30-EFT.WP.Propagation.TensionPotential 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 Aim
  Establish end-to-end consistency baselines and self-checks—from notation to gauges, from metrology to implementation—define points of alignment with the Core volumes and mechanisms for handling conflicts, and compile the unresolved theoretical, metrological, and implementation questions alongside a forward roadmap.
• II. Scope & Non-Goals
• Covered: consistency baselines; a cross-volume comparison checklist; compatibility and evolution strategies; falsification and conflict-resolution workflows; open problems and milestones.
• Non-goals: no re-derivation of Chapter 3 equations; no replacement for the metrology (Chapter 7) or implementation (Chapter 9) details; no device-level mechanical/electrical designs.
• III. Minimal Terms & Symbols
• Potential & gradient: Phi_T(x,t), grad_Phi_T(x,t).
• Effective index & speed: n_eff(x,t,f), c_ref, c_loc = c_ref / n_eff.
• Path & measure: gamma(ell), d ell, segmented gamma_i, interface set Sigma.
• Arrival-time gauges: T_arr = (1/c_ref) * ∫ n_eff d ell, or T_arr = ∫ ( n_eff / c_ref ) d ell.
• Decomposition & terms: n_eff = n_common + n_path; directional term b1 · dot( grad_Phi_T , t_hat ).
• Conventions: n_eff ≥ 1; strict name isolation between T_fil and T_trans, and between n and n_eff.
• IV. Consistency Baselines (C1 … C12)
• C1 Notation consistency
  Wrap inline symbols in backticks; keep path/measure/gradient/divergence aligned with EFT.WP.Core.Equations v1.1.
• C2 Dimensional consistency
  Run check_dimension at entry; enforce dim(T_arr) = [T], dim(n_eff) = 1, dim(c_loc) = [L][T^-1].
• C3 Gauge & boundary consistency
  Fix Phi_T(x_ref,t_ref) = 0 and boundary_config; if observables depend only on grad_Phi_T, they are invariant under Phi_T → Phi_T + const.
• C4 Two-gauge agreement
  eta_T = | T_arr^{const} − T_arr^{gen} | must be below threshold.
• C5 Feasible domain & lower bound
  Always maintain n_eff ≥ 1 and T_arr ≥ L_path / c_ref.
• C6 Path additivity & reparameterization invariance
  Splicing is additive; reparameterization does not change integral values.
• C7 Interfaces & energy consistency
  Matching rules satisfy R_sigma + T_trans + A_sigma = 1; both one-sided limits keep n_eff ≥ 1.
• C8 Term identifiability
  For n_eff = n_common + n_path, residuals go to u_sys and stay below threshold; ΔT_arr is linear in-band or matches the prescribed polynomial order.
• C9 Directional-term significance
  Regression on dot( grad_Phi_T , t_hat ) is significant; model-selection metrics beat the isotropic alternative.
• C10 Metrological traceability
  c_ref calibration, path/quadrature logs, and coordinate/unit contracts are complete; hashes support replay.
• C11 Errors & guardband
  GUM and MC agree (or are consistently reconciled); GB = k_guard · u_c is enforced.
• C12 Naming isolation
  Never mix T_fil with T_trans; never mix n with n_eff.
• V. Cross-Volume Comparison Checklist (execute in order)
• Terminology check: reconcile English/Chinese names for Thread, Sea, Density, Tension, Tension Gradient, Tension Potential with EFT.WP.Core.Terms v1.0.
• Tension mapping check: verify the monotonic and scaling settings of Phi_T = G(T_fil) with EFT.WP.Core.Tension v1.0 (S12-*).
• Sea stratification check: align layered structure and interface metadata with EFT.WP.Core.Sea v1.0 (S08-*), ensuring Sigma labels match.
• Equation/notation check: align path integrals, gradient, divergence, etc. with EFT.WP.Core.Equations v1.1 (S06-*).
• Metrology chain check: align c_ref calibration, traceability, and logging with EFT.WP.Core.Metrology v1.0 (M05-, M10-).
• Error-model check: align GUM/MC propagation and correlation handling with EFT.WP.Core.Errors v1.0 (M20-*).
• Path-correction check: align coordinates, pathing, and corrections with EFT.WP.Metrology.PathCorrection v1.0 (S03-*).
• Data-spec check: align I/O fields, units, and encodings with EFT.WP.Core.DataSpec v1.0.
• VI. Compatibility & Evolution Strategies
• Forward compatibility: when Core volumes upgrade, keep interfaces stable; add new fields as optional; legacy reports must replay.
