28-EFT.WP.Propagation.PathRedshift v1.0 | Foreword

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Foreword

One-sentence positioning: This volume defines a unified engineering convention for Path Redshift—a computable, auditable, and publishable framework that integrates the impacts of kinematics / gravity / media / cosmology / instrumentation / processing on frequency and arrival time, and binds them to consistent contracts and manifests.

I. Purpose & Positioning

• Purpose. Decompose the observed frequency shift z and the arrival time T_arr into measurable, configurable, and replayable components, and compose them into a single path observable:

1 + z_path = (1+z_kin)(1+z_grav)(1+z_med)(1+z_cos)(1+z_inst)(1+z_proc) (small-signal limit reduces to a linear sum).

• Scenarios. Deep-space TT&C and planetary links, ground-to-satellite downlinks, mixed-media optical paths (fiber + free space), and high-stability frequency transfer.
• Deliverables. The component set z_parts = { z_kin, z_grav, z_med, z_cos, z_inst, z_proc }, the composed z_path, the harmonized arrival time T_arr*, and the signed manifest manifest.redshift.* with cross-domain contracts C65-* and strategy cards.

II. Scope & Objects

• Objects. Worldline / path gamma(ell); dispersive media and frequencies n_eff(f,x), n_phi(f), n_g(f); gravitational potential phi_grav; cosmological scale factor a(t); local clock parameters offset / skew / J.
• Inputs. TX/RX state vectors (velocity / attitude / rotation Omega), ephemerides / potentials / media profiles, observed data streams (PLL / CFO / spectral-line fits), and RefCond.
• Outputs. Per-component shifts z_parts, the composite z_path, the harmonized arrival time T_arr*, dual-form discrepancy delta_form, uncertainty u / U, and panel fields for operations.
• Boundary. Strong-field, nonlinear, or quantum corrections are out of default scope; where required, publish them as extended entries with sources and assumptions.

III. Numbering & Conventions (mandatory)

1. Unified numbering: Postulates P65-*, Minimal Equations S65-*, Metrology Pipelines M65-*, Implementation Bindings I65-*, Contracts C65-*.
2. Two-form arrival time (cross-volume reuse):
   • Constant-factored: T_arr = ( 1 / c_ref ) * ( ∫_{gamma(ell)} n_eff d ell )
   • General: T_arr = ( ∫_{gamma(ell)} ( n_eff / c_ref ) d ell )
   • Publication: record delta_form = | ( 1 / c_ref ) * ( ∫ n_eff d ell ) - ( ∫ ( n_eff / c_ref ) d ell ) | and assert delta_form ≤ tol_Tarr.
3. Redshift definition: 1 + z = f_emit / f_obs = lambda_obs / lambda_emit, with check_dim(z) = "1".

IV. Methodology & Master Flow M65-1

1. Ready. Establish RefCond (ephemerides / potentials / media / meteorology / time zone / timebase); unify coordinates and the monotone timeline tau_mono / ts; load the path/device inventories with hash / validity.
2. Model / Estimate. Compute per-component contributions:
   • z_kin (Doppler / Sagnac / non-inertial),
   • z_grav (weak-field / PN path terms),
   • z_med (Fizeau / plasma / troposphere / ionosphere),
   • z_cos (FRW / low-z approximations),
     and estimate the observation z_meas from PLL/CFO/line-fits.
3. Harmonize. Compose z_path and the time axis

T_arr* = T_form2 + ΔT_geom + ΔT_med + ΔT_inst + ΔT_proc + ΔT_sync

with every correction booked as corr_env(x; RefCond).

4. Verify. Check the two-form difference delta_form, run check_dim on all units/dimensions, and calibrate via baseline/loopback (frequency-ratio chains / reference lines). Compute uncertainties u / U using GUM/MC.
5. Publish. Generate and sign manifest.redshift, persisting { z_parts, z_path, T_arr* }, contract outcomes, strategy cards, panel fields, and replay pointers.

V. Reader Paths & Role Mapping

• Engineering: Chapters 2 → 3 → 4 → 5 → 8 → 9 → 10 → 11 → 12 → 13 → 14.
• Algorithm & modeling: Chapters 2 → 3 → 4 → 5 → 7 → 8 → 9 → 10 → 13.
• Ops & compliance: Chapters 10 → 12 → 13 → 14 → Appendices B/C/D/E.

VI. Data, Metrology & Compliance

• Data hygiene. Worldlines/ephemerides/potentials/media profiles, time-frequency observations, and device/path inventories must include unit / dim / hash and validity windows; any log↔linear conversions are recorded via scale.note in the manifest.
• Metrology conventions. Windowing/resolution for PLL/CFO/line fits; geometric conventions for Sagnac and non-inertial frames; clear distinction of n_phi / n_g for dispersion; cross-instrument calibration and RefCond consistency.
• Compliance modules. Two-form gate, monotone worldlines and paths, freshness of potentials/ephemerides/media, panel freshness and coverage—governed by C65-*.

VII. Cross-References (strong dependencies)

• Timebase & synchronization: see the Energies Timebase/Sync volume (tau_mono / ts / offset / skew / J).
• Path integrals & media: see EFT.WP.Metrology.PathCorrection v1.0 (two forms / dispersion / arrival time).
• Instrumentation & loopback: see EFT.WP.Metrology.Instrument v1.0 (references / loopbacks / uncertainties).
• Cleaning & publication: see EFT.WP.Methods.Cleaning v1.0 (dual forms / contract persistence).

VIII. Deliverables & Acceptance

• Artifacts: I65-* implementations (kinematics / gravity / media / cosmology / observation / fusion / publication), C65-* contract cards, manifest.redshift exemplars, and panel fields.
• SLI / SLO: delta_form_p99, z_bias, z_drift, panel_freshness, RefCond_coverage.
• Audit. Version/dependency/random seeds and data-source hashes; two-environment recomputation with two-form diff ≤ ε_dual; verifiable signature chain and complete replay scripts.

IX. Risks & Rollback

• Ephemerides / potential / media drift or gaps → switch to conservative models, inflate guardbands, and lower publication cadence.
• Non-inertial / geometric mis-modeling → revert to a simplified frame and correct Omega / A.
• Observation z_meas mismatch → raise SNR or switch lines/windows.
• Contract failure → Fail-Closed: pause updates or bypass to the previous signed version, recording strategy cards and evidence.

X. Structural Guide

• Chapter 1: Definitions & scope
• Chs. 2–6: Baseline models for redshift decomposition (kinematic / gravitational / media / cosmological)
• Chs. 7–9: Dispersion & worldlines, observation conventions
• Chs. 10–11: Fusion & calibration
• Chs. 12–13: Contracts & uncertainty
• Chs. 14–15: Runtime & use cases
• Appendices: interfaces / contracts / manifests / metrics / uncertainty & data models

This foreword is the execution and compliance anchor for the volume. All subsequent chapters inherit the numbering, two-form parallelism, and dimensional checks defined here; all releases are governed by manifest.redshift.*.