31-EFT.WP.BH.TensionWall v1.0 | Chapter 7 — Metrology & Observable Design

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Chapter 7 — Metrology & Observable Design

• I. One-Sentence Aim
  Establish a traceable metrology scheme and an observable system around the Tension Wall Sigma_TW, covering c_ref calibration, wall identification and classification, estimation of the energy triplet R_TW, T_trans, A_sigma, inversion of TWProfile parameters, two-gauge consistency and lower-bound checks, band differencing to isolate the path term, GUM/MC uncertainty propagation, and logging/audit practices.
• II. Scope & Non-Goals
• Covered: metrology targets and measurability definitions; observables and control forms; general experimental design; stepwise flows M40-*; uncertainty propagation; traceability and logging; acceptance criteria and falsification lines; interface mapping and data packaging.
• Not covered: re-derivation of Chapter 3 models or Chapter 5 parameterization details; replacements for Chapter 9 numerical implementation and performance optimization; device-level mechanical/electrical solutions.
• III. Minimal Terms & Symbols
• Key quantities: c_ref, T_arr, n_eff(x,t,f), Phi_T(x,t), grad_Phi_T(x,t).
• Geometry & interface: Sigma_TW, r_H, Delta_w, intersections { ell_i }, path gamma(ell) and line element d ell.
• Energy triplet: R_TW, T_trans, A_sigma, with R_TW + T_trans + A_sigma = 1.
• Differentials & echoes: ΔT_arr(f1,f2), ΔT_echo(k).
• Gauges & modes: mode ∈ {constant, general}; control forms in Section IV.
• Naming isolation: never mix T_fil with T_trans; never mix n with n_eff.
• IV. Metrology Targets & Measurability Definitions
• Measurable arrival time (single band, single path): T_arr_obs(f, gamma) in seconds.
• In-band differential (same path): ΔT_arr_obs(f1,f2, gamma) = T_arr_obs(f1, gamma) − T_arr_obs(f2, gamma).
• Echo-order delay (if multi-path exists): ΔT_echo_obs(k).
• Interface measurables: crossing count N_cross, solver tolerances for { ell_i }, interface-type labels.
• Energy-triplet estimators: R_TW_hat(f), T_trans_hat(f), A_sigma_hat(f).
• Gauge control forms (by call to Chapters 3 & 6)
• Constant factored out: T_arr_mod = ( 1 / c_ref ) * ( ∫ n_eff d ell )
• General gauge: T_arr_mod = ( ∫ ( n_eff / c_ref ) d ell )
• Differential: ΔT_arr_mod(f1,f2) = ( 1 / c_ref ) * ( ∫ [ n_path(f1) − n_path(f2) ] d ell )（or the corresponding general-gauge form）
• V. General Experimental Design
• Same-path multi-band: prefer ΔT_arr to cancel n_common and isolate the path term.
• Multi-path, multi-angle: identify non-sphericity and directional terms (dot( grad_Phi_T , t_hat ), dot( grad_Phi_T , n_vec )).
• Explicit wall segmentation: integrate piecewise at { ell_i }; apply ΔT_sigma consistently across frequencies when used.
• Dual-gauge computation: report both gauges for T_arr_mod and the consistency metric eta_T.
• Energy-consistency audit: for each band, report the residual of R_TW_hat + T_trans_hat + A_sigma_hat = 1.
• Traceability minimum: hash(Phi_T), hash(n_eff), hash(gamma), SolverCfg, coords_spec, units_spec, RNG seed.
• VI. Stepwise Flows (M40-19 … M40-30)
• M40-19 Reference-speed calibration (c_ref)
• Choose gamma_ref with reference T_arr_ref;
• Solve c_ref = ( ∫ n_eff_ref d ell ) / T_arr_ref (constant-factored), or solve numerically under the general gauge;
• Record environment blocks and uncertainties u_stat(c_ref), u_sys(c_ref).
• M40-20 Path & interface acquisition
• Capture { gamma[k], Δell[k] }, detect { ell_i }, persist solver tolerances and endpoints;
• Emit interface_marks, N_cross, and interface-type labels.
• M40-21 Multi-band & multi-path orchestration
• Design f ∈ { f_m } and { gamma_a }; same-path multi-band for ΔT_arr, multi-path for directional and non-spherical identification.
• M40-22 Energy-triplet estimation
• From incidence/exit pairs, contrast levels, and power balance, infer R_TW_hat, T_trans_hat, A_sigma_hat;
• Output in-band curves with clamping intervals.
• M40-23 Wall profile & parameter inversion
• With TWProfile parameter vector theta (see Chapter 5), minimize
  min_theta ∑ ( ( T_arr_obs − T_arr_mod(theta) ) / u_c )^2 + R(theta );
• Output theta_hat and covariance.
• M40-24 Two-gauge consistency audit
• Compute eta_T = | T_arr^{const} − T_arr^{gen} |;
• If out of spec, revisit c_ref calibration, n_eff decomposition, and consistency of ΔT_sigma.
• M40-25 Differential isolation & out-of-band assessment
• Compare ΔT_arr_obs(f1,f2) vs ΔT_arr_mod by correlation and slope;
• Route out-of-band power to u_sys and log leakage ratios.
• M40-26 Directional & non-spherical identification
• Regress ΔT_arr on dot( grad_Phi_T , t_hat ) and dot( grad_Phi_T , n_vec );
• Compare BIC/AIC with/without directional terms and control overfitting.
