30-EFT.WP.Propagation.TensionPotential v1.0 | Chapter 11 — Validation Experiments & Benchmark Datasets

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Chapter 11 — Validation Experiments & Benchmark Datasets

• I. One-Sentence Aim
  Validate the correctness of modeling for Phi_T(x,t), n_eff(x,t,f), and arrival time T_arr using reproducible experiments and benchmark datasets. Quantify two-gauge consistency, lower-bound feasibility, separability of the path term, inter-layer interface matching, and anisotropic responses, and define falsification criteria and audit procedures.
• II. Scope & Non-Goals
• Covered: validation dimensions and metrics, general experimental design, six experiment groups (A…F), benchmark datasets (D1…D5), statistical methods, reproducibility and audit standards, falsification lines and reporting requirements.
• Non-goals: no re-derivation of Chapter 3 equations; no replacement of Chapter 7 metrology and uncertainty flows; no device-level mechanical/electrical details.
• III. Minimal Terms & Symbols
• Observations & model: T_arr_obs(f, gamma), T_arr_mod(f, gamma), Residual = T_arr_obs − T_arr_mod.
• Two-gauge consistency: eta_T = | T_arr^{const} − T_arr^{gen} |.
• Lower bound: LB = L_path / c_ref (semantics of the constant-factored gauge; the general gauge has the equivalent bound embedded in the integrand).
• Band differencing: ΔT_arr(f1,f2) to isolate the path term.
• Interfaces & matching: Sigma, C_sigma, J_sigma, R_sigma, T_trans (strictly distinct from T_fil).
• Uncertainty: u_stat, u_sys, combined u_c, guardband GB = k_guard · u_c.
• IV. Validation Dimensions & Metric Definitions
• M1 Arrival-time residuals: Residual(f, gamma) = T_arr_obs − T_arr_mod; report mean(Residual), std(Residual), and the distribution of normalized z = Residual / u_c.
• M2 Two-gauge consistency: eta_T; require eta_T ≤ threshold; if exceeded, revisit c_ref calibration and n_eff decomposition (see Chapter 7).
• M3 Lower-bound check: verify T_arr_obs ≥ LB; edge samples may be included within a tolerance band k · u_c but must be listed separately.
• M4 Band-differencing identifiability: correlation coefficient and slope between measured ΔT_arr(f1,f2) and model differentials; should be linear over the target band or match the polynomial order set in Chapter 5.
• M5 Anisotropy significance: regression of ΔT_arr against dot( grad_Phi_T , t_hat ) across differently oriented path sets; report significance and effect size.
• M6 Interface consistency: difference in T_arr before/after segmented integration, trigger rate and magnitude of interface corrections, and energy consistency R_sigma + T_trans + A_sigma = 1.
• M7 Convergence & stability: error slope under refinement ratio r, with | T_arr^{(fine)} − T_arr^{(coarse)} | ≤ eps_T.
• M8 Reproducibility & auditability: hash consistency, complete logs, replayable RNG seeds, and coordinate/unit contracts.
• V. General Experimental Design
• Gauge preference: use the constant-factored gauge by default; if c_ref exhibits measurable weak dependence on band/state, use the general gauge and provide c_ref(x,t,f) estimates and uncertainties at input.
• Multi-band × multi-path: same-path multi-band data separate n_common vs. n_path; multi-path data identify geometric vs. medium differences and anisotropy.
• Explicit interfaces: perform segmented integration at interfaces; record { ell_i } and correction terms; do not interpolate across interfaces.
• Dual uncertainty methods: compute u_c via both GUM and MC; MC must use seedable randomness.
• Minimal logging set: hash(Phi_T), hash(grad_Phi_T), hash(n_eff), hash(gamma), SolverCfg, mode, eps_T, eta_T, GB, u_c, and coordinate/unit contracts.
• VI. Experiment Group A | Lower Bound & Two-Gauge Consistency
• Goal: verify T_arr ≥ LB and the threshold for eta_T.
• Steps:
• A1: calibrate c_ref using benchmark path gamma_ref.
• A2: measure multiple paths in uniform/slowly varying media.
• A3: compute T_arr_mod with both gauges and compare eta_T.
• Pass criteria: T_arr_obs − LB ≥ −k · u_c and eta_T ≤ threshold; failing samples enter the falsification list.
• VII. Experiment Group B | Band Differencing to Isolate the Path Term
• Goal: on the same path, use ΔT_arr(f1,f2) to cancel n_common and test the band structure of n_path.
• Steps:
• B1: choose frequencies f1,f2,… within the bandwidth assumptions of Chapter 5.
• B2: measure T_arr_obs(f_m) and compute differentials.
• B3: fit polynomial coefficients of n_path and compare with model ΔT_arr_mod.
• Pass criteria: correlation and slope within thresholds; out-of-band leakage residuals enter u_sys; overall differentials within GB.
