@@ -189,7 +189,7 @@ The TNFR grammar system is **mathematically derived** from the **4 universal rel
 
 **Every grammar constraint derives inevitably from physics** - no arbitrary rules exist.
 
-**Complete Derivations**: [UNIFIED_GRAMMAR_RULES.md](UNIFIED_GRAMMAR_RULES.md)  
+**Complete Derivations**: [UNIFIED_GRAMMAR_RULES.md](theory/UNIFIED_GRAMMAR_RULES.md)  
 **Quick Reference**: [AGENTS.md § Unified Grammar](AGENTS.md#unified-grammar-u1-u6)
 
 1. **U1 - INITIATION & CLOSURE**: Mathematical necessity at EPI=0, action potential endpoints
 
@@ -1,6 +1,6 @@
 # Microbenchmarks
 
-> DEPRECATION NOTICE (Docs): Benchmark documentation is developer-focused and not part of the centralized user documentation. For canonical docs, start with `docs/source/index.rst` and `docs/DOCUMENTATION_INDEX.md`.
+> DEPRECATION NOTICE (Docs): Benchmark documentation is developer-focused and not part of the centralized user documentation. For canonical docs, start with `docs/README.md` and `AGENTS.md`.
 
 This directory hosts **targeted microbenchmarks** for hot paths in the TNFR
 engine. Each script isolates a specific optimisation and contrasts it with a
@@ -763,7 +763,7 @@ PYTHONPATH=src python benchmarks/comprehensive_cache_profiler.py \
 * `sense_index`: 0.7% hit rate, 100% buffer reuse (expected - creates new structural arrays)
 * `dnfr_laplacian`: 0.0% hit rate, 100% buffer reuse (by design - stateless gradients)
 
-For detailed analysis see `docs/CACHE_OPTIMIZATION_ANALYSIS.md` and `ARCHITECTURE.md`.
+For detailed analysis see `ARCHITECTURE.md`.
 
 **Usage Examples:**
 
 
@@ -278,7 +278,7 @@ Publishers should copy `LICENSE_SNAPSHOT.md` alongside the archives to satisfy Z
 licensing policy and attach the generated `dist/sha256.txt` checksum file described in
 `ZENODO_PUBLICATION_GUIDE.md`.
 
-Operator-sequence certificate design notes now live in `docs/OPERATOR_CERTIFICATES.md`.
+Operator-sequence certificate design notes are maintained with the certificate tooling in this lab.
 They outline how future releases will prove factor claims via canonical sequences (e.g.,
 `[AL, UM, RA, IL, SHA, THOL, NAV]`) so gcd corroboration becomes supportive rather than
 primary evidence.
 
@@ -134,7 +134,7 @@ When writing factory functions, follow these steps to maintain stub synchronizat
 3. **Verify the stub**: Check that `.pyi` matches your signatures
 4. **Commit both files**: `.py` and `.pyi` together
 
-See [Architecture Guide — Factory Patterns](../docs/source/advanced/ARCHITECTURE_GUIDE.md#factory-patterns) for factory function guidelines.
+See [Architecture Guide — Factory Patterns](../ARCHITECTURE.md) for factory function guidelines.
 
 ### Troubleshooting
 
@@ -160,8 +160,8 @@ If a file is reported as outdated but hasn't changed:
 
 ### Related Documentation
 
-- [Architecture Guide — Factory Patterns](../docs/source/advanced/ARCHITECTURE_GUIDE.md#factory-patterns) - Factory function guidelines
-- [Architecture Guide](../docs/source/advanced/ARCHITECTURE_GUIDE.md) - Consolidated architecture and patterns
+- [Architecture Guide — Factory Patterns](../ARCHITECTURE.md) - Factory function guidelines
+- [Architecture Guide](../ARCHITECTURE.md) - Consolidated architecture and patterns
 - [mypy stubgen documentation](https://mypy.readthedocs.io/en/stable/stubgen.html)
 
