28-EFT.WP.Propagation.PathRedshift v1.0 | Chapter 12 — Contracts & Metrics (Quality / Integrity / Security)

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Chapter 12 — Contracts & Metrics (Quality / Integrity / Security)

One-sentence goal: Define the Quality / Integrity / Security metric families and the contract suite C65-* for publishing path redshift z_path and arrival time T_arr, grounded in two-form parallelism, dimensional compliance, and RefCond traceability, with computable rules and implementation interfaces.

I. Scope & Objects

1. Inputs
   • Components & composition: z_parts = { z_kin, z_grav, z_med, z_cos, z_inst, z_proc }, composite z_path;
   • Arrival time: T_arr^{form1/form2}, harmonized T_arr*, and delta_form;
   • Observations & fusion: z_meas (Ch. 9), RefCond and sync offset / skew / J (Ch. 10);
   • Runtime & panels: windowed metrics, coverage/freshness, evidence URIs.
2. Outputs
   • Metric families: Q_z / Q_T (Quality), Int_* (Integrity), Sec_* (Security) with quantiles;
   • Contract assertions and disposition guidance;
   • Manifest: manifest.redshift.contracts.* (rules, reports, thresholds, strategy cards).
3. Boundary
   Metrics & contracts constrain publication behavior; modeling & numerics are in Chs. 2–11; uncertainty propagation is in Ch. 13 and Appendices C/E.

II. Terms & Variables

• Two-form gap: delta_form = | T_arr^{form1} − T_arr^{form2} |.
• Quality residual: resid_z = z_meas − z_path; bias/drift: z_bias = ⟨resid_z⟩_W, z_drift = d⟨resid_z⟩/dt.
• Arrival-time consistency: ΔT_obs = | T_arr* − t̂_cont | (Chs. 8/9).
• Coverage & freshness: coverage (spatial/temporal), age(source) (time since last update).
• Security/Integrity: E_balance_z (component-composition consistency), Spec_anom (spectral anomaly from Ch. 9), Timing_anom (arrival-time gate, see Chs. 8/10).
• Dimensions: unit(z) = 1, unit(T) = [T], unit(age) = [T], unit(coverage) = 1.

III. Postulates P65-12x

• P65-1201 (Two-form parallel): Every publication window must provide T_arr^{form1/form2} and delta_form, recorded in manifests and panels.
• P65-1202 (Analytic vs observation): Publish z_path and z_meas in parallel; record resid_z and its quantiles.
• P65-1203 (Dimensions & RefCond): All metrics pass check_dim( y − f(x) ); every record binds RefCond.hash and source hashes.
• P65-1204 (Windowing & measures): Metrics use explicit windows/measures ( ∫_{t∈W} • dt ) and quantiles { p50, p95, p99 }; windowing/resampling conventions are persisted.
• P65-1205 (Fail-Closed): On critical contract failures, degrade / bypass / rollback to the last signed version, and persist the strategy card with evidence URIs.

IV. Minimal Equations S65-12x

1. Quality (Q)

• S65-1201 (Two-form arrival time): delta_form = | T_arr^{form1} − T_arr^{form2} |.
• S65-1202 (Redshift residual): resid_z = z_meas − z_path; window quantile resid_z,p95 = quantile( |resid_z|, 0.95 ).
• S65-1203 (Bias & drift): z_bias = ⟨resid_z⟩_W, z_drift = d⟨resid_z⟩/dt (regression/differencing).
• S65-1204 (Arrival-time consistency): ΔT_obs = | T_arr* − t̂_cont |; window quantile ΔT_obs,p95.

2. Integrity (Int)

• S65-1205 (RefCond coverage/freshness): coverage = ( valid samples / total samples ); age(source) = ts_now − ts_source.
• S65-1206 (Component composition):
  E_balance_z = | z_path − compose( z_kin, z_grav, z_med, z_cos, z_inst, z_proc ) |.
• S65-1207 (Time/phase consistency): Timing_anom = ΔT_obs / T_sym (requires the symbol time T_sym).

3. Security (Sec)

• S65-1208 (Spectral/observation anomaly placeholder):
  Spec_anom = 1_{ D_spec > τ_spec or ACLR < ACLR_min or OBB > OBB_max } (from Ch. 9).
• S65-1209 (Source consistency):
  Params_cons = 1_{ age(source) ≤ Δt_max ∧ coverage ≥ cov_min }.