• VIII. Experiment Group C | Anisotropy Detection
• Goal: determine whether the term b1 · dot( grad_Phi_T , t_hat ) (see Chapter 5) is significant.
• Steps:
• C1: design a sector of paths { gamma_a } with varied incidence directions.
• C2: regress ΔT_arr against dot( grad_Phi_T , t_hat ).
• C3: compare BIC/AIC between isotropic and directional models.
• Pass criteria: statistical significance met with controlled overfitting metrics; otherwise revert to the isotropic approximation.
• IX. Experiment Group D | Inter-Layer Interfaces & Segmented Integration
• Goal: validate matching conditions and correction terms on Sigma.
• Steps:
• D1: identify interfaces; classify as continuous / potential-jump / flux-jump / anisotropic.
• D2: compare segmented integration vs. zero-thickness interface corrections.
• D3: test energy consistency R_sigma + T_trans + A_sigma = 1.
• Pass criteria: differences between segmented and corrected results below threshold; energy consistency holds; n_eff ≥ 1 on both sides.
• X. Experiment Group E | Reference-Speed Stability & Drift
• Goal: test the stability of c_ref calibration and its environmental drift.
• Steps:
• E1: repeat c_ref calibration across environmental blocks (temperature/humidity, timebase sources).
• E2: cross-apply calibrated c_ref to independent path sets.
• E3: monitor drift over time.
• Pass criteria: drift within specified band; cross-application maintains eta_T within threshold.
• XI. Experiment Group F | Noise Injection & Robustness (including TBN)
• Goal: assess the impact of TBN(x,t) on estimates of n_eff and T_arr, and robustness to noise.
• Steps:
• F1: inject calibrated broadband noise in simulation, controlling SNR.
• F2: re-estimate n_common and n_path and compare parameter drift.
• F3: report the increment of u_sys and the triggered clamping ratio.
• Pass criteria: key metrics M1…M4 remain within GB; clamping trigger rate controlled and logged.
• XII. Benchmark Datasets (D1…D5)
• D1 Uniform-medium set: n_eff ≡ 1; end-to-end dimensional and lower-bound checks.
• D2 Linear-potential-gradient set: Phi_T = Phi_0 + a · x; has analytic approximations; tests step-size and error control.
• D3 Two-layer-interface set: two constant n_eff layers with optional corrections; validates segmentation and matching.
• D4 Anisotropic-channel set: specified grad_Phi_T and angular distribution of t_hat; detects significance of b1.
• D5 Band-dispersion set: multiple frequency points across the band; generate n_path per Chapter 5 polynomial order; evaluates differencing and out-of-band suppression.
• Minimal metadata: coords_spec, units_spec, f_grid, gamma[k], Δell[k], optional t_hat[k], Sigma with interface labels, c_ref or its calibration pairs, hash(Phi_T), hash(n_eff), licensing and citation conventions.
• XIII. Statistical Methods & Falsification Criteria
• Hypotheses:
• H0: two gauges are consistent; E[eta_T] does not exceed the threshold.
• H0: T_arr_obs ≥ LB.
• H0: ΔT_arr matches model differentials in-band (linear region or prescribed polynomial order).
• H0: interface energy consistency and n_eff ≥ 1 both hold.
• Pass / falsification rules:
• If any H0 is rejected and metrology/implementation errors are excluded, record a falsification sample.
• Three independent repeat falsifications on the same dimension trigger a review at the model/axiom level (Chapter 2 P20-*).
• XIV. Traceability & Reproducibility
• Artifact packaging: bundle minimal sets of data, code, parameters, RNG seeds, contracts, and logs; produce a hash manifest.
• Replay entry: provide a runlist and SolverCfg snapshot for one-click replay.
• Audit views: metric time series, falsification sample lists, interface trigger statistics, and energy-consistency margins.
• XV. Audit & Reporting
• Report structure:
• Overview: datasets, paths, bands, modes, thresholds.
• Metrics: M1…M8.
• Falsification lines: failing cases and categorized causes.
• Reproducibility: hashes, seeds, contracts, and log references.
• Release convention: report results as mean ± k · u_c; when using differentials, also report correlation coefficients and out-of-band residuals.
• XVI. Cross-References
• EFT.WP.Propagation.TensionPotential v1.0 Chapters 3, 5, 6, 7, 8, 9
• EFT.WP.Core.Metrology v1.0 M05-, M10-
• EFT.WP.Core.Errors v1.0 M20-*
• EFT.WP.Core.Equations v1.1 S06-*
• XVII. Deliverables
• Validation checklist and scripting conventions: steps and I/O definitions for experiment groups A…F.
• Benchmark dataset specifications: metadata fields and packaging conventions for D1…D5.
• Audit templates: metric dashboards, falsification lists, replay instructions, and hash manifests.