 ## Other Scripts
 
@@ -52,9 +52,9 @@ result = TNFR.create(100).evolve(10).auto_optimize().results()
 
 ## 📚 **Documentation**
 
-- **Theory**: [AGENTS.md](../../AGENTS.md) - Single Source of Truth
-- **Grammar**: [UNIFIED_GRAMMAR_RULES.md](../../UNIFIED_GRAMMAR_RULES.md) 
-- **Examples**: [examples/](../../examples/) - Sequential tutorials
+- **Theory**: [AGENTS.md](../../../AGENTS.md) - Single Source of Truth
+- **Grammar**: [UNIFIED_GRAMMAR_RULES.md](../../../theory/UNIFIED_GRAMMAR_RULES.md) 
+- **Examples**: [examples/](../../../examples/) - Sequential tutorials
 - **Individual engines**: See README.md in each subdirectory
 
 ## 🎯 **Engine Selection Guide**
 
@@ -13,11 +13,11 @@ Scope and guarantees:
 If any other document disagrees with this README on core computational mathematics, defer to this README and file an issue to reconcile the inconsistency.
 
 Quick pointers:
-- Formal theory: [docs/source/theory/mathematical_foundations.md](../../../docs/source/theory/mathematical_foundations.md)
+- Formal theory: [docs/source/theory/mathematical_foundations.md](../../../theory/MATHEMATICAL_DYNAMICS_BASIS.md)
 - Symbolic suite: [src/tnfr/math](../math/README.md)
 - Fields (Φ_s, |∇φ|, K_φ, ξ_C): [src/tnfr/physics/fields.py](../physics/fields.py) and docs sections below
-- Number theory guide (ΔNFR prime criterion): [docs/TNFR_NUMBER_THEORY_GUIDE.md](../../../docs/TNFR_NUMBER_THEORY_GUIDE.md)
-- Interactive notebook: [examples/tnfr_prime_checker.ipynb](../../../examples/tnfr_prime_checker.ipynb)
+- Number theory guide (ΔNFR prime criterion): [docs/TNFR_NUMBER_THEORY_GUIDE.md](../../../theory/TNFR_NUMBER_THEORY.md)
+- Interactive notebook: [examples/tnfr_prime_checker.ipynb](../../../examples/07_number_theory/40_arithmetic_number_theory.py)
 
 ## Module Organization
 
@@ -101,7 +101,7 @@ isometry_factory = build_isometry_factory(
 
 ## Factory Design Patterns
 
-All factories in this module follow the patterns documented in [Architecture Guide — Factory Patterns](../../../docs/source/advanced/ARCHITECTURE_GUIDE.md#factory-patterns):
+All factories in this module follow the patterns documented in [Architecture Guide — Factory Patterns](../../../ARCHITECTURE.md):
 
 1. **Clear naming**: `make_*` for operators, `build_*` for generators
 2. **Input validation**: Dimension checks, spectrum validation, topology verification
@@ -189,11 +189,11 @@ See [tests/mathematics](../../../tests/mathematics) for the complete test suite.
 
 ## Related Documentation
 
-- [Architecture Guide — Factory Patterns](../../../docs/source/advanced/ARCHITECTURE_GUIDE.md#factory-patterns) — Comprehensive factory design patterns
+- [Architecture Guide — Factory Patterns](../../../ARCHITECTURE.md) — Comprehensive factory design patterns
 - [TNFR Paradigm](../../../TNFR.pdf) — Theoretical foundations
 - [AGENTS.md](../../../AGENTS.md) — Structural invariants and contracts
-- [API Overview](../../../docs/source/api/overview.md) — Package-level documentation
-- [Mathematical Foundations (theory)](../../../docs/source/theory/mathematical_foundations.md) — Complete derivations
+- [API Overview](../../../AGENTS.md) — Package-level documentation
+- [Mathematical Foundations (theory)](../../../theory/MATHEMATICAL_DYNAMICS_BASIS.md) — Complete derivations
 
