33-EFT.WP.Cosmo.EarlyObjects v1.0 | Chapter 14 — Consistency, Cross-Volume Alignment, and Open Questions

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

I. One-Sentence Goal

Establish a consistency baseline and self-check pipeline for early objects that spans notation, dimensionality, the two arrival-time forms, energy closure, thin/thick layer consistency, data contracts, and implementation interfaces. Define cross-volume comparison rules and conflict-handling with the Core / Propagation / LayeredSea / BH.TensionWall volumes, and consolidate open questions and a roadmap so multi-team outputs remain aligned, auditable, and reproducible.

II. Scope & Non-Goals

• Covered: the consistency baseline (C_EO), a cross-volume verification checklist, compatibility/evolution strategy, a turnkey self-check pipeline, conflict detection and remediation, open questions (O_EO) and the roadmap (R_EO).
• Not covered: re-deriving technical content of Chs. 3–13; replacing validation and uncertainty procedures of Chs. 11–12; instrument/pipeline specifics.

III. Minimal Terms & Symbols

• Objects & state: Catalog / Seeds / Trajectory; state = { M, R, J, a_bh, SFR, Z, … }.
• Fields & environment: T_fil, Phi_T = G(T_fil), grad_Phi_T; SeaProfile, Sigma_env.
• Propagation & path: n_eff(x,t,f) (dimensionless, ≥ 1), c_ref, gamma(ell), d ell, endpoints { ell_i }.
• Two-form arrival time:
  T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell ) (constant pull-out)
  T_arr = ( ∫ ( n_eff / c_ref ) d ell ) (general form)
• Consistency & thresholds: eta_T (two-form), tau_switch (thin/thick), eps_T (quadrature convergence), eta_w (thin-layer gate).
• Energy & naming: R_env + T_trans + A_sigma = 1 ; T_fil ≠ T_trans, n ≠ n_eff.
• Contracts: coords_spec / units_spec / metric_spec, SolverCfg, hash(*), DimReport.

IV. Consistency Baseline (C_EO1 … C_EO12)

• C_EO1 — Notation: inline symbols use backticks; operators and symbols follow Core.Equations v1.1.
• C_EO2 — Dimensionality: check_dimension at all ingress points enforces dim(T_arr)=[T], dim(n_eff)=1, dim(c_ref)=[L][T^-1], dim(d ell)=[L], dim(Delta_T_sigma)=[T], and declares dim(L_nu / F_nu) in the Contract.
• C_EO3 — Metric→arclength mapping: metric_spec must state chi → d ell; persist DimReport in logs.
• C_EO4 — Two-form agreement: eta_T = | T_arr^{const} − T_arr^{gen} | stays within threshold; if not, back-trace c_ref calibration, n_eff decomposition, and segmentation.
• C_EO5 — Lower bound & feasibility: every segment keeps n_eff ≥ 1; globally T_arr ≥ L_path / c_ref.
• C_EO6 — Thin/Thick coherence: tau_switch = | T_arr^{thick} − ( T_arr^{thin} + Delta_T_sigma ) | within gate; enforce “dual-run” in the eta_w neighborhood.
• C_EO7 — Energy closure: for each interface event, R_env + T_trans + A_sigma = 1 and sided limits n_eff^± ≥ 1.
• C_EO8 — Explicit segmentation: endpoints { ell_i } are included explicitly in quadrature; no cross-interface interpolation; record interface_marks and endpoint tolerances.
• C_EO9 — Differential consistency: same-path multi-frequency differentials reuse the identical { gamma[k], Δell[k] } plus the same Delta_T_sigma configuration; report OOB leakage and fold into u_sys.
• C_EO10 — Spectrum–arrival coupling: joint residuals for F_nu / LC with T_arr / Delta_T_arr must pass; K-correction and D_L stance must match the Contract.
• C_EO11 — Contracts & replay: fields for Contract / SeaProfile / Path / Field / RTParams / Report are complete; hash(*), SolverCfg, metric_spec, and seed make runs replayable.
• C_EO12 — Naming isolation: T_fil vs T_trans, and n vs n_eff are strictly separated.

V. Cross-Volume Verification Checklist (in order)

• Terminology: reconcile Thread / Sea / Tension / Tension Gradient / Tension Potential names and symbols with Core.Terms v1.0.
• Tension mapping: check monotonicity and scaling of Phi_T = G(T_fil) with Core.Tension v1.0 (S12-*).
• Path & two forms: verify path expression, two forms, and differentials with Propagation.TensionPotential v1.0 (S20-*, Chs. 4–7).
• Layer & matching: verify layer profiles, segmentation, thin correction, and thick integration coherence against Cosmo.LayeredSea v1.0 (Chs. 6–8).
• Tension walls (BHSeed): align interface naming and energy semantics with BH.TensionWall v1.0.
• Metrology chain: align c_ref calibration, traceability, and logging with Core.Metrology v1.0 (M05-, M10-).
• Error model: align GUM/MC, falsification, and report format with Core.Errors v1.0 (M20-*).
• Data specs: ensure Appendix A/B dimensionality and I/O fields match template v0.1.

