32-EFT.WP.Cosmo.LayeredSea v1.0 | Chapter 14 — Consistency, Cross-Volume Alignment & Open Questions

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Chapter 14 — Consistency, Cross-Volume Alignment & Open Questions

• I. One-Sentence Objective
  One-sentence goal: Establish baseline standards and self-check workflows for consistency across notation, formulations, metrology, implementation, and data for the layered Energy Sea; define cross-volume alignment and conflict-resolution rules against the Core / Propagation / TensionWall volumes; and curate open questions and a roadmap so that multi-team deliverables remain aligned, auditable, and reproducible.
• II. Scope & Non-Goals
• Coverage: consistency baselines (C_LS), a cross-volume action checklist, compatibility and evolution strategies, a self-inspection pipeline, conflict identification and handling, open questions (O_LS) and milestones (R_LS).
• Non-Goals: no repetition of technical details from Chapters 3–13; no discussion of device-level hardware or external observing pipelines; no replacement for the validation and error details in Chapters 11 and 12.
• III. Minimal Terms & Symbols
• Layers & profiles: SeaProfile, W_k(chi), Xi_k(chi)=|dW_k/dchi|, Delta_k, Sigma_sea.
• Fields & propagation: Phi_T(x,t), grad_Phi_T(x,t), n_eff(x,t,f), c_ref, T_arr (two formulations).
• Path & measure: gamma(ell), d ell, intersections { ell_i }, piecewise segments gamma_i.
• Energy & events: R_sea, T_trans, A_sigma with R_sea + T_trans + A_sigma = 1.
• Constraints & isolation: n_eff ≥ 1, T_arr ≥ L_path / c_ref; T_fil ≠ T_trans, n ≠ n_eff.
• Template interface family & realization: template v0.1 (I.Build / Path / Arrival / RT / Consistency / Uncertainty / Report) ↔ suggested implementations I60-*.
• IV. Consistency Baselines (C_LS1 … C_LS12)
• C_LS1 Notation: wrap inline symbols in backticks; operators and notation follow Core.Equations v1.1.
• C_LS2 Dimensions: at entry, check_dimension enforces dim(T_arr)=[T], dim(n_eff)=1, dim(c_ref)=[L][T^-1], dim(d ell)=[L].
• C_LS3 Metric→arclength mapping: metric_spec must state chi → d ell; persist a DimReport.
• C_LS4 Two-formulation agreement: eta_T = |T_arr^{const} − T_arr^{gen}| within threshold; if exceeded, first backtrack c_ref and segmentation.
• C_LS5 Lower bound & feasibility: n_eff ≥ 1 on every segment; globally T_arr ≥ L_path / c_ref.
• C_LS6 Thin/thick agreement: tau_switch = |T_arr^{thick} − (T_arr^{thin} + Delta_T_sigma)| within limit; enforce dual runs near the threshold neighborhood.
• C_LS7 Energy consistency: for every interface event, R_sea + T_trans + A_sigma = 1; one-sided n_eff^± ≥ 1.
• C_LS8 Explicit segmentation: include { ell_i } endpoints explicitly; forbid cross-interface interpolation; maintain interface_marks logs.
• C_LS9 Component identifiability: ensure n_eff = n_common + n_path with residuals folded into u_sys and below threshold; Delta_T_arr must lie in the linear region / specified order.
• C_LS10 Directional-term audit (if enabled): regressions for b1 / b1_n are significant; BIC/AIC improves over isotropic models; generalization is controlled.
• C_LS11 Data contract & reproducibility: Contract / SeaProfile / Path / Field / NeffParams / RTParams / Report complete; hash(*), SolverCfg, metric_spec, and seed enable replay.
• C_LS12 Name isolation: T_trans means transmission coefficient only; n and n_eff are strictly distinct.
• V. Cross-Volume Alignment Checklist (execute in order)
• Terminology mapping: align English/Chinese terms and symbols for Thread / Sea / Tension / Tension Gradient / Tension Potential with Core.Terms v1.0.
• Tension mapping: verify Phi_T = G(T_fil) monotonicity and scale with Core.Tension v1.0 (S12-*).
• Path & two formulations: adopt path expression, dual formulations, and differencing from Propagation.TensionPotential v1.0 (S20-*, Chs. 4–7).
• Interfaces & matching: align semantics for continuous / potential-jump / flux-jump with Propagation.TensionPotential v1.0 Ch. 8 and BH.TensionWall v1.0 Ch. 8.
• Metrology chain: c_ref calibration, traceability, and logging as in Core.Metrology v1.0 (M05-, M10-).
• Error model: GUM/MC, correlation terms, and falsification with Core.Errors v1.0 (M20-*).
• Path correction (geo/engineering coords): coordinate transforms and tolerances via Metrology.PathCorrection v1.0 (S03-*).
• Data conventions: dimensional tables and I/O fields in Appendices A/B must align with template v0.1.
• VI. Compatibility & Evolution Strategy
• Forward compatibility: keep core APIs stable; add new fields as optional and persisted; legacy reports remain replayable.
• Graceful downgrade: if the general formulation is unstable, degrade to the constant-factored form; record eta_c and an impact assessment.