 ## Canonical equations and contracts
 
@@ -340,7 +340,7 @@ Outputs include:
 
 A ready-to-use notebook verifies a number’s primality using only the TNFR pressure equation ΔNFR (no factorization or external primality tests):
 
-- Path: [examples/tnfr_prime_checker.ipynb](../../../examples/tnfr_prime_checker.ipynb)
+- Path: [examples/tnfr_prime_checker.ipynb](../../../examples/07_number_theory/40_arithmetic_number_theory.py)
 - Cells: explanation, imports, `tnfr_is_prime(n)` function, interactive and batch tests
 
 Logic: `tnfr_is_prime(n) := (ΔNFR_n == 0)` with ΔNFR_n as defined above. This complies with U1–U4 and preserves the invariants (ΔNFR as structural pressure, νf in Hz_str, no ad-hoc EPI mutations).
@@ -352,8 +352,8 @@ Notes:
 ## Classical mechanics emergence (cross-reference)
 
 For the emergence of classical mechanics from TNFR (mass m = 1/νf; force as coherence gradient), see:
-- [docs/source/theory/07_emergence_classical_mechanics.md](../../../docs/source/theory/07_emergence_classical_mechanics.md)
-- [docs/source/theory/08_classical_mechanics_euler_lagrange.md](../../../docs/source/theory/08_classical_mechanics_euler_lagrange.md)
-- [docs/source/theory/09_classical_mechanics_numerical_validation.md](../../../docs/source/theory/09_classical_mechanics_numerical_validation.md)
+- [docs/source/theory/07_emergence_classical_mechanics.md](../../../theory/PHYSICAL_REGIME_CORRESPONDENCES.md)
+- [docs/source/theory/08_classical_mechanics_euler_lagrange.md](../../../theory/TNFR_VARIATIONAL_PRINCIPLE.md)
+- [docs/source/theory/09_classical_mechanics_numerical_validation.md](../../../examples/02_physics_regimes/12_classical_mechanics_demo.py)
 
 This README serves as the hub; the above documents contain full derivations and validation results.
@@ -20,7 +20,7 @@ TNFR dynamics begins with a fundamental equation governing each node:
 - **ΔNFR**: Reorganization gradient (structural pressure)
 
 **Emergent principles** from this equation:
-- **U1-U6**: Unified grammar → [`UNIFIED_GRAMMAR_RULES.md`](../../../UNIFIED_GRAMMAR_RULES.md)
+- **U1-U6**: Unified grammar → [`UNIFIED_GRAMMAR_RULES.md`](../../../theory/UNIFIED_GRAMMAR_RULES.md)
 - **Canonical invariants** → [`AGENTS.md`](../../../AGENTS.md)
 - **Physical foundations** → [`TNFR.pdf`](../../../TNFR.pdf) §1-2
 
@@ -33,7 +33,7 @@ From the nodal equation emerge **four canonical fields** that characterize the s
 ### **Structural Tetrad (Canonical Definitions)**
 
 - 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)
+- Grammar / U6 safety roles and Hexad taxonomy → [`docs/grammar/U6_STRUCTURAL_FIELD_TETRAD.md`](../../../docs/STRUCTURAL_FIELDS_TETRAD.md)
 
 Brief overview (see docs above for full details):
 
@@ -43,11 +43,11 @@ Brief overview (see docs above for full details):
 4. **ξ_C (Coherence Length)**: Spatial correlation scale / critical behavior
 
 **Implementation**: [`src/tnfr/physics/fields.py`](fields.py)  
-**Extended canonical fields (flux pair & spectra)**: see [`docs/EXTENDED_FIELDS_INTEGRATION_SUMMARY.md`](../../../docs/EXTENDED_FIELDS_INTEGRATION_SUMMARY.md)
+**Extended canonical fields (flux pair & spectra)**: see [`docs/EXTENDED_FIELDS_INTEGRATION_SUMMARY.md`](../../../theory/EXTENDED_FIELDS_AND_DERIVED_QUANTITIES.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)
+- Canonical correlation narrative → [`benchmarks/results/ozil_hi_correlation_summary.md`](../../../benchmarks/README.md)
+- Aggregated snapshots / dashboards → [`benchmarks/results/precision_walk_dashboard.md`](../../../benchmarks/README.md)
 
