32-EFT.WP.Cosmo.LayeredSea v1.0 | Chapter 2 — Postulates & Applicability

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Chapter 2 — Postulates & Applicability

• I. One-Sentence Objective
  One-sentence goal: Set out the minimal postulates P60-* and applicability limits for the layered Energy Sea, enforce hard constraints on the two arrival-time formulations, energy consistency, and the feasible set, and provide executable procedures that are metrologically traceable, auditable, and reproducible.
• II. Scope & Non-Goals
• Coverage: existence/measurability of layer profiles and layer interfaces; feasible set and energy consistency; thin/thick layer switching and equivalence; two-formulation consistency and band decomposition; path integrability and numerical convergence; default boundaries and recording conventions.
• Non-Goals: no derivation of specific cosmological metric equations; no device-level hardware or end-to-end observing pipeline details; no superluminal constructs or violations of n_eff ≥ 1.
• III. Minimal Set of Terms & Symbols
• Layered “Sea” & Geometry: SeaProfile; layer index k = 1…K; layer profile W_k(chi); layer strength Xi_k(chi) = | dW_k/dchi |; thickness Delta_k; interface set Sigma_sea.
• Coordinates & Path: eta (conformal time), chi (comoving radial), scale factor a(eta); path gamma(ell) and line element d ell.
• Field & Propagation: T_fil(x,t), Phi_T(x,t), grad_Phi_T(x,t); n_eff(x,t,f) (dimensionless, with n_eff ≥ 1), c_ref, and local speed c_loc = c_ref / n_eff.
• Events & Energy: R_sea, T_trans, A_sigma, satisfying R_sea + T_trans + A_sigma = 1.
• Two Formulations: constant factored out T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell ); general form T_arr = ( ∫ ( n_eff / c_ref ) d ell ).
• Name Isolation: T_fil ≠ T_trans; n ≠ n_eff (strictly no conflation).
• IV. Postulates & Constraints P60-*
• P60-1 Layer Existence & Unique Intersections
  Within the target scale and coherence window, SeaProfile is representable by a set of monotonically transitioning layer functions W_k(chi). For any path and any layer interface, there exists locally a unique intersection or a finite, indexable sequence { ell_i }, numerically localizable.
• P60-2 Feasible Set & Lower Bound
  The effective index always satisfies n_eff(x,t,f) ≥ 1, hence T_arr ≥ L_path / c_ref (equivalently expressed in the general integrand).
• P60-3 Energy Consistency
  For any interface event, reflection, transmission, and loss satisfy R_sea + T_trans + A_sigma = 1; all are dimensionless and measurable within the band.
• P60-4 Gauge & Invariance
  On a simply connected domain there exists Phi_T = G(T_fil) with fixed gauge Phi_T(x_ref,t_ref) = 0. If n_eff = F( grad_Phi_T, … ) + H_sea(·) contains no absolute Phi_T, it is insensitive to Phi_T → Phi_T + const.
• P60-5 Thin/Thick Switching & Equivalence
  When Delta_k / L_char ≤ eta_w (threshold), a zero-thickness correction Delta_T_sigma may equivalently represent wall-layer contributions; otherwise, use explicit thick-layer volumetric integration. Their difference is audited by tau_switch and must stay below its limit.
• P60-6 Two-Formulation Consistency & Band Decomposition
  Within the target bandwidth there exists a decomposition n_eff = n_common(x,t) + n_path(x,t,f), and the consistency metric eta_T between the constant-factored and general formulations stays under threshold; if exceeded, backtrack c_ref calibration and decomposition residuals.
• V. Default Boundary Conditions & Consistency Constraints
• Far-Field Boundary (choose one and record): Dirichlet: Phi_T → 0; Neumann: dot( grad_Phi_T , n_vec ) = 0; or Robin: alpha · Phi_T + beta · dot( grad_Phi_T , n_vec ) = g(x,t).
• Two-Formulation Control (piecewise):
  T_arr = ( 1 / c_ref ) * ∑_i ∫_{gamma_i} n_eff d ell or T_arr = ∑_i ∫_{gamma_i} ( n_eff / c_ref ) d ell.
• Hard Constraints: n_eff ≥ 1 and T_arr ≥ L_path / c_ref; energy consistency R_sea + T_trans + A_sigma = 1; name isolation for T_fil/T_trans and n/n_eff.
• VI. Applicable Scales & Neglected Terms
• Coherence Window: spatial ell_coh, temporal tau_coh. Assume quasi-steady, piecewise smooth behavior within the window; faster-than-tau_coh bursts are recorded as pulse corrections.
• Thin-Layer Condition: if Delta_k / L_char ≤ eta_w, enable zero-thickness correction; run thin/thick dual-computation in the neighborhood and report tau_switch.
• Geometry & Metric: the metric and the mapping from chi to physical length must be declared in the Contract to keep d ell in meters; small curvature is treated by piecewise-smooth approximation.
