Empirical confrontation arm; Riemann/NS nodal-pulse re-founding; docs refresh

Empirical arm (validation/signal_confrontation.py): data-agnostic confront_signal reads the emergent geometry (tetrad, pulse, universal coherence kernel, xi_C via the spectral gap). The two-face diagnosis is EMERGENT via emergent_wave_fraction (per-mode AR(2) on the L_sym eigenmodes: damping read from the emergent dynamics, not an input-spectrum proxy). nodal_prediction_skill confronts the nodal equation dEPI/dt = nu_f*dNFR as a one-step predictor (EPI channel = graph diffusion) vs persistence and AR-1. Adds example 159, tests, and docs/EMPIRICAL_CONFRONTATION_EEG.md.

Real-data validation (scratch, no data bundled): the local tetrad K_phi/grad-phi carries cross-subject labelled state (eegmmidb eyes-open/closed, K_phi 10/10, p~0.002); the two-face reading discriminates EEG (wave) from a real thermal field (diffusive); the nodal predictor is diffusion-selective. Structural fidelity only: closes nothing, no new physics, no superiority over baselines.

Riemann re-founding: eliminate the obsolete combinatorial-Laplacian track; found on the emergent prime-NFR nodal pulse (nodal_pulse.py, pulse_coherence.py). Navier-Stokes re-founding: the two-face reading (linear NS = diffusive over-damped projection; blow-up = the nonlinear K_phi cascade), with conservative_face.py and a spectral Taylor-Green solver in operator.py. Retired modules, tests, examples and benchmarks pruned.

physics: estimate_coherence_length falls back to the spectral-gap 1/sqrt(lambda_2) (never nan); complex-safe Fiedler slow-rate in verify_overdamped_projection. Docs: current-state refresh, version-history narrative removed, counts corrected. Full suite: 1603 passed, 2 skipped.

Author: TNFR AI Agent

.github/agents/my-agent.md

@@ -482,7 +482,7 @@ program history** (the full milestone/gap/branch threads live in the notes).
 |---------|--------|-----------|
 | **TNFR-Riemann** | `σ_c → ½` numerically verified; ζ↔L attack surface shipped (P12–P49). The bridge to RH is the open conjecture **T-HP** (gap G4), paused at the oscillatory residue `S(T) = (1/π)·arg ζ(½+iT)`. | [TNFR_RIEMANN_RESEARCH_NOTES.md](theory/TNFR_RIEMANN_RESEARCH_NOTES.md) |
 | **REMESH-∞ closure** | The 13-operator catalog is closed under the `τ_g → ∞` limit (N15, Branch A); universality is structural/operational, not spectral. | [REMESH_INFINITY_DERIVATION.md](theory/REMESH_INFINITY_DERIVATION.md) |
-| **TNFR-Navier–Stokes** | `K_φ` cascade and a BKM-analogue U2 blow-up criterion; NS advection+viscosity maps faithfully to a VAL-vs-IL U2 enstrophy budget read in structural time `τ_str = ν_f·t` (fixed-Re compliant; peak debt grows with Re — relocates Clay, closes nothing); 2D asymmetry closed at the discrete level; continuum closure NS-G1 open. | [TNFR_NAVIER_STOKES_RESEARCH_NOTES.md](theory/TNFR_NAVIER_STOKES_RESEARCH_NOTES.md) |
+| **TNFR-Navier–Stokes** | The two-face reading: incompressible NS is first-order, so its *linear* part is the **diffusive (over-damped) projection** of the substrate wave (`ν_f = ν`; `verify_diffusive_face` VALID for every physical viscosity) — blow-up is a purely **nonlinear `K_φ` cascade** (the vortex-stretching VAL source), not a linear resonance. Measured: peak enstrophy debt grows with Re at matched `τ_str = ν·t` (bounded at fixed Re — the diffusive face regularises); the `Re → ∞` cascade bound = Clay, **open**. Closes nothing. | [TNFR_NAVIER_STOKES_RESEARCH_NOTES.md](theory/TNFR_NAVIER_STOKES_RESEARCH_NOTES.md) |
 | **Number theory** | Primality as `ΔNFR = 0` (canonical **unit** coefficients, §4.2 coefficient independence); arithmetic structural triad; the arithmetic network as an NFR (multinodal topology + emergent symplectic geometry); the cyclotomy law `s_k(p) = gcd(k, p−1) + 1` (proved), read as the **arithmetic pulse** (the residue-NFR's tone-count — a prime is its most degenerate chord). | [TNFR_NUMBER_THEORY.md](theory/TNFR_NUMBER_THEORY.md) |
 | **Millennium reformulations** | P vs NP, BSD, Hodge, Yang–Mills: TNFR-internal structural reformulations and diagnostics — none a proof. | `theory/TNFR_*_RESEARCH_NOTES.md` |
 