 ---
 
@@ -82,10 +82,10 @@ When patterns achieve **sufficient self-organization**, autopoietic behavior eme
 - **M (Stability Margin)**: Robustness against perturbations
 
 **Theoretical documentation**:
-- Conceptual framework → [`docs/LIFE_EMERGENCE_THEORETICAL_FRAMEWORK.md`](../../../docs/LIFE_EMERGENCE_THEORETICAL_FRAMEWORK.md)
-- Mathematical derivation → [`docs/LIFE_MATHEMATICAL_DERIVATION.md`](../../../docs/LIFE_MATHEMATICAL_DERIVATION.md)
+- Conceptual framework → [`docs/LIFE_EMERGENCE_THEORETICAL_FRAMEWORK.md`](../../../AGENTS.md)
+- Mathematical derivation → [`docs/LIFE_MATHEMATICAL_DERIVATION.md`](../../../AGENTS.md)
 
-**Experimental validation**: [`examples/life_experiments.py`](../../../examples/life_experiments.py)
+**Experimental validation**: [`examples/life_experiments.py`](../../../examples/07_number_theory/emergent_chemistry_particles_demo.py)
 
 ---
 
@@ -112,8 +112,8 @@ Upon the autopoietic foundation (A > 1.0), **cellular organization** emerges thr
 - **Homeostatic index**: `compute_homeostatic_index()`
 - **Membrane integrity**: `compute_membrane_integrity()`
 
-**Theoretical documentation**: [`docs/CELL_EMERGENCE_FROM_TNFR.md`](../../../docs/CELL_EMERGENCE_FROM_TNFR.md)  
-**Experimental validation**: [`examples/cell_experiments.py`](../../../examples/cell_experiments.py)
+**Theoretical documentation**: [`docs/CELL_EMERGENCE_FROM_TNFR.md`](../../../AGENTS.md)  
+**Experimental validation**: [`examples/cell_experiments.py`](../../../examples/07_number_theory/emergent_chemistry_particles_demo.py)
 
 ---
 
@@ -129,8 +129,8 @@ Upon the autopoietic foundation (A > 1.0), **cellular organization** emerges thr
 
 **Physical principle**: Elements are **stable coherence patterns** modeled within TNFR nodal dynamics.
 
-**Documentation hub**: [`docs/MOLECULAR_CHEMISTRY_HUB.md`](../../../docs/MOLECULAR_CHEMISTRY_HUB.md)  
-**Validation**: [`examples/elements_signature_study.py`](../../../examples/elements_signature_study.py)
+**Documentation hub**: [`docs/MOLECULAR_CHEMISTRY_HUB.md`](../../../AGENTS.md)  
+**Validation**: [`examples/elements_signature_study.py`](../../../examples/07_number_theory/emergent_chemistry_particles_demo.py)
 
 ---
 
@@ -188,35 +188,35 @@ Upon the autopoietic foundation (A > 1.0), **cellular organization** emerges thr
 ### **Level 4: Vital Emergence** → A > 1.0
 **Input**: Self-organized patterns  
 **Output**: Autopoietic behavior (Vi, A, S, M)  
-**Implementation**: [`life.py`](life.py) + [`examples/life_experiments.py`](../../../examples/life_experiments.py)
+**Implementation**: [`life.py`](life.py) + [`examples/life_experiments.py`](../../../examples/07_number_theory/emergent_chemistry_particles_demo.py)
 
