49-Error Budget Card Template v1.0 | Chapter 9 — Alignment with Quality Gates & Threshold Mapping

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Chapter 9 — Alignment with Quality Gates & Threshold Mapping

I. Purpose & Scope

• Establish one-to-one threshold mappings and decision rules linking uncertainty assessments to Quality Gates (G1–G8) and Stop Criteria (S1–S5), yielding an executable, auditable release convention.
• When path quantities (arrival time/phase) are involved, explicitly show gamma(ell) and the measure d ell in text, and record delta_form ∈ {general, factored} in data/metadata; publication requires p_dim = 1.0.

II. Prerequisites & Inputs

• Propagation outputs: per Chapter 6, obtain u(x_i), u_c, U = k·u_c (or quantile bands), Σ = Cov(x), and the target y = f(x).
• Correlation structure: kernel/parameter set from Chapter 5 (σ^2, L_c, …) and design effects (DEFF/ν_eff).
• Interval type: confidence/credible/quantile (Chapter 8) stated in text with coverage level k/α/quantiles.
• Data & compliance: check_dim_report.json passed; see[]/references[] use “volume + version + anchor (P/S/M/I)”, with anchor coverage ≥ 90%.

III. Gate Mapping

• G4 | Dimensional closure → S1
  Criterion: p_dim = 1.0 (mandatory). Any unit/dimension failure for target quantities → trigger S1 stop.
• G5 | Calibration freshness
  Criterion: |ts_start − calib.timestamp| ≤ τ_calib and clock_state = locked; exceedance → recalibrate or enter Restricted.
• G6 | Noise & residuals (Q_res)
  Criterion: Q_res ∈ [Q_min, Q_max] (from baseline and robust surrogate). Out of band → switch to robust flow and report second-order surrogate.
• G7 | Conservation consistency (ε_flux)
  Criterion: P95(ε_flux) ≤ ε_flux_guard; exceedance → model switch or segmented, shorter T_coh/L_coh.
• G3 | Path–measure integrity
  Criterion: len(gamma_ell)=len(d_ell)=len(n_eff) ≥ 2 and synchronized; else reject and fallback.
• G2 | Citation compliance → S5
  Criterion: anchor coverage ≥ 90%, no external links/aliases; unmet → S5 block release.
• G1/G8 | Schema & uniqueness
  Criterion: fields/indices complete, unique record_id, non-duplicated checksum; failures require fix or rejection.

IV. Threshold Mapping Rules

• Arrival-time residual ΔT_arr
  Decision: positive if |ΔT_arr| + U(T_arr) ≤ τ_T; else negative/Restricted.
• Phase consistency r_phi
  Decision: positive if LB(r_phi) ≥ r_phi_min (Fisher-z or bootstrap lower bound) after reference-window alignment.
• Conservation error ε_flux
  Decision: positive if P95(ε_flux) ≤ ε_flux_guard; include paraxial-conservation diagnostics.
• Dimensional-closure rate p_dim
  Decision: hard gate p_dim = 1.0; otherwise S1.
• Robust residual Q_res
  Decision: in-band; for Huber/quantile losses, use the robust second-order surrogate for band judgement.
• Pass-rate/proportion
  Decision: Wilson/Clopper–Pearson CI vs task threshold; or Beta–Binomial posterior interval.

V. Decision Logic (Positive / Negative / Restricted)

• Positive (Pass): all core gates (G4/G5/G6/G7/G3/G2) pass and key metrics satisfy Section IV thresholds.
• Negative (Fail): any core gate fails or key thresholds unmet.
• Restricted ([Restricted]): when core assumptions (paraxial/coherence/dimensional closure) partially fail or freshness expires yet trends must be shown—publish qualitative intervals and diagnostics only, appending [Restricted] to figure titles.

VI. Reporting & Release

• Compliance block: on the results page list check_dim_report summary, anchor_coverage / ver_presence, clock_state / τ_calib, Q_res band decision, and P95(ε_flux) comparison.
• Figures: core metrics with ±U(k) or quantile bands; captions state interval type, coverage, delta_form (for path quantities), and see[]/version.
• Audit: log thresholds, kernel params, B/seed, design effects, and final decision to audit.jsonl.

VII. Machine-Readable Templates

A. gate_map.yaml

version: "1.0.0"

gates:

G4: { p_dim: 1.0 }

G5: { tau_calib_s_max: 86400, clock_state: "locked" }

G6: { Q_res_band: [0.0, 0.2], robust_surrogate: true }

G7: { epsilon_flux_guard_p95: 0.02 }

G3: { path_min_len: 2, sync: true }

G2: { anchor_coverage_min: 0.90, forbid_external_links: true }

thresholds:

tau_T_s: "3*u(T_arr)"

r_phi_min: 0.60

decision:

DeltaT_arr: "abs(DeltaT_arr)+U_T <= tau_T_s"

r_phi: "LB_r >= r_phi_min"

epsilon_flux: "P95_epsilon <= epsilon_flux_guard_p95"

labels:

restricted: "[Restricted]"

see:

- "EFT.WP.Core.Metrology v1.0:check_dim"

- "EFT.WP.Core.Equations v1.1:S20-1"

B. compliance_table.csv

metric,point,interval_or_band,gate,threshold,decision,notes

DeltaT_arr,1.2e-9,"±U(k=2)",G4/G5,"<= tau_T_s",pass,"dim OK; freshness OK"

r_phi,0.72,"[0.61,0.80]",G6,">= r_phi_min",pass,"Fisher-z back-transform"

epsilon_flux,0.006,"P95=0.011",G7,"<= 0.02",pass,"paraxial guard satisfied"

Q_res,0.13,"band in [0,0.2]",G6,"in-band",pass,"robust surrogate used"

p_dim,1.0,"—",G4,"= 1.0",pass,"check_dim_report attached"

VIII. Cross-References

• Propagation results & intervals: Ch. 6 and Ch. 8.
• Correlation structure & design effects: Ch. 5 and Ch. 7.
• Results presentation & scoring: Ch. 11.
• Machine-readable configs & lists: Ch. 12.

IX. Checklist

• Each core metric has a mapped decision formula against its gate threshold and is evaluated.
• check_dim_report.json passed; clock_state = locked, τ_calib compliant.
• For path quantities, explicit gamma(ell)/d ell shown and delta_form recorded; thresholds and interval types are transparent.
• Results page includes compliance block, figures (with units and coverage), and audit items; anchor coverage ≥ 90%.
• Non-compliant items handled via [Restricted] or trigger S1–S5 (stop/fallback/recalibrate).