AGENTS.md

@@ -520,7 +520,7 @@ program history** (the full milestone/gap/branch threads live in the notes).
 |---------|--------|-----------|
 | **TNFR-Riemann** | `σ_c → ½` numerically verified; ζ↔L attack surface shipped (P12–P49). The bridge to RH is the open conjecture **T-HP** (gap G4), paused at the oscillatory residue `S(T) = (1/π)·arg ζ(½+iT)`. | [TNFR_RIEMANN_RESEARCH_NOTES.md](theory/TNFR_RIEMANN_RESEARCH_NOTES.md) |
 | **REMESH-∞ closure** | The 13-operator catalog is closed under the `τ_g → ∞` limit (N15, Branch A); universality is structural/operational, not spectral. | [REMESH_INFINITY_DERIVATION.md](theory/REMESH_INFINITY_DERIVATION.md) |
-| **TNFR-Navier–Stokes** | `K_φ` cascade and a BKM-analogue U2 blow-up criterion; NS advection+viscosity maps faithfully to a VAL-vs-IL U2 enstrophy budget read in structural time `τ_str = ν_f·t` (fixed-Re compliant; peak debt grows with Re — relocates Clay, closes nothing); 2D asymmetry closed at the discrete level; continuum closure NS-G1 open. | [TNFR_NAVIER_STOKES_RESEARCH_NOTES.md](theory/TNFR_NAVIER_STOKES_RESEARCH_NOTES.md) |
+| **TNFR-Navier–Stokes** | The two-face reading: incompressible NS is first-order, so its *linear* part is the **diffusive (over-damped) projection** of the substrate wave (`ν_f = ν`; `verify_diffusive_face` VALID for every physical viscosity) — blow-up is a purely **nonlinear `K_φ` cascade** (the vortex-stretching VAL source), not a linear resonance. Measured: peak enstrophy debt grows with Re at matched `τ_str = ν·t` (bounded at fixed Re — the diffusive face regularises); the `Re → ∞` cascade bound = Clay, **open**. Closes nothing. | [TNFR_NAVIER_STOKES_RESEARCH_NOTES.md](theory/TNFR_NAVIER_STOKES_RESEARCH_NOTES.md) |
 | **Number theory** | Primality as `ΔNFR = 0` (canonical **unit** coefficients, §4.2 coefficient independence); arithmetic structural triad; the arithmetic network as an NFR (multinodal topology + emergent symplectic geometry); the cyclotomy law `s_k(p) = gcd(k, p−1) + 1` (proved), read as the **arithmetic pulse** (the residue-NFR's tone-count — a prime is its most degenerate chord). | [TNFR_NUMBER_THEORY.md](theory/TNFR_NUMBER_THEORY.md) |
 | **Millennium reformulations** | P vs NP, BSD, Hodge, Yang–Mills: TNFR-internal structural reformulations and diagnostics — none a proof. | `theory/TNFR_*_RESEARCH_NOTES.md` |
 