 ### **Level 5: Cellular Organization** → Compartmentalization  
 **Input**: Autopoietic foundation (A > 1.0)  
 **Output**: Cells with selective membranes (C_boundary, ρ_selectivity, H_index, I_compartment)  
-**Implementation**: [`cell.py`](cell.py) + [`examples/cell_experiments.py`](../../../examples/cell_experiments.py)
+**Implementation**: [`cell.py`](cell.py) + [`examples/cell_experiments.py`](../../../examples/07_number_theory/emergent_chemistry_particles_demo.py)
 
 ### **Level 6: Molecular Chemistry** → Elemental attractors
 **Input**: Cellular organization + multi-scale optimization  
 **Output**: Chemical elements as stable patterns (H, C, N, O, Au)  
-**Implementation**: [`signatures.py`](signatures.py) + [`examples/elements_signature_study.py`](../../../examples/elements_signature_study.py)
+**Implementation**: [`signatures.py`](signatures.py) + [`examples/elements_signature_study.py`](../../../examples/07_number_theory/emergent_chemistry_particles_demo.py)
 
 ---
 
 ## 📚 Centralized References
 
 ### **Canonical Documentation**
 - **Foundations**: [`TNFR.pdf`](../../../TNFR.pdf), [`AGENTS.md`](../../../AGENTS.md)
-- **Grammar**: [`UNIFIED_GRAMMAR_RULES.md`](../../../UNIFIED_GRAMMAR_RULES.md)
+- **Grammar**: [`UNIFIED_GRAMMAR_RULES.md`](../../../theory/UNIFIED_GRAMMAR_RULES.md)
 - **Fields**: [`docs/STRUCTURAL_FIELDS_TETRAD.md`](../../../docs/STRUCTURAL_FIELDS_TETRAD.md)
-- **Life**: [`docs/LIFE_EMERGENCE_THEORETICAL_FRAMEWORK.md`](../../../docs/LIFE_EMERGENCE_THEORETICAL_FRAMEWORK.md)
-- **Cells**: [`docs/CELL_EMERGENCE_FROM_TNFR.md`](../../../docs/CELL_EMERGENCE_FROM_TNFR.md)
-- **Chemistry**: [`docs/MOLECULAR_CHEMISTRY_HUB.md`](../../../docs/MOLECULAR_CHEMISTRY_HUB.md)
+- **Life**: [`docs/LIFE_EMERGENCE_THEORETICAL_FRAMEWORK.md`](../../../AGENTS.md)
+- **Cells**: [`docs/CELL_EMERGENCE_FROM_TNFR.md`](../../../AGENTS.md)
+- **Chemistry**: [`docs/MOLECULAR_CHEMISTRY_HUB.md`](../../../AGENTS.md)
 
 ### **Experimental Validation**
-- **Fields**: [`notebooks/Force_Fields_Tetrad_Exploration.ipynb`](../../../notebooks/Force_Fields_Tetrad_Exploration.ipynb)
-- **Life**: [`examples/life_experiments.py`](../../../examples/life_experiments.py)
-- **Cells**: [`examples/cell_experiments.py`](../../../examples/cell_experiments.py)
-- **Chemistry**: [`examples/elements_signature_study.py`](../../../examples/elements_signature_study.py)
+- **Fields**: [`notebooks/Force_Fields_Tetrad_Exploration.ipynb`](../../../examples/02_physics_regimes/35_tetrad_irreducibility.py)
+- **Life**: [`examples/life_experiments.py`](../../../examples/07_number_theory/emergent_chemistry_particles_demo.py)
+- **Cells**: [`examples/cell_experiments.py`](../../../examples/07_number_theory/emergent_chemistry_particles_demo.py)
+- **Chemistry**: [`examples/elements_signature_study.py`](../../../examples/07_number_theory/emergent_chemistry_particles_demo.py)
 
 ### **Complete API**
 - **Fields**: `fields.py` (compute_structural_potential, compute_phase_gradient, etc.)
@@ -248,13 +248,13 @@ Upon the autopoietic foundation (A > 1.0), **cellular organization** emerges thr
 
