33-EFT.WP.Cosmo.EarlyObjects v1.0 | Chapter 11 — Validation Experiments & Benchmark Datasets

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Chapter 11 — Validation Experiments & Benchmark Datasets

I. One-Sentence Goal

Deliver reproducible experiments and benchmark datasets that validate the end-to-end modeling of early-epoch objects—from causation → evolution → radiation → propagation → observation—and quantify: two-form consistency eta_T, the propagation lower bound, energy closure {R_env, T_trans, A_sigma}, thin/thick equivalence tau_switch, differential identifiability, and spectrum–light-curve coherence. Provide falsification criteria and an auditable workflow.

II. Scope & Non-Goals

Covered: validation dimensions and metrics, design of experiment groups (A…F), definitions and metadata of benchmark datasets (D1…D7), statistical methods and falsification lines, reproducibility and audit norms, publication and report structure.
Not covered: re-derivation of the physics/numerics in Chs. 3–9; the full details of uncertainty propagation (Ch. 12); instrument response or external observatory pipelines.

III. Terms & Minimal Notation

• Observation vs. model:
  T_arr_obs/Mod(f, gamma), Delta_T_arr_obs/Mod(f1,f2, gamma), F_nu_obs/Mod(f), LC_obs/Mod(t);
  Residual: Residual = Obs − Mod.
• Consistency indices:
  Two-form: eta_T = | T_arr^{const} − T_arr^{gen} |;
  Thin/thick: tau_switch = | T_arr^{thick} − ( T_arr^{thin} + Delta_T_sigma ) |.
• Lower bound: LB = L_path / c_ref (constant-pull-out semantics; general form is equivalent inside the integrand).
• Energy & sidedness: {R_env, T_trans, A_sigma} with R_env + T_trans + A_sigma = 1; n_eff^± ≥ 1.
• Guardrails: n_eff ≥ 1; naming isolation: T_fil ≠ T_trans, n ≠ n_eff.

IV. Validation Dimensions & Metric Definitions

• M1 Arrival-time residual: Residual_T(f, gamma) = T_arr_obs − T_arr_Mod; report mean/std and normalized residual z = Residual_T / u_c distribution.
• M2 Two-form consistency: eta_T under threshold; statistics by path/band and the out-of-spec ratio.
• M3 Lower-bound check: verify T_arr_obs ≥ LB; edge samples may fall within −k•u_c but must be isolated and annotated.
• M4 Thin/thick consistency: tau_switch ≤ gate; monotone decrease with step refinement.
• M5 Energy closure & sidedness: for each interface, verify the band-wise residual curve of R_env + T_trans + A_sigma = 1 and n_eff^± ≥ 1.
• M6 Differential identifiability: correlation and slope between Delta_T_arr_obs and Delta_T_arr_Mod; report out-of-band leakage residuals.
• M7 Spectrum–light-curve–arrival coherence: joint consistency across F_nu, LC, and T_arr/Delta_T_arr (multi-objective residuals and correlation panels).
• M8 Convergence & stability: | T_arr^{(fine)} − T_arr^{(coarse)} | ≤ eps_T; if not, trace back segmentation/endpoints/step size.
• M9 Clamping supervision: frequency of n_eff ∈ [1, n_max] clamp triggers and their estimated bias on T_arr.

V. Experimental Design Principles

• Same-path multi-band: use Delta_T_arr_obs to cancel n_common and isolate the path term; the two bands must share the same { gamma[k], Δell[k] }, segmentation, and Delta_T_sigma configuration.
• Multi-angle, multi-path: break structural/orientation and geometric degeneracies; enable significance tests for dot( grad_Phi_T , t_hat / n_vec ) if the model includes directionality.
• Explicit segmentation: include { ell_i } endpoints in the integral; no cross-interface interpolation; symmetric step refinement around endpoints.
• Two-form dual run: compute T_arr^{const} and T_arr^{gen} in parallel and archive eta_T; if exceeding threshold, back-trace c_ref calibration and n_eff decomposition first.
• Thin/thick dual chain: execute both in the eta_w neighborhood and report tau_switch; if out of bounds, lock thick and back-trace SeaProfile and endpoint tolerances.
• Minimal logging & traceability: record hash(Catalog/Seeds/Trajectory/SeaProfile/Phi_T/n_eff/gamma), coords_spec/units_spec/metric_spec, SolverCfg, seed, and DimReport.

VI. Group A — Lower Bound & Two-Form Consistency

Goal: verify T_arr ≥ LB and the eta_T gate.
Steps: A1 calibrate c_ref; A2 sample multiple paths in uniform/slowly varying media; A3 compute T_arr_Mod (both forms) and aggregate the eta_T distribution.
Pass: T_arr_obs − LB ≥ −k•u_c and eta_T ≤ threshold; failing samples are registered as falsifications.

VII. Group B — Thin/Thick Equivalence (Delta_T_sigma vs. Volume Integral)

Goal: validate equivalence between thin-layer correction and volumetric thick-layer integration.
Steps: B1 choose representative families (tanh/logistic/spline); B2 compute T_arr^{thick} and T_arr^{thin}+Delta_T_sigma; B3 plot tau_switch(refinement_ratio) over step/endpoint tolerances.
Pass: tau_switch ≤ gate; otherwise, lock thick and back-trace SeaProfile or { ell_i } tolerances.