• Graceful downgrade: if the general gauge is unavailable, fall back to the constant-factored gauge and explicitly report eta_c and its impact.
• Parameter migration: when n_eff parameterization evolves, provide mapping scripts to keep n_common/n_path comparable.
• Interface evolution: before adding new interface types, ship a zero-thickness correction approximation and an energy-consistency check.
• VII. Consistency Self-Checks (I-layer landing)
• check_dimension(expr) -> DimReport — dimensional self-test.
• check_dual_arrival_consistency(inputs) -> eta_T — two-gauge agreement.
• emit_interface_log(…) and rt_estimator(data) — interface matching and energy consistency.
• convergence_scan(problem, cfg_list) -> Report — audit of refinement and step policies.
• benchmark_suite(runlist) -> Summary — pass status for Benchmarks 1–5.
• log_artifacts(meta, hashes, metrics) -> Log — persist hashes, thresholds, clamping triggers, and falsification samples.
• VIII. Falsification & Conflict Handling
• Triggers
  n_eff < 1; T_arr < L_path / c_ref; eta_T over threshold; broken energy consistency; non-identifiable decomposition.
• Order of actions
• Re-audit metrology and unit contracts; replay with the same data and SolverCfg.
• Switch gauges or re-calibrate c_ref; re-fit with differencing and term separation.
• Inspect Sigma and segmentation; enable correction terms and recompute.
• If still failing, record as a falsification sample and escalate to Chapter 11 audit and Chapter 2 axiom review.
• IX. Open Questions (O1 … O12)
• O1 Minimal sufficiency of F: what is the smallest complete term set for n_eff = F(Phi_T, grad_Phi_T, rho, f) and its sufficiency criteria?
• O2 Uniqueness of decomposition: identifiability conditions for n_common/n_path and the influence of priors.
• O3 Directional mechanisms: microscopic origins and alternative formulations of b1 · dot( grad_Phi_T , t_hat ).
• O4 Interface micro-layers: physicalization of zero-thickness corrections and coupling to thickness/band.
• O5 Time-varying Sea: definitions of T_arr and stable numerics under strong nonstationarity.
• O6 c_ref drift: optimal calibration and guarding across environments and over time.
• O7 TBN spectrum: how TBN spectral shape and correlation lengths bias n_eff estimates.
• O8 Inversion well-posedness: regularization and priors under sparse paths and geometric degeneracy.
• O9 Complexity & scalability: upper bounds for parallelism and caching with multi-band/multi-path workloads.
• O10 Conservation & constraints: how energy consistency and n_eff ≥ 1 jointly constrain feasible parameter regions.
• O11 Synchronization & timebase: sensitivity of ΔT_arr to timebase error/jitter and compensations.
• O12 Cross-volume constraint propagation: automated consistency checks and migration work-orders when Core volumes update.
• X. Roadmap & Milestones (R1 … R6)
• R1 Standard test suite v1: release Benchmarks 1–5 and audit scripts; define a unified acceptance line.
• R2 Term-separation identifiability: complete theory + experiments on n_common/n_path uniqueness and out-of-band leakage.
• R3 Directional-channel program: publish datasets with directional terms and recommended significance thresholds.
• R4 Interface micro-layer model: upgrade zero-thickness corrections to parameterized micro-layers; enhance energy checks.
• R5 Time-varying gauge: extend T_arr to strongly time-varying Seas with implementation interfaces.
• R6 Automated audit: build a cross-volume consistency pipeline that emits alignment and migration reports.
• XI. Cross-References
• EFT.WP.Propagation.TensionPotential v1.0 Chapters 3, 5, 6, 7, 8, 9, 11, 12, 13
• EFT.WP.Core.Terms v1.0 P10-*
• EFT.WP.Core.Tension v1.0 S12-*
• EFT.WP.Core.Sea v1.0 S08-*
• EFT.WP.Core.Equations v1.1 S06-*
• EFT.WP.Core.Metrology v1.0 M05-, M10-
• EFT.WP.Core.Errors v1.0 M20-*
• EFT.WP.Metrology.PathCorrection v1.0 S03-*
• XII. Deliverables
• Consistency cards C1 … C12 and a self-check script roster.
• Cross-volume alignment & migration templates: side-by-side checks for terminology, equations, metrology, errors, path corrections, and data specs.
• Open-issues & roadmap board: status and audit entries for O1 … O12 and R1 … R6.