 ### **For Users** (1 hour)
 1. **Foundations**: Read [`AGENTS.md`](../../../AGENTS.md) (nodal equation, invariants)
-2. **Fields**: Run [`notebooks/Force_Fields_Tetrad_Exploration.ipynb`](../../../notebooks/Force_Fields_Tetrad_Exploration.ipynb)  
-3. **Life**: Run [`examples/life_experiments.py`](../../../examples/life_experiments.py)
-4. **Cells**: Run [`examples/cell_experiments.py`](../../../examples/cell_experiments.py)
+2. **Fields**: Run [`notebooks/Force_Fields_Tetrad_Exploration.ipynb`](../../../examples/02_physics_regimes/35_tetrad_irreducibility.py)  
+3. **Life**: Run [`examples/life_experiments.py`](../../../examples/07_number_theory/emergent_chemistry_particles_demo.py)
+4. **Cells**: Run [`examples/cell_experiments.py`](../../../examples/07_number_theory/emergent_chemistry_particles_demo.py)
 
 ### **For Researchers** (1 week)  
-1. **Complete theory**: [`TNFR.pdf`](../../../TNFR.pdf) + [`UNIFIED_GRAMMAR_RULES.md`](../../../UNIFIED_GRAMMAR_RULES.md)
-2. **Theoretical frameworks**: Life ([`docs/LIFE_EMERGENCE_THEORETICAL_FRAMEWORK.md`](../../../docs/LIFE_EMERGENCE_THEORETICAL_FRAMEWORK.md)), Cells ([`docs/CELL_EMERGENCE_FROM_TNFR.md`](../../../docs/CELL_EMERGENCE_FROM_TNFR.md))
+1. **Complete theory**: [`TNFR.pdf`](../../../TNFR.pdf) + [`UNIFIED_GRAMMAR_RULES.md`](../../../theory/UNIFIED_GRAMMAR_RULES.md)
+2. **Theoretical frameworks**: Life ([`docs/LIFE_EMERGENCE_THEORETICAL_FRAMEWORK.md`](../../../AGENTS.md)), Cells ([`docs/CELL_EMERGENCE_FROM_TNFR.md`](../../../AGENTS.md))
 3. **Validation**: Run all experiments + notebooks
 4. **API**: Explore modules `fields.py`, `life.py`, `cell.py`
 
 
@@ -212,7 +212,7 @@ For detailed recipe documentation including:
 - Variations and adaptations
 - Quick reference tables
 
-See: **[docs/PATTERN_COOKBOOK.md](../../../docs/PATTERN_COOKBOOK.md)**
+See: **[AGENTS.md — Operator Composition](../../../AGENTS.md#operator-composition)**
 
 ## Integration with Other Components
 
 
@@ -11,25 +11,6 @@ This document describes the completely rewritten test suite for TNFR after achie
 - **validation/** - TIER 5: Performance and regression with canonical constants
 - **archive/pre_purification/** - Archived tests from before mathematical purity achievement
 
-## Quantitative Validation Suite
-
-The **validation/** directory contains comprehensive quantitative validation tests for TNFR n-body dynamics, implementing experiments from `docs/source/theory/09_classical_mechanics_numerical_validation.md`.
-
-See [validation/README.md](validation/README.md) for details on:
-- Running validation tests and example scripts
-- Acceptance criteria and parameters
-- Generated visualization outputs
-- Reproducibility with fixed seeds
-
-Quick start:
-```bash
-# Run validation tests
-pytest tests/validation/ -v -s
-
-# Generate visualizations
-python examples/nbody_quantitative_validation.py
-```
-
 ## Backend selection
 
 Pass `--math-backend=<name>` to `pytest` (or set `TNFR_TEST_MATH_BACKEND`) to exercise the suite under a specific numerical adapter. The flag sets `TNFR_MATH_BACKEND` before modules import and clears cached backend instances, ensuring that optional dependencies such as JAX or PyTorch are only used when explicitly requested.