VIII. Group C — Differential Isolation of the Path Term

Goal: test differential identifiability and out-of-band leakage control.
Steps: C1 select in-band frequencies { f_m }; C2 compute Delta_T_arr_obs/Mod, report correlation and slope; C3 report OOB residuals (folded into u_sys).
Pass: correlation & slope within spec; OOB residuals absorbed by guardband; overall pass.

IX. Group D — Energy Closure & Interface Audit

Goal: verify R_env + T_trans + A_sigma = 1 and the sidedness lower bounds n_eff^± ≥ 1 at every interface.
Steps: D1 detect and label Sigma_env; D2 pair ingress/egress paths to estimate {R_env, T_trans, A_sigma}; D3 compare thin/thick chains and check sidedness.
Pass: closure residuals and sidedness meet gates; otherwise falsify the interface or profile configuration.

X. Group E — Joint Consistency of Spectrum, Light Curve, and Arrival

Goal: joint consistency and identifiability across F_nu / LC / T_arr / Delta_T_arr.
Steps: E1 form a joint likelihood and fit θ_state, θ_sed, θ_path; E2 inspect residual panels and the correlation matrix; E3 cross-validate generalization error.
Pass: joint residuals within spec with good identifiability; if degenerate, redesign path/band geometry or strengthen priors.

XI. Group F — Noise Injection & Robustness (incl. TBN)

Goal: quantify the impact and robustness to TBN(x,t) and out-of-band leakage on T_arr / Delta_T_arr / F_nu / LC.
Steps: F1 inject calibrated noise and OOB leakage in simulation; F2 invert parameters and compare drift; F3 report clamping rate and tail risk.
Pass: key metrics M1…M7 remain within guardbands; clamping rate controlled and logged.

XII. Benchmark Datasets (D1…D7)

• D1 Uniform Medium: n_eff ≡ 1; lower bound & two-form consistency (Group A).
• D2 Single Thin Layer: includes Delta_T_sigma baseline; thin/thick consistency (Group B).
• D3 Thick-Layer Profiles: explicit Delta_k and spline params; volumetric integration (Group B).
• D4 Matched-Interface Set: labels {continuous, jump_phi, jump_flux} with C_sigma, J_sigma; energy closure (Group D).
• D5 Band Dispersion Set: multi-frequency coverage and specified order; differential identification (Group C).
• D6 Spectrum–Light-Curve Joint Set: synchronized L_nu, LC, and arrival times; joint consistency (Group E).
• D7 Noise-Robustness Set: TBN injections and OOB leakage labels; robustness (Group F).

Minimal metadata: coords_spec / units_spec / metric_spec, f_grid, gamma[k], Δell[k], Sigma_env and { ell_i }, c_ref or CalibCref, hash(Catalog/Seeds/SeaProfile/Phi_T/n_eff), license and citation stance.

XIII. Statistical Methods & Falsification Criteria

Hypotheses (examples):

• H0-1: two-form consistency holds, eta_T ≤ threshold.
• H0-2: T_arr_obs ≥ LB.
• H0-3: thin/thick consistency holds, tau_switch ≤ gate.
• H0-4: Delta_T_arr vs. model differential agrees in the linear/specified order regime.
• H0-5: R_env + T_trans + A_sigma = 1 and n_eff^± ≥ 1.
• H0-6: joint residuals of F_nu/LC/T_arr/Delta_T_arr meet gates.

Falsification line: if any H0 is rejected and implementation/metrology mistakes are excluded, record as a falsification sample. If three independent reproducible runs falsify the same dimension, trigger a postulate/parameterization review (cf. Chs. 2/5).

XIV. Traceability & Reproducibility

• Packaging: data, code, parameters, RNG seeds, contracts/logs, and hash manifests.
• Replay entry: supply runlist, SolverCfg snapshot, and metric_spec for one-click replay.
• Audit views: metric time series, falsification samples, Delta_T_sigma trigger statistics, energy-closure and tau_switch curves, two-form consistency dashboards.

XV. Audit & Reporting

Report structure

• Overview: datasets, paths & bands, modes & thresholds.
• Metrics: panels for M1…M9.
• Falsification: failed cases with cause taxonomy.
• Reproducibility: hashes, seeds, contract and log references.

Publication stance: report results as mean ± k•u_c; for differentials, publish correlation/slope and OOB residuals; for thin/thick, publish the tau_switch curve and gate.

XVI. Cross-References

• EFT.WP.Cosmo.EarlyObjects v1.0: Ch. 3 (minimal equations), Ch. 5 (coupling & growth laws), Ch. 6 (radiation & propagation), Ch. 7 (metrology design), Ch. 9 (numerical implementation), Ch. 12 (uncertainty budget).
• EFT.WP.Propagation.TensionPotential v1.0: Ch. 11 (validation & benchmarking).
• EFT.WP.Cosmo.LayeredSea v1.0: Ch. 11 (validation & benchmarking).
• EFT.WP.Core.Metrology v1.0 / Core.Errors v1.0: statistical and uncertainty baselines.

XVII. Deliverables

• Validation checklists & script contracts: procedural I/O for Groups A…F.
• Benchmark dataset specs: metadata schemas and packaging rules for D1…D7.
• Audit templates: metric dashboards, falsification registry, replay instructions, hash manifest, and reports on tau_switch / eta_T / energy closure.