V. Metrology Pipeline M65-12 (Ready → Compute → Assert → Persist)

• Ready: freeze RefCond, window W, and quantiles { p50, p95, p99 }; load z_meas / z_path, T_arr^{form1/form2}, t̂_cont, and source hashes.
• Compute: evaluate all Q/Int/Sec metrics per S65-12x; produce window quantiles and EWMA.
• Assert: apply C65-12x contracts; produce a contracts.report and trigger strategy cards when necessary.
• Persist:
  manifest.redshift.contracts = { rules, report, thresholds, window, metrics:{ Q, Int, Sec }, RefCond.hash, evidence_uri[], signature }.

VI. Contracts & Assertions C65-12x (suggested thresholds)

1. Two forms & arrival time
   • C65-1201: delta_form_p95 ≤ tol_Tarr (Ch. 2; suggest tol_Tarr = 1e−3 • T_arr or link-specific).
   • C65-1202: ΔT_obs_p95 ≤ tol_align (Chs. 8/9; suggest tol_align = 0.02 • T_sym or 1e−3 • T_f).
2. Analytic vs observation
   • C65-1203: resid_z_p95 ≤ tol_z (SNR/window dependent).
   • C65-1204: | z_bias | ≤ z_bias_max, | z_drift | ≤ z_drift_max (engineering ranges e.g., 1e−12–1e−10, per use case).
3. Integrity / Security
   • C65-1205: age(source) ≤ Δt_max and coverage ≥ cov_min; otherwise degrade or reject.
   • C65-1206: E_balance_z_p95 ≤ τ_zbal; Timing_anom_p95 ≤ τ_T.
   • C65-1207: Spec_anom = 0 (or anomaly rate ≤ τ_spec_rate).
4. Dimensions & freshness
   C65-1208: all metrics pass check_dim; panel & manifest refresh ≤ Δt_panel_max.

VII. Implementation Bindings I65-12* (interfaces, I/O, invariants)

• I65-121 evaluate_quality(z_meas, z_path, Tarr_forms, t_cont, W) -> { delta_form_p95, resid_z_stats, ΔT_obs_p95 }
• I65-122 evaluate_integrity(sources, RefCond, z_parts) -> { coverage, age_stats, E_balance_z, Timing_anom }
• I65-123 evaluate_security(obs_metrics) -> { Spec_anom, Params_cons }
• I65-124 assert_redshift_contracts(metrics, rules) -> { report, pass, actions[] }
• I65-125 plan_guardband(metrics, risk_policy) -> { tol_updates, runtime_overrides }
• I65-126 emit_contract_manifest(results, policy) -> manifest.redshift.contracts
  Invariants: two_forms_present = true; unit/dim checks pass; RefCond.hash and evidence URIs traceable; thresholds and strategy versions are re-verifiable.

VIII. Cross-References

• Redshift baseline & two forms: Ch. 2; components: Chs. 3–6; dispersion mapping: Ch. 7; paths & integrals: Ch. 8; observations: Ch. 9; fusion & sync: Ch. 10; calibration: Ch. 11;
• Uncertainty & guardband: Ch. 13 and Appendices C/E; runtime & panels: Ch. 14.

IX. Quality & Risk Control

• Panel keys: delta_form_p95, resid_z_p95, ΔT_obs_p95, z_bias / z_drift, age(source)_p95, coverage, Spec_anom_rate, panel_freshness.
• Fallback sequence: guardband ↑ → window ↓ → model back-write/re-estimate → bypass/rollback, with all actions logged in strategy.cards[].
• Audit: threshold sources & versions, evidence URIs, compliance reports, signature chain, and replay scripts.

Summary

• This chapter standardizes Quality (Q) / Integrity (Int) / Security (Sec) metrics and contracts, anchored by three rigid requirements: two-form pairing, dimensions, and RefCond.
• With I65-12* and the manifest.redshift.contracts manifest, the publication of path redshift becomes measurable, governable, and rollback-capable, paving the way for Chapter 13 on uncertainty and the runtime release flow in Chapter 14.