28-EFT.WP.Propagation.PathRedshift v1.0 | Chapter 15 — Use Cases & Reference Implementations

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Chapter 15 — Use Cases & Reference Implementations

One-sentence goal: Deliver reproducible, end-to-end use cases that chain together the full pipeline from Chs. 2–14—component modeling → observation → fusion/synchronization → calibration → uncertainty/guardband → runtime publication—and produce a signed, replayable, rollback-ready delivery path via manifest.redshift.*.

I. Scope & Objects

• Objects: z_parts = { z_kin, z_grav, z_med, z_cos, z_inst, z_proc }, composite z_path; arrival time T_arr^{form1/form2} and harmonized T_arr*; manifests and strategy cards.
• Inputs: use-case configuration
  profile = { geometry, carrier, bandwidth, SNR, ephemeris/gravity models, n_field/TEC/met sources, timebase, osc }; SLO/thresholds and the contract library.
• Outputs: end-to-end manifests
  { redshift.ray, redshift.obs, redshift.refcond, redshift.cal, redshift.u, redshift.contracts, redshift.rt }, panel snapshots, and audit evidence URIs.
• Boundary: all profiles default to weak-field / weak-dispersion engineering conventions; strong-field/strong-dispersion cases are captured as extended fields with source and assumption annotations.

II. Terms & Keys

• Key quantities: z_path, z_meas, resid_z = z_meas − z_path, delta_form = | T_arr^{form1} − T_arr^{form2} |, ΔT_obs = | T_arr* − t̂_cont |.
• Configuration keys: RefCond.hash, ephemeris.hash, gravity.hash, n_field.hash, TEC/met.hash, osc.hash, algo.hash.
• QC keys: tol_Tarr, tol_z, tol_map, SNR_min, Δt_max, coverage.

III. Postulates P65-15x

• P65-1501 (Dual-form end-to-end): Each use case must publish T_arr^{form1/form2} with delta_form, and the windowed residual between z_path and z_meas.
• P65-1502 (Rigid dimensions / RefCond): Every record passes check_dim( y − f(x) ); RefCond and data provenance are traceable.
• P65-1503 (Fail-Closed): If any critical contract fails → execute strategy cards (degrade / bypass / rollback); persist actions and evidence in the manifest.
• P65-1504 (Replayable): Each manifest contains the minimal sufficient fields and version hashes to recompute z_path / T_arr*.

IV. Minimal Equations S65-15x (End-to-End Assembly)

• S65-1501
  1+z_path = ∏_{i∈{kin,grav,med,cos,inst,proc}} (1+z_i), with the small-signal approximation z_path ≈ ∑ z_i.
• S65-1502
  T_arr^{form1} = (1/c_ref)( ∫ n_eff d ell ), T_arr^{form2} = ( ∫ ( n_eff / c_ref ) d ell ), delta_form = |…|.
• S65-1503
  resid_z = z_meas − z_path, window quantile resid_z,p95; ΔT_obs = | T_arr* − t̂_cont |.
• S65-1504
  Coverage interval U = k•u_c (Ch. 13); go/no-go gate: metric + k•u(metric) ≤ threshold.

V. Metrology Pipeline M65-15 (Ready → Execute → Validate → Sign → Publish)

1. Ready: load the profile and sources (ephemerides / potentials / media / meteorology / timebase); set window W/H, SLOs, and contract thresholds; freeze RefCond.
2. Execute:
   • Geometry & path (Ch. 8): solve_ray → integrate_path → T_arr^{form1/form2};
   • Components (Chs. 3–6): build z_kin / z_grav / z_med / z_cos;
   • Observation (Ch. 9): produce z_meas (PLL/CFO/LINE);
   • Fusion & sync (Ch. 10): RefCond + offset/skew/J, yielding z_pred;
   • Calibration (Ch. 11): z_cal / T_arr_cal (optional);
   • Uncertainty (Ch. 13): compute u/U and guardbands;
   • Runtime (Ch. 14): stream windows and update panels.
3. Validate: apply two-form, analytic-vs-observation, mapping, and conservation gates; compute residuals/quantiles and panel SLIs.
4. Sign: canonicalize and sign manifest.redshift.*; create a rollback pointer and strategy cards.
5. Publish / canary: canary → ramp; enable panel and contract guardians; archive audit evidence.

VI. Contracts & Assertions C65-15x (End-to-End, scenario-overridable)

• C65-1501: delta_form_p95 ≤ tol_Tarr; ΔT_obs_p95 ≤ tol_align.
• C65-1502: resid_z_p95 ≤ tol_z; | z_bias | ≤ z_bias_max, | z_drift | ≤ z_drift_max.
• C65-1503: source freshness age(source) ≤ Δt_max; coverage ≥ cov_min.
• C65-1504: publication coverage coverage(U) ≥ 95%; 0.8 ≤ ρ(GUM/MC) ≤ 1.25.
• C65-1505: panel freshness ≤ Δt_panel_max; rollback chain intact and verifiable.

VII. Implementation Bindings I65-15* (end-to-end wrappers)

• I65-151 build_usecase(profile) -> { graph, sources.hashes, RefCond, thresholds }
• I65-152 run_pipeline(profile, inputs) -> { manifests[], panels[], kpis } (chains this volume’s I65-*)
• I65-153 validate_end2end(manifests, kpis, rules) -> { report, pass }
• I65-154 publish_end2end(manifests, report) -> { uri, signature }
• I65-155 rollback_end2end(manifest_uri, reason) -> { status }
  Invariants: two_forms_present = true; check_dim(*) passes; signature chain verifiable; strategy cards and replay scripts included.