• Out-of-Band Leakage: energy outside the analysis band is aggregated into u_sys, with the leakage ratio logged.
• VII. Minimal Equations & Invocations S60-*
• S60-1 Layer families W_k(chi) and strengths Xi_k(chi) (Chapter 3).
• S60-2 Potential mapping & chain relation: Phi_T = G(T_fil), grad_Phi_T = g_T(T_fil) · grad(T_fil) (Chapter 3).
• S60-3 n_eff = F( Phi_T, grad_Phi_T, rho, f ) + H_sea( {W_k, Xi_k}, f ) (Chapter 3).
• S60-4 Band decomposition: n_eff = n_common + n_path (Chapter 3).
• S60-5 Piecewise integration for the two formulations & the lower bound (Chapter 6).
  This chapter provides invocation anchors; full forms and derivations are in Chapters 3 and 6.
• VIII. Metrology & Calibration Flows M60-*
• M60-1 Calibrate c_ref: Use a reference path gamma_ref and reference arrival time T_arr_ref to calibrate c_ref, recording environment and uncertainty.
• M60-2 Layer Identification & Typing: Detect Sigma_sea; classify as continuous / potential jump / flux jump; produce { ell_i } with type labels.
• M60-3 Band Decomposition & Differential Isolation: On the same path, estimate n_path via multi-frequency differencing; fold residuals into u_sys.
• M60-4 Two-Formulation Consistency Audit: Compute both formulations in parallel and output eta_T; if over threshold, backtrack c_ref calibration and n_eff decomposition.
• M60-5 Energy & Thin/Thick Consistency: Audit R_sea + T_trans + A_sigma = 1 at interfaces; run thin/thick dual-computation near eta_w and report tau_switch.
• M60-6 Archiving & Reproduction: Freeze contracts, logs, and hashes; register falsification samples and replay handles.
• IX. Implementation Bindings & Interfaces I60-*
• build_layered_sea_profile( params ) -> SeaProfile
• apply_sea_matching( Phi_T, SeaProfile ) -> Phi_T_matched
• estimate_neff_sea( Phi_T, grad_Phi_T, rho, f, SeaProfile ) -> n_eff
• detect_sea_intersections( gamma, SeaProfile ) -> { ell_i, layer_id }
• interface_correction_sea( gamma, SeaProfile, params ) -> Delta_T_sigma
• arrival_time_in_sea( n_eff, gamma, mode, c_ref ) -> T_arr
• delta_arrival_in_sea( n_path_params, f1, f2, gamma, mode, c_ref ) -> Delta_T_arr
• estimate_RT_sea( data, SeaProfile ) -> R_sea, T_trans, A_sigma
  Constraints: mandatory dimensional checks and lower-bound enforcement at entry; name isolation and energy consistency are required checks; logs must include hash(SeaProfile), hash(gamma), mode, eta_T, tau_switch.
• X. Cross-References
• EFT.WP.Cosmo.LayeredSea v1.0: Ch. 3 (Minimal Equations & Layered Representation), Ch. 6 (Propagation & Arrival Time), Ch. 8 (Interface Matching), Ch. 9 (Numerical Implementation), Ch. 11 (Validation & Benchmarks).
• EFT.WP.Propagation.TensionPotential v1.0: two formulations and path expressions.
• EFT.WP.Core.Tension v1.0: potential mapping and chain relations.
• EFT.WP.Core.Metrology v1.0: metrology and traceability.
• XI. Verification & Falsification Lines
• Verification: T_arr ≥ L_path / c_ref; eta_T within target; R_sea + T_trans + A_sigma = 1 with residuals under threshold; tau_switch within limits; acceptable residuals for the differential fit of n_eff = n_common + n_path.
• Falsification: any stable occurrence of n_eff < 1 for some path/band; persistent two-formulation disagreement with no successful backtracking; violation of energy consistency; tau_switch exceeding threshold; missing segmentation or interpolation across interfaces.
• XII. Systematic Error Protection
• Path & Segmentation: include endpoints { ell_i } explicitly in integrals; forbid interpolation across interfaces; enforce step-size reduction where | dW_k/dchi | is large.
• Band Leakage: for differencing, reuse the same { gamma[k], Δell[k] } and correction setup; fold out-of-band residuals into u_sys.
• Thin/Thick Switching: perform dual-computation near eta_w and record tau_switch; if beyond threshold, fix to thick-layer volumetric integration.
• Names & Units: unify coords_spec and units_spec at entry; run check_dimension and persist a DimReport.
• XIII. Deliverables
• Postulate cards P60-1 … P60-6 with invocation guidance.
• Audit checklists for two-formulation and energy consistency, and for thin/thick consistency (including threshold fields).
• Segmentation & interface log template: { ell_i }, type labels, tau_switch, eta_T, energy residuals, and a falsification-sample register.