ARCHITECTURE.md

@@ -42,7 +42,10 @@ src/tnfr/                          # ~346 files, ~104k LOC
 ├── metrics/                        # Coherence, Si, phase sync
 ├── telemetry/                      # Unified field monitoring
 ├── sdk/                            # Fluent API + Simple SDK + builders
-├── riemann/                        # TNFR-Riemann operator implementation
+├── validation/                      # Structural health + empirical-arm signal confrontation
+├── riemann/                         # TNFR-Riemann program (nodal-pulse foundation)
+├── navier_stokes/                   # TNFR-Navier-Stokes program (conservative two-face reading)
+├── yang_mills/                      # TNFR-Yang-Mills gap diagnostics
 └── factorization/                  # Spectral factorization workflow
 ```
 
@@ -535,7 +538,7 @@ TNFR Engine is a complex-systems framework grounded in the nodal equation:
 | **Self-Optimization** | COMPLETE | Autonomous structural improvement |
 | **Telemetry** | COMPLETE | Complete system observability |
 | **Developer Experience** | COMPLETE | Fluent API + Simple SDK (tetrad, conservation, telemetry) |
-| **Production Readiness** | COMPLETE | 1,655 tests passing + benchmarks + validation |
+| **Production Readiness** | COMPLETE | 1,599 tests passing + benchmarks + validation |
 
 ### Architectural Principles (Canonical)
 

CHANGELOG.md

@@ -40,26 +40,37 @@ All notable changes to this project will be documented in this file.
   **equal temperament** / the chosen scale are imposed. Woven into
   `EMERGENT_ONTOLOGY.md` §5.5 + the `form → dimension → dynamics` synthesis (§2.1).
 
-### Added — NS U2-compliance read in structural time (Navier–Stokes reformulation)
-
-- **3D Navier–Stokes mapped to a faithful U2 budget, read in TNFR structural time.**
-  `benchmarks/u2_compliance_navier_stokes_structural_time.py` + theory §21. The
-  vorticity dynamics maps term-by-term to operators — `(ω·∇)u` = **VAL** (destabilizer,
-  production `P`), `ν Δω` = **IL** (stabilizer, the nodal-equation diffusion `D_ens`),
-  advection = **NAV** and pressure = **UM** (both enstrophy-neutral *analytically*:
-  pressure vanishes under the curl, transport is skew). So the **U2 debt**
-  `∫(P − D_ens)dt = Ω(t) − Ω(0)` is exactly the enstrophy budget, and U2-compliance ⟺
-  bounded enstrophy ⟺ classical regularity (a faithful re-expression, not a surrogate).
-- **Structural time `τ_str = νf·t` is the correct clock** (the eigenmode-decay clock of
-  the nodal equation). Two operator clocks — IL (dissipation) on `τ_str`, VAL (stretching)
-  on the ν-independent advective eddy clock — with `Re` = their ratio = the U2 debt rate.
-  Measured (TG, `n=32`): every fixed-Re run **saturates** (enstrophy peaks & decays →
-  U2-compliant, the Lyapunov closes), and the **peak debt grows with Re** (1.0 → 1.5 →
-  2.4; resolving at `n=48` *raises* the Re~1257 point to 2.89 — coarse grids under-state
-  the production).
-- **HONEST SCOPE:** closes nothing. The faithful reformulation **relocates** Clay to
-  *"is the peak structural-time U2 debt uniformly bounded in Re?"* — it does not lower the
-  wall; no uniform-in-Re bound is produced. Clay open.
+### Changed — TNFR–Navier–Stokes re-founded on the two-face reading
+
+- **The NS program was re-founded on the current paradigm.** The previous
+  diffusive-face enstrophy-budget program — the `u2_compliance` structural-time
+  benchmark, the N1–N14 milestone examples (77–86, 104, 105) and the old
+  `operator.py` — was retired. New foundation `src/tnfr/navier_stokes/`: a faithful
+  lean pseudo-spectral 3D integrator (`TNFRNavierStokes`, rotational form, exact
+  Leray projection, integrating-factor RK2) + `conservative_face.py`
+  (`verify_diffusive_face`, `face_of_flow`, `vorticity_modal_spectrum`,
+  `measure_cascade_frontier`).
+- **The honest two-face reading.** Incompressible NS is first order, so its *linear*
+  part is the **diffusive (over-damped) projection** of the substrate wave
+  (`ν_f = ν`; `verify_diffusive_face` VALID for every physical viscosity, recovering
+  `ν_f = ν`). Blow-up is therefore a purely **nonlinear `K_φ` cascade** (the
+  vortex-stretching VAL source), not a linear resonance — unlike oscillatory data
+  (EEG), which sits on the under-damped conservative face.
+- **The blow-up frontier, measured** (`measure_cascade_frontier`, example 158): at
+  matched structural time `τ_str = ν·t` every run saturates at fixed Re (the
+  diffusive face regularises) and the peak enstrophy debt grows with Re
+  (1.00 → 1.04 → 1.68 at Re 126/314/628). The `Re → ∞` cascade bound = Clay, **open**.
+- **HONEST SCOPE:** closes nothing; global 3D NS regularity stays open.
+
+### Added — the empirical-confrontation pipeline (TNFR-IA → engine)
+
+- **`examples/10_applications/159_empirical_confrontation_pipeline.py`** packages the
+  empirical arm's workflow with engine primitives: map a multichannel signal onto the