Use-Case Set (Profiles)

U15-A Deep-Space TT&C Link (Ka/Ka′, Deep-Space Probe)

1. Profile: carrier = 32 GHz, BW = 10 kHz, range = 1 AU–10 AU, SNR ≥ 20 dB/Hz; ephemerides = JPL DE, gravity = PN(1).
2. Execution:
   • Geometry/path: straight-line approx + heliocentric/geocentric switch (Ch. 8);
   • Components: z_kin (relativistic Doppler + Sagnac), z_grav (potential difference + Shapiro), z_med (plasma via solar-wind TEC), z_cos ≈ 0;
   • Observation: PLL-derived z_meas;
   • Fusion/sync: EKF (offset/skew/J + ephemerides) → RefCond;
   • Calibration: frequency-ratio chain + ground-station loop-back (optional);
   • Uncertainty: GUM + MC (V_ξ includes TEC and ephemerides/gravity);
   • Runtime: W = 60 s, lateness = 5 s, watermark = event-time.
3. KPIs & Gates: resid_z_p95 ≤ 3e−12; delta_form_p95 ≤ 1e−3•T_arr; |ΔT_obs|_p95 ≤ 0.02•T_sym.
4. Manifests: full set manifest.redshift.{ ray, obs, refcond, cal, u, contracts, rt }.

U15-B Ground → Satellite Downlink (LEO/GEO, Dual-Frequency Iono Suppression)

1. Profile: carrier = 8.4 / 32 GHz; LEO 500–800 km / GEO 36 Mm; real-time met / iono.
2. Execution:
   • solve_ray (tropospheric refraction) + integrate_path;
   • z_kin (Doppler + Sagnac), z_grav (Earth potential difference), z_med (tropo + iono, dual-frequency differencing);
   • z_meas (fused CFO + PLL);
   • RefCond (GNSS / meteorology / TEC fusion, PPS or Two-Way sync);
   • u/U (sources include met/TEC and clock PSD);
   • Runtime window = 10 s.
3. KPIs & Gates: resid_z_p95 ≤ 1e−11; ΔT_map_p95 ≤ 0.1•tol_Tarr; age(TEC/met) ≤ Δt_max.
4. Manifests: as in U15-A, with dual-frequency mapping and ΔT_map annotations.

U15-C Fiber Frequency Transfer (Round-Trip / Co-path)

1. Profile: carrier = 193 THz (1550 nm); fiber 100–1000 km; co-path/round-trip symmetry and controlled connector reflections.
2. Execution:
   • solve_ray (routing + segment table), integrate_path → T_arr^{form1/form2};
   • z_med (T/P/RH → n_eff, Fizeau = 0; record moving segments if any);
   • z_kin / z_grav ≈ 0 (co-located, same potential/speed);
   • z_meas (coherent PLL);
   • Loop-back calibration τ_loop → ΔT_bias (Ch. 11);
   • u/U (from u(n_eff) and connector/backscatter approximations);
   • Runtime window = 1 s.
3. KPIs & Gates: resid_z_p95 ≤ 1e−13; delta_form_p95 ≤ 1e−3•T_arr; |Δτ_asym|_p95 ≤ τ_asym.
4. Manifests: emphasize segments.hash / Σ and ΔT_bias.

U15-D Ground-based Astronomical Line Redshift (Engineering Estimate)

1. Profile: band = optical/radio; high-SNR lines (Voigt fitting), T_obs set by resolution.
2. Execution: fit_spectral_line → z_meas; z_kin (Earth spin/orbit), z_grav (surface potential), z_med (atmosphere) as z_pred.
3. KPIs & Gates: | z_meas − z_pred |_p95 ≤ tol_z; u(z_meas) from Fisher/covariance; two-form T_arr recorded for alignment (non-controlling).
4. Manifests: manifest.redshift.obs + contracts; method = LINE, with line-library hash.

U15-E Hybrid Path (Fiber + FSO) with Edge Gateway

1. Profile: terrestrial fiber + rooftop FSO; carrier = 193 THz; FSO 1–5 km.
2. Execution:
   • Path split: gamma = gamma_fiber ⊕ gamma_fso;
   • z_med: fiber (T/P/RH) + FSO (turbulence / pointing / weather; cf. Packets.Light FSO chapter);
   • z_kin (short spans, negligible), z_grav (elevation differences negligible or folded into ΔT_grav);
   • Observation, fusion, calibration, u/U, and runtime as above.
3. KPIs & Gates: joint resid_z_p95 and FSO Avail; age(TEC/met) ≤ Δt_max.
4. Manifests: segment-level sources & windows in RefCond; full manifest.redshift.{ ray, med, obs, u, rt }.

VIII. Cross-References

• Upstream: Chs. 2–11 (components / observation / fusion / calibration).
• Guardians: Chs. 12–14 (contracts / uncertainty / runtime).
• Companions: Appendices A/B/C/D/E (interfaces / contracts / manifests / metrics / uncertainty propagation).

IX. Quality & Risk Control

• End-to-end SLI/SLO: delta_form_p95, resid_z_p95, ΔT_obs_p95, coverage, age(source)_p95, panel_freshness.
• Fallback gradient: guardband ↑ → window ↓ → model back-write / re-estimate → bypass / rollback (persisted in strategy cards).
• Audit: compare against baseline.manifest; record KPI drifts, contract failures and dispositions, panel snapshots, and signature chains.

Summary

• This chapter consolidates the volume’s conventions into operational, end-to-end use cases: grounded in dual-form + contracts + uncertainty + manifests to ensure z_path / T_arr* are reproducible, auditable, and rollbackable.
• With the I65-15* wrappers, engineering teams can instantiate and publish path-redshift services from templates, and operate them stably via panels and strategy cards.