• M40-27 GUM uncertainty propagation
• Use first-order sensitivities (Chapter 3 S40-20 … S40-21) to synthesize u_c(T_arr) and u_c(ΔT_arr);
• Report mean ± k·u_c.
• M40-28 MC uncertainty propagation
• Sample { c_ref, n_eff[k], Δell[k] } respecting correlations; report distribution and quantiles;
• Use as the primary gauge under clamping/nonlinearity or interface jumps.
• M40-29 Energy & lower-bound checks
• Verify R_TW_hat + T_trans_hat + A_sigma_hat = 1;
• Verify T_arr_obs ≥ L_path / c_ref (constant-factored semantics; equivalently in the general gauge integrand).
• M40-30 Archival & audit
• Produce the metrology report and a reproducible package: contracts, data, code, hash(*), SolverCfg, falsification samples, and replay entry.
• VII. Uncertainty Models & Propagation (GUM/MC)
• GUM (constant-factored discrete form)
• T_arr ≈ (1/c_ref) * ∑ n_eff[k] · Δell[k]
• Sensitivities: ∂T/∂c_ref = −T_arr/c_ref, ∂T/∂n_eff[k] = Δell[k]/c_ref, ∂T/∂Δell[k] = n_eff[k]/c_ref
• Compose with correlation coefficients and covariance terms.
• GUM (general-gauge discrete form)
• T_arr ≈ ∑ ( n_eff[k] / c_ref[k] ) · Δell[k]
• Sensitivities: ∂T/∂n_eff[k] = Δell[k]/c_ref[k], ∂T/∂c_ref[k] = − n_eff[k] · Δell[k]/c_ref[k]^2
• MC
• Sample from the joint of { c_ref, n_eff, Δell }, report median, quantiles, and tail metrics;
• Prefer MC when clamping n_eff ∈ [1, n_max] or interface jumps induce strong nonlinearity.
• VIII. Traceability & Minimal Logs
• Physics & geometry: hash(Phi_T), hash(grad_Phi_T), hash(n_eff), hash(gamma), Sigma_TW labels and { ell_i } tolerances.
• Gauges & thresholds: mode, eps_T, eta_T, eta_c, lower-bound margin T_arr_obs − L_path/c_ref.
• Energy & differentials: R_TW_hat, T_trans_hat, A_sigma_hat and residual, ΔT_arr linear region and out-of-band leakage ratio.
• Uncertainty: u_stat, u_sys, u_c, GUM/MC configs, k, RNG seed.
• Clamping & corrections: n_eff clamping trigger rate; ΔT_sigma counts and magnitudes.
• Reproducibility: SolverCfg, coords_spec, units_spec, runtime environment, and hash manifest.
• IX. Acceptance Criteria & Falsification Lines
• Acceptance
• T_arr_obs ≥ L_path / c_ref;
• eta_T ≤ threshold;
• ΔT_arr matches model differentials in-band (linear or specified polynomial order);
• R_TW_hat + T_trans_hat + A_sigma_hat = 1;
• Inversion residuals lie within GB = k_guard · u_c.
• Falsification
• Stable n_eff < 1 or broken energy consistency;
• Persistent two-gauge inconsistency not repairable by calibration;
• Failure of the differential in-band linear region not due to out-of-band leakage;
• Thin- vs thick-wall discrepancy beyond threshold or inconsistency between ΔT_sigma and volume integration.
• X. Interfaces & Implementation Bindings (I40-16 … I40-24)
• calibrate_c_ref( gamma_ref, T_arr_ref, n_eff_ref, mode ) -> c_ref
• capture_path( raw_track, coord_spec ) -> { gamma[k], Δell[k] }
• detect_TW_intersections( gamma, TWProfile ) -> { ell_i }
• estimate_RT_TW( data, TWProfile ) -> R_TW, T_trans, A_sigma
• fit_TW_profile( observations, Phi_T, grad_Phi_T, prior, model_spec ) -> theta_hat, Cov
• delta_arrival_TW( n_path_params, f1, f2, gamma, mode, c_ref ) -> ΔT_arr
• propagate_uncertainty_GUM( inputs ) -> u_c
• propagate_uncertainty_MC( inputs, Nsamples, seed ) -> dist(T_arr)
• emit_measurement_report( contract, logs, artifacts ) -> Report
• Constraint: at ingress, unify dimensions and enforce dim(T_arr) = [T], dim(n_eff) = 1; energy-consistency and lower-bound checks are mandatory.
• XI. Data Packaging & Publication Conventions
• Objects: Contract / Path / Observations / TWProfile / CalibCref / Interfaces / Report.
• Formats: prefer JSONL/Parquet; grid fields may use Zarr/NetCDF.
• Conventions: no external links in the body; references, hashes, and replay commands appear at the end of the report.
• Minimal bundle: data, code, parameters, SolverCfg, RNG seed, hash(*), audit logs, and the falsification roster.
• XII. Cross-References
• EFT.WP.BH.TensionWall v1.0 Chapter 3 (Minimal Equations & Structural Model), Chapter 5 (Wall Construction & Parameterization), Chapter 6 (Propagation & Arrival Time), Chapter 8 (Interface Matching), Chapter 11 (Validation & Benchmarks), Chapter 12 (Error Budget).
• EFT.WP.Propagation.TensionPotential v1.0 Chapter 7 (Metrology & Calibration).
• EFT.WP.Core.Metrology v1.0 M05-, M10-; EFT.WP.Core.Errors v1.0 M20-*.