+  emergent phase-locking graph, read the canonical magnitudes (the pulse, the tetrad,
+  `ξ_C`, Kuramoto `R`), and **diagnose its face** with the engine's own
+  `verify_overdamped_projection` — making the theory falsifiable against data (the face
+  is *measured*, not assumed). Cross-program face map: oscillatory data → conservative
+  face; linear NS → diffusive face.
 
 ### Changed (emergent derivation — the grammar temporal windows from the pulse)
 

README.md

@@ -52,18 +52,18 @@ TNFR is more than dynamics on a graph. The graph is only the substrate; the noda
 
 Two clearly-separated layers:
 
-**Solid and verified.** The engine, the tetrad, grammar U1–U6, conservation laws, and the emergent transport + symplectic geometry are implemented, anchored to experimentally-established phenomena, and covered by 2,041 tests.
+**Solid and verified.** The engine, the tetrad, grammar U1–U6, conservation laws, and the emergent transport + symplectic geometry are implemented, anchored to experimentally-established phenomena, and covered by 1,599 tests.
 
 **Open research programs.** TNFR is also used to probe famous open problems. These are honest, in-progress programs that **do not claim proofs**:
 
-| Program | Done | Open |
-|---------|------|------|
-| TNFR–Riemann (P1–P49) | discrete operator σ_c → 1/2; ζ↔L attack surface | Riemann Hypothesis (gap G4) — **paused at T-HP** |
-| TNFR–Navier–Stokes (N1–N17) | NS-G5 closed at discrete-operator level | continuum limit / Clay (NS-G1..G4) — **open** |
-| TNFR–Yang–Mills (Y1–Y5) | finite U(1) structural diagnostics | non-Abelian mass gap — **open** (Branch B) |
-| TNFR–P vs NP (PNP-1) | coherence verification O(\|E\|) vs synthesis trapping | worst-case separation — **open** (Branch B) |
-| TNFR–BSD (BSD-1) | rank separation via structural-pressure accumulation | rank ↔ order of vanishing — **open** (Branch B) |
-| TNFR–Hodge (HC-1) | discrete Hodge = homology exactly (Eckmann) | (p,p) bigrading + algebraicity — **structurally blind** (Branch B3-leaning) |
+| Program | What it does | Status |
+|---------|--------------|--------|
+| TNFR–Riemann | reads ζ as the integer-NFR **nodal pulse**; `S(T)` is the pulse phase and the critical line is its coherence axis | Riemann Hypothesis — **open** |
+| TNFR–Navier–Stokes | the **two-face reading**: linear NS is the diffusive (over-damped) projection, so blow-up is the nonlinear `K_φ` cascade, read through the emergent coherence attractor | 3D global regularity (Clay) — **open** |
+| TNFR–Yang–Mills | structural gap diagnostics on the gauge sector | non-Abelian mass gap — **open** |
+| TNFR–P vs NP | coherence verification O(\|E\|) vs synthesis trapping | worst-case separation — **open** |
+| TNFR–BSD | rank via structural-pressure accumulation | rank ↔ order of vanishing — **open** |
+| TNFR–Hodge | discrete Hodge = homology exactly (Eckmann) | (p,p) bigrading + algebraicity — **open** (structurally blind) |
 
 See [AGENTS.md](AGENTS.md) and the `theory/` research notes for the full, audited status.
 
@@ -152,21 +152,21 @@ src/tnfr/
 ├── physics/           # Tetrad, conservation, emergent symplectic substrate, structural diffusion (29 modules)
 ├── engines/           # Self-optimization, pattern discovery, GPU/FFT (8 modules across 5 subpackages)
 ├── dynamics/           # Nodal equation integration
-├── riemann/           # TNFR–Riemann program (61 modules, P1–P49; paused at T-HP, RH open)
-├── navier_stokes/     # TNFR–Navier–Stokes program (N1–N17; NS-G5 closed at discrete level, Clay open)
-├── yang_mills/        # TNFR–Yang–Mills diagnostics (Y1–Y5; Branch B, mass gap open)
+├── riemann/           # TNFR–Riemann program (52 modules; nodal-pulse foundation, RH open)
+├── navier_stokes/     # TNFR–Navier–Stokes program (conservative two-face reading, Clay open)
+├── yang_mills/        # TNFR–Yang–Mills diagnostics (mass gap open)
 ├── sdk/               # Simplified & Fluent API (7 modules)
 │   └── simple.py      # Tetrad, conservation, symplectic substrate, grammar-aware dynamics
 ├── mathematics/       # Number theory, backends
 ├── constants/         # Canonical constants (mpmath 35-digit precision)
 ├── metrics/           # Coherence, Si, phase sync, telemetry
-├── validation/        # Structural health monitoring
+├── validation/        # Structural health monitoring + empirical-arm signal confrontation
 └── factorization/     # Spectral factorization workflow
 
-examples/              # 162 examples in 10 thematic subfolders (see examples/README.md)
-tests/                 # 2,041 tests
+examples/              # 150 examples in 10 thematic subfolders (see examples/README.md)
+tests/                 # 1,599 tests
 theory/                # Theoretical derivations
-benchmarks/            # 50 performance & structural-validation scripts
+benchmarks/            # performance & structural-validation scripts
 ```
 
