔ |∇φ|: Local dynamic evolution (|∇φ| < γ/π ≈ 0.184)
- π ↔ K_φ: Geometric spatial constraints (|K_φ| < φ×π ≈ 5.083)
- e ↔ ξ_C: Correlational memory decay (C(r) ~ exp(-r/ξ_C))
Documentation: Structural Fields and Universal Tetrahedral Correspondence
Bifurcation Trigger
Operators that may trigger phase transitions.
Set: BIFURCATION_TRIGGERS = {dissonance, mutation}
Physics: Can cause ∂²EPI/∂t² > τ (bifurcation)
Grammar Rule: U4a (requires handlers)
See: UNIFIED_GRAMMAR_RULES.md § U4a
Bifurcation Handler
Operators that manage structural reorganization during bifurcations.
Set: BIFURCATION_HANDLERS = {self_organization, coherence}
Physics: Provide stability during phase transitions
Grammar Rule: U4a (BIFURCATION DYNAMICS)
See: UNIFIED_GRAMMAR_RULES.md § U4a
Transformer Operator
Operators that perform graduated destabilization for phase transitions.
Set: TRANSFORMERS = {mutation, self_organization}
Physics: Require recent destabilizer for threshold energy
Grammar Rule: U4b (requires context + prior IL for ZHIR)
See: UNIFIED_GRAMMAR_RULES.md § U4b
Related Documentation
Core References (Essential)
- AGENTS.md ⭐ - Single source of truth for TNFR agent guidance, invariants, and philosophy
- UNIFIED_GRAMMAR_RULES.md ⭐ - Grammar single source of truth (U1-U6 complete derivations)
- Mathematical Foundations ⭐ - SINGLE SOURCE FOR ALL MATH (formalization, proofs, spectral theory)
Theory & Physics
- TNFR.pdf - Original theoretical companion (paradigm, nodal equation, foundational physics)
- docs/grammar/U6_STRUCTURAL_POTENTIAL_CONFINEMENT.md - U6 complete specification
- TNFR_FORCES_EMERGENCE.md - Structural fields validation (Φ_s, phase gradients)
- SHA_ALGEBRA_PHYSICS.md - Silence operator physical basis
Implementation & API
- ARCHITECTURE.md - System design and architecture patterns
- Foundations - Runtime/API guide
- API Overview - Package architecture
- Structural Operators - Operator implementation details
- Examples - Runnable scenarios across domains
Grammar & Migration
- MIGRATION_GUIDE.md - Migration from C1-C3/RC1-RC4 to U1-U6
- docs/grammar/ - Grammar documentation directory (U6, fundamental concepts, etc.)
- GLYPH_SEQUENCES_GUIDE.md - Operator sequence patterns
Testing & Development
- TESTING.md - Test conventions and invariant verification
- CONTRIBUTING.md - Detailed contribution guidelines
- REPRODUCIBILITY.md - Determinism requirements
Cross-References and Documentation Hub
Primary Sources:
- AGENTS.md - Single source of truth for TNFR theory
- UNIFIED_GRAMMAR_RULES.md - Complete U1-U6 grammar derivations
- Structural Fields and Universal Tetrahedral Correspondence - Mathematical foundations
Implementation References:
- src/tnfr/physics/fields.py - Unified Structural Field Tetrad (Canonical)
- src/tnfr/dynamics/self_optimizing_engine.py - Intrinsic agency & auto-optimization
- docs/STRUCTURAL_FIELDS_TETRAD.md - Technical field specifications
- docs/grammar/PHYSICS_VERIFICATION.md - Grammar physics verification
Development Resources:
- src/tnfr/sdk/ - Simplified & Fluent API
- examples/ - Complete tutorial suite
- ARCHITECTURE.md - System design patterns
Molecular Chemistry from TNFR
Technical approach: Chemistry modeled via TNFR nodal dynamics without additional postulates.