• Thin/thick switching: dual-run near eta_w, persist tau_switch; if persistently over limit, lock thick-layer chain and backtrack SeaProfile.
• Parameter migration: provide mapping and validation scripts for SeaProfile and NeffParams / RTParams upgrades.
• Interface extension: prototype new layer/interface types with zero-thickness approximations plus energy-consistency audits before formalizing.
• VII. Self-Inspection Pipeline (bound to I layer / template family)
• ensure_units_and_coords(contract, …) -> DimReport: units/coordinates/metric self-check.
• check_dimension(expr) -> DimReport: dimensional validation for both formulations and piecewise discretizations.
• check_dual_arrival_consistency(inputs) -> eta_T: two-formulation agreement.
• consistency_thin_vs_thick_LS(inputs) -> tau_report: thin/thick agreement.
• estimate_RT_sea(data) -> RTParams: energy-consistency audit at interfaces.
• benchmark_suite_LS(runlist) -> Summary: pass Benchmarks 1–5 and verify error slopes.
• log_artifacts_LS(meta, hashes, metrics) -> Log: persist thresholds, trigger statistics, hashes, and falsification samples.
• VIII. Conflict Identification & Handling
• Triggers: n_eff < 1, T_arr < L_path / c_ref, eta_T over threshold, tau_switch over threshold, R_sea + T_trans + A_sigma ≠ 1, failure of Delta_T_arr linear region (not due to out-of-band leakage), dimensional/metric inconsistencies.
• Resolution order
• Re-verify contract/dimensions and metric_spec; replay with the same SolverCfg.
• Switch formulation or recalibrate c_ref; re-decompose n_common / n_path.
• Recheck { ell_i } segmentation and Delta_T_sigma consistency; if needed, switch to thick-layer volumetrics.
• Adjust SeaProfile parameters or interface classification (continuous / jump / flux / directional).
• If still failing: register a falsification sample and trigger a review of P60-* and Chapter 5 parameterization.
• IX. Open Questions (O_LS1 … O_LS12)
• O_LS1 Micro-structure of layers: minimal sufficient physical model for Delta_T_sigma and its band coupling.
• O_LS2 Component uniqueness: identifiability conditions and prior dependence for n_common / n_path in multi-layer scenes.
• O_LS3 Directional origins: microscopic sources of b1 / b1_n and more robust measurable surrogates.
• O_LS4 Dynamic layers: generalizing both formulations and energy consistency to W_k(chi,t) and chi_k(t).
• O_LS5 STG/TBN coupling: systematic impacts of STG and TBN spectra on n_eff and echo orders.
• O_LS6 Thick-layer upper bounds: optimal step size, error bounds, and fast audit criteria for volumetrics.
• O_LS7 Robust echo inversion: identifiability of multi-path weights w_m and remedies for ill-posedness.
• O_LS8 High-order non-sphericity: truncation limits for a_{lm}^{(k)} and the overfitting boundary.
• O_LS9 Formulation fusion: unbiased fusion of the two formulations under weak c_ref drift.
• O_LS10 Thin–thick mapping limit: proof of error order as tau_switch → 0 and empirical threshold laws.
• O_LS11 Interface-type learning: automated classification of continuous/jump/flux/directional interfaces with uncertainty quantification.
• O_LS12 High-frequency dispersion: optimal order selection for n_path and out-of-band suppression as bandwidth grows.
• X. Roadmap & Milestones (R_LS1 … R_LS6)
• R_LS1 Benchmark suite v1: release Layered-Sea-specific benchmarks (thin/thick, echo, matching) and audit scripts.
• R_LS2 Component-uniqueness study: deliver theory/simulation on n_common / n_path identifiability and out-of-band leakage.
• R_LS3 Directional-channel dataset: build a reference set with dot( grad_Phi_T , t_hat / n_vec ) and significance thresholds.
• R_LS4 Thin–thick white paper: formalize tau_switch error order and practical limits; add to implementation checklists.
• R_LS5 Dynamic-layer formulation: introduce W_k(chi,t) / chi_k(t) arrival-time generalization and interfaces.
• R_LS6 Audit automation: integrate the self-inspection pipeline to auto-generate consistency/falsification reports and migration tickets.
• XI. Cross-References
• EFT.WP.Cosmo.LayeredSea v1.0: Ch. 3 (Minimal Equations & Layered Representation), Ch. 5 (Layer Structure Parameterization), Ch. 6 (Propagation Formulations), Ch. 7 (Metrology Design), Ch. 8 (Interface Matching), Ch. 9 (Numerical Realization), Ch. 11 (Validation), Ch. 12 (Error Budget).
• EFT.WP.Propagation.TensionPotential v1.0: dual formulations, path, and interface conventions.
• EFT.WP.Core.: Terms / Tension / Sea / Equations / Metrology / Errors.
• EFT.WP.Metrology.PathCorrection v1.0: coordinates and path correction.
• XII. Deliverables
• Consistency baseline cards C_LS1 … C_LS12 and the self-inspection script list.
• Cross-volume alignment & migration templates: terminology, tension mapping, layered profiles, dual formulations, metrology chain, error model, and data conventions.
• Open-questions & roadmap board: status, audits, and ticket entries for O_LS1 … O_LS12 and R_LS1 … R_LS6.