 ---
@@ -180,12 +180,13 @@ benchmarks/            # 50 performance & structural-validation scripts
 | [theory/FUNDAMENTAL_THEORY.md](theory/FUNDAMENTAL_THEORY.md) | Structural-field tetrad & field scales |
 | [docs/STRUCTURAL_FIELDS_TETRAD.md](docs/STRUCTURAL_FIELDS_TETRAD.md) | Field implementation specifications |
 | [docs/STRUCTURAL_INTERFACE_THEORY.md](docs/STRUCTURAL_INTERFACE_THEORY.md) | Structural-interface programme: pipelines, fair benchmarks, validated results, limitations |
+| [docs/EMPIRICAL_CONFRONTATION_EEG.md](docs/EMPIRICAL_CONFRONTATION_EEG.md) | Empirical confrontation of canonical magnitudes with real signals (the falsifiable arm) |
 | [theory/TNFR_RIEMANN_RESEARCH_NOTES.md](theory/TNFR_RIEMANN_RESEARCH_NOTES.md) | TNFR-Riemann program |
 | [theory/TNFR_NAVIER_STOKES_RESEARCH_NOTES.md](theory/TNFR_NAVIER_STOKES_RESEARCH_NOTES.md) | TNFR-Navier–Stokes program |
-| [theory/TNFR_YANG_MILLS_RESEARCH_NOTES.md](theory/TNFR_YANG_MILLS_RESEARCH_NOTES.md) | TNFR–Yang–Mills structural gap programme (Y1–Y5; Branch B classified) |
-| [theory/TNFR_P_VS_NP_RESEARCH_NOTES.md](theory/TNFR_P_VS_NP_RESEARCH_NOTES.md) | TNFR–P vs NP synthesis-vs-verification programme (PNP-1; Branch B, not a proof) |
-| [theory/TNFR_BSD_RESEARCH_NOTES.md](theory/TNFR_BSD_RESEARCH_NOTES.md) | TNFR–Birch–Swinnerton-Dyer structural-pressure programme (BSD-1; Branch B, not a proof) |
-| [theory/TNFR_HODGE_RESEARCH_NOTES.md](theory/TNFR_HODGE_RESEARCH_NOTES.md) | TNFR–Hodge discrete cochain programme (HC-1; Branch B3-leaning strong negative, not a proof) |
+| [theory/TNFR_YANG_MILLS_RESEARCH_NOTES.md](theory/TNFR_YANG_MILLS_RESEARCH_NOTES.md) | TNFR–Yang–Mills structural gap programme (mass gap open, not a proof) |
+| [theory/TNFR_P_VS_NP_RESEARCH_NOTES.md](theory/TNFR_P_VS_NP_RESEARCH_NOTES.md) | TNFR–P vs NP synthesis-vs-verification programme (not a proof) |
+| [theory/TNFR_BSD_RESEARCH_NOTES.md](theory/TNFR_BSD_RESEARCH_NOTES.md) | TNFR–Birch–Swinnerton-Dyer structural-pressure programme (not a proof) |
+| [theory/TNFR_HODGE_RESEARCH_NOTES.md](theory/TNFR_HODGE_RESEARCH_NOTES.md) | TNFR–Hodge discrete cochain programme (structurally blind, not a proof) |
 | [theory/GLOSSARY.md](theory/GLOSSARY.md) | Terminology and definitions |
 | [examples/](examples/) | Sequential tutorials |
 | [ARCHITECTURE.md](ARCHITECTURE.md) | System design |
@@ -196,7 +197,7 @@ benchmarks/            # 50 performance & structural-validation scripts
 ## Testing
 
 ```bash
-pytest                             # all tests (2,041 under tests/)
+pytest                             # all tests (1,599 under tests/)
 pytest tests/sdk/                  # SDK tests (tetrad, conservation, grammar)
 pytest tests/unit/                 # unit tests
 .\make.cmd smoke-tests             # smoke tests (Windows)