Element Signatures
Code: tnfr.physics.signatures
What: Structural field-based classification of coherent patterns
Metrics: ξ_C, |∇φ|, |K_φ|, ΔΦ_s drift, stability classification
API: compute_element_signature(G), compute_au_like_signature(G)
Physics: Elements as coherent attractors in structural space
Au-like Patterns
Symbol: Au (from Latin 'aurum')
What: Complex coherent patterns exhibiting metallic properties
Criteria: Extended ξ_C, phase synchrony (|∇φ| < 2.0), evolution stability
Detection: compute_au_like_signature()["is_au_like"]
Physics: Optimal multi-scale coordination under nodal dynamics
Chemical Bonds (TNFR Redefinition)
Traditional: Force between atoms
TNFR: Phase synchronization with U3 verification: |φᵢ - φⱼ| ≤ Δφ_max
API: Coupling operators with phase compatibility check
Strength: Determined by phase coherence and coupling stability
Chemical Reactions (TNFR Redefinition)
Traditional: Collision/transition state theory
TNFR: Operator sequences: [Dissonance→Mutation→Coupling→Coherence]
Grammar: Must satisfy U1-U6 constraints
API: Sequence validation via grammar.py
Example: Bond formation = [OZ, ZHIR, UM, IL] sequence
Molecular Geometry (TNFR Redefinition)
Traditional: VSEPR, orbital hybridization
TNFR: ΔNFR minimization in coupled network topology
Prediction: Stable configurations minimize reorganization pressure
API: Network topology analysis after coupling sequences
Complete Theory: MOLECULAR_CHEMISTRY_FROM_NODAL_DYNAMICS.md
Implementation: Physics README § 9-10
Self-Optimizing Engine (v0.0.1)
Intrinsic Agency: The TNFR engine possesses self-optimization capabilities using unified field telemetry.
Core Components
TNFRSelfOptimizingEngine: src/tnfr/dynamics/self_optimizing_engine.py
Purpose: Closes feedback loop via unified field monitoring
Monitors: Complex Geometric Field (Ψ), Chirality (χ), Symmetry Breaking (𝒮), Coherence Coupling (𝒞)
Detects: Inefficiencies via tensor invariants (Energy Density ℰ, Topological Charge 𝒬)
Usage: engine = TNFRSelfOptimizingEngine(G); success, metrics = engine.step(node_id)
Auto-Optimization API
Fluent Integration: TNFRNetwork(G).focus(node).auto_optimize().execute()
Field Analysis: analyze_optimization_potential(G) - Mathematical structure analysis
Strategy Recommendations: recommend_field_optimization_strategy(G) - Optimization strategies
Automatic Execution: auto_optimize_field_computation(G) - Self-optimizing computation
Unified Field Framework (Nov 2025)
Mathematical Unification: Discovery of complex field relationships and conservation laws.
Complex Geometric Field (Ψ)
Definition: Ψ = K_φ + i·J_φ (unifies geometry + transport)
Evidence: r(K_φ, J_φ) = -0.854 to -0.997 (near-perfect anticorrelation)
API: compute_complex_geometric_field(G)
Usage: Unified geometry-transport analysis
Emergent Fields
Chirality (χ): χ = |∇φ|·K_φ - J_φ·J_ΔNFR - Handedness detection
Symmetry Breaking (𝒮): Phase transition indicator
Coherence Coupling (𝒞): Multi-scale connector field
API: compute_emergent_fields(G)
Tensor Invariants
Energy Density (ℰ): ℰ = Φ_s² + |∇φ|² + K_φ² + J_φ² + J_ΔNFR²
Topological Charge (𝒬): 𝒬 = |∇φ|·J_φ - K_φ·J_ΔNFR
Conservation Law: ∂ρ/∂t + ∇·𝐉 = 0
API: compute_tensor_invariants(G)
Unified Telemetry: compute_unified_telemetry(G) - Complete field suite
Contributing Guidelines
When adding new functionality:
- Verify theoretical foundation: Align with AGENTS.md physics
- Preserve canonical invariants: Follow optimized 6-invariant set
- Use established terminology: Reference this glossary for consistency
- Map to canonical operators: All functions must correspond to 13 canonical operators
- Validate grammar compliance: Ensure U1-U6 satisfaction
- Maintain English-only policy: All documentation in English for canonical terminology
- Write comprehensive tests: Cover invariants and operator contracts
Development Workflow:
1. Read AGENTS.md completely - SINGLE SOURCE OF TRUTH
2. Study UNIFIED_GRAMMAR_RULES.md for physics foundations
3. Follow CONTRIBUTING.md for detailed guidelines
4. Test with TESTING.md requirements
Version: 0.0.1 (November 29, 2025)
Status: Complete operational reference for current TNFR implementation
Language: English only (canonical documentation policy)