VI. Compatibility & Evolution Strategy

• Forward compatibility: keep the core I70-* API stable; add new fields as optional; maintain replay of older manifests.
• Graceful downgrade: if the general form is unstable, fall back to constant pull-out while logging eta_c and impact assessment.
• Layer switching: enforce dual-run in the eta_w band; persist tau_switch. If persistently high, lock thick-layer chain and back-trace SeaProfile and endpoint tolerances.
• Parameter migration: provide mapping and validation scripts for upgrades in θ_state / θ_sed / θ_path or SeaProfile.
• Interface extension: pilot new interface types or directional terms with zero-thickness approximation + energy audit before formalizing.

VII. Self-Check Pipeline (mapped to template interfaces / I70-*)

• ensure_units_and_coords(contract, …) -> DimReport — units/coordinates/metric self-check (C_EO2, C_EO3).
• check_dimension(expr) -> DimReport — two-form and segmented discretization dimensional checks (C_EO2, C_EO8).
• check_dual_arrival_consistency(inputs) -> eta_T — two-form agreement (C_EO4).
• consistency_thin_vs_thick_EO(inputs) -> tau_report — thin/thick coherence (C_EO6).
• estimate_energy_triplet(data) -> RTParams — energy closure (C_EO7).
• benchmark_suite_EO(runlist) -> Summary — pass Baselines 1–5 and error slopes (Ch. 9).
• log_artifacts_EO(meta, hashes, metrics) -> Log — thresholds, trigger stats, hashes, falsification samples (C_EO11).

VIII. Conflict Detection & Remediation

Triggers: n_eff < 1; T_arr < L_path/c_ref; eta_T or tau_switch over threshold; R_env + T_trans + A_sigma ≠ 1; differential linear region breaks (non-OOB cause); dimensional / metric / unit mismatch; naming violations.

Remediation order:

• Re-validate Contract (coords_spec / units_spec / metric_spec) and DimReport; replay with the same SolverCfg.
• Switch form or re-calibrate c_ref; re-decompose n_common / n_path.
• Re-check segmentation { ell_i } and Delta_T_sigma; if necessary, use thick integration.
• Adjust SeaProfile or reclassify interface type (continuous / jump_phi / jump_flux / anisotropic).
• If still failing, register a falsification sample and trigger P70-* or Ch. 5 parametrization review.

IX. Open Questions (O_EO1 … O_EO12)

• O_EO1 — Minimal priors: lower-bound parametrization and identifiability for seed / trigger priors.
• O_EO2 — Nonlinear growth stability: stability domains for coupled dM/dt, dR/dt, dJ/dt, da_bh/dt, dSFR/dt.
• O_EO3 — Joint inversion: weighting and diagnostics for jointly fitting L_nu/F_nu/LC with T_arr/Delta_T_arr.
• O_EO4 — Directional physics: micro-origins and robust alternatives for b1 / b1_n.
• O_EO5 — Thin/thick gating: theoretical/empirical calibration of eta_w and tau_switch.
• O_EO6 — OOB control: spectral windowing vs multi-frequency differential trade-offs.
• O_EO7 — Multipath weights: robust extraction of echo components and mitigation of ill-posedness.
• O_EO8 — Cosmology systematics: how D_L and K-correction uncertainties propagate into F_nu and joint fits.
• O_EO9 — Shared correlations: modeling joint correlations among c_ref / n_eff / Δell and θ_state / θ_sed / θ_path in GUM/MC.
• O_EO10 — Low-SNR limit: biases from clamping/saturation on T_arr / Delta_T_arr and debiasing strategies.
• O_EO11 — Real-pipeline coupling: interfaces and error closure with operational data pipelines.
• O_EO12 — Open benchmarks: standardization of extended D1…D7 datasets and audit scripts across teams.

X. Roadmap & Milestones (R_EO1 … R_EO6)

• R_EO1 — Benchmark Suite v1: release “uniform / thin / thick / directional / band-dispersion / joint-spectrum” benchmarks plus audit scripts.
• R_EO2 — Priors & growth evaluations: identifiability and robustness assessments for seed/trigger and θ_growth.
• R_EO3 — Joint inversion toolchain: implement end-to-end fitting across L_nu / F_nu / LC / T_arr / Delta_T_arr with reporting.
• R_EO4 — Layer-switch whitepaper: empirical thresholds and implementation rules linking eta_w ↔ tau_switch.
• R_EO5 — Pipeline pilot: pilot integrations with external processing chains and error-closure practice.
• R_EO6 — Audit automation: wire the self-check pipeline to auto-generate consistency/falsification reports and migration tickets.

XI. Cross-References

• EFT.WP.Cosmo.EarlyObjects v1.0: Chs. 3–13 (objects / causation / growth / radiation / propagation / metrology / interfaces / numerics / error / scenarios).
• EFT.WP.Cosmo.LayeredSea v1.0: layer profiles, segmentation, matching, and tau_switch.
• EFT.WP.Propagation.TensionPotential v1.0: two-form arrivals and differential flows.
• EFT.WP.Core.: Terms / Tension / Equations / Metrology / Errors.

XII. Deliverables

• Consistency baseline cards C_EO1…C_EO12 and a self-check script kit.
• Cross-volume alignment & migration templates for terminology, tension mapping, layered profiles, two-form arrivals, metrology, error models, and data specs.
• Open-issues & roadmap board listing O_EO1…O_EO12 and R_EO1…R_EO6 with status and ticket links.