51-Pipeline Card Template v1.0 | Chapter 10 — Uncertainty Propagation & Feedback Calibration (UQ Coupling)

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Chapter 10 — Uncertainty Propagation & Feedback Calibration (UQ Coupling)

I. Purpose & Scope

• Specify coupling between the pipeline and Uncertainty Quantification (UQ) and the feedback calibration loop, covering integration of Delta/MC/Bootstrap at stage and end-to-end levels, gate mapping with recirculation/recalibration, to ensure quantifiable credibility and traceability of released results.
• For stages involving path quantities (arrival time/phase), the text must explicitly show gamma(ell) and d ell, and the data side records delta_form ∈ {general, factored}; publication requires p_dim = 1.0.

II. Prerequisites & Inputs

• Control equations & stages: control.form (parenthesized) and I/O contracts are defined in stage.yaml (see Ch. 6).
• Parameters & covariance: Parameter Card registers uncertainty{…} and cov_group; covariance configuration aligns with Error Budget Ch. 5; citations use “volume + version + anchor (P/S/M/I)”, anchor coverage ≥ 90%.
• Timebase & sync: Chapter 5 thresholds satisfied (clock_state="locked", σ_y(τ), |δt_abs|/|Δτ_ch|).
• Path consistency: len(gamma_ell)=len(d_ell)=len(n_eff)≥2, Δell compliant; missing items are rejected.

III. UQ Coupling Models

• Stage-level Delta (first order): for y=f(x), u^2(y) ≈ J · Σ · Jᵀ, with J=∂f/∂x|_{x̂}, Σ=Cov(x); attach references or summaries of J/Σ at stage outputs when applicable.
• Link-level composition: propagate uncertainties downstream across stages; at joins, compose block covariances or synthesize under independence assumptions.
• MC/Bootstrap: sample stages or subgraphs (B ≥ 10^4); for heavy tails/outliers, use robust quantiles (P2.5–P97.5) or Huber surrogates and report convergence diagnostics.
• Coverage harmonization: choose one mode across stages and pipeline—k-coverage / alpha / quantile—and present consistently on results pages and manifests.

IV. Normative Path-Integral Forms

• Arrival time (two equivalent forms):
  T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell ) ; T_arr = ( ∫ ( n_eff / c_ref ) d ell ).
• Phase:
  Phi = ( 2π / λ_ref ) * ( ∫ n_eff d ell ).

Text must show gamma(ell) and d ell; data side records delta_form; dimensional closure includes check_dim_report.json.

V. Gate Mapping & Quality Decisions

• G4 | Dimensional closure: p_dim = 1.0; failure triggers S1.
• G6 | Coverage: intervals consistent across stage and pipeline (k/alpha/quantile).
• G7 | Covariance consistency: cov_group/Σ aligned with Error Budget and Σ PD; failures trigger S4.
• Output decisions: pipeline-level gates such as |ΔT_arr| + U(T_arr) ≤ τ_T, LB(r_phi) ≥ r_phi_min, P95(ε_flux) ≤ ε_flux_guard; if unmet, degrade or mark [Restricted].

VI. Feedback Calibration Loop

• Triggers: gate failures, drift in bias, Q_res out of band, degraded σ_y(τ).
• Actions: call Parameter Card I25-check_freshness, I20-register_param to update/rollback calibration; synchronize manifest and stage configs; record audit.
• Re-estimate & replay: recompute key stages with new parameters/covariance and replay in reverse topological order; produce before/after UQ reports and deltas.
• Convergence & release: release when gates pass and intervals stabilize (diagnostics OK); otherwise keep [Restricted] and iterate.

VII. Machine-Readable Configs
A. uq_coupling.yaml

version: "1.0.0"

methods:

arrival: { type: "delta", jacobian: "auto", cov_group: "medium" }

phase: { type: "mc", draws: 10000, quantile: [0.025,0.975] }

coverage:

mode: "k" # k|alpha|quantile

k: 2

gates:

tau_T_s: "3*u(T_arr)"

r_phi_min: 0.60

flux_guard_p95: 0.02

outputs:

attach_reports: ["J_summary.json","cov_blocks.json","uq_summary.json"]

B. feedback_plan.yaml

version: "1.0.0"

triggers: ["gate_fail","drift_detected","q_res_over"]

actions:

- name: "recalibrate"

call: "I20-register_param"

- name: "validate_freshness"

call: "I25-check_freshness"

- name: "replay_subgraph"

order: "reverse_topology"

verification:

compare: ["delta_metrics","interval_overlap"]

release: ["pass_gates","stability_ok"]

C. uq_summary.json (example)

{
  "T_arr": { "point": 1.23e-08, "U_k2": 1.5e-09 },
  "Phi": { "median": 0.035, "q025": 0.028, "q975": 0.043 },
  "r_phi": { "value": 0.72, "lb": 0.61, "ub": 0.8 }
}

VIII. Validation & Monitoring

• /validate: return stage and pipeline G1–G8 status, UQ coverage/covariance checks, interval vs gate thresholds, and stops_triggered.
• Online KPIs: Latency_P50/P95, Throughput, Q_res, u(T_arr), U = k·u_c, interval_overlap, spectral radius of Σ.
• Alerts: gate breaches, non-PD covariance, convergence failures, interval instability; support suppression and escalation.

IX. Anti-Patterns & Fixes

• Anti: reporting means without intervals → Fix: add k/alpha/quantile intervals with convergence diagnostics.
• Anti: T_arr = ∫ n_eff / c_ref d ell (missing parentheses) → Fix: T_arr = ( ∫ ( n_eff / c_ref ) d ell ).
• Anti: covariance blocks inconsistent with Error Budget → Fix: unify cov_group/Σ and ensure PD.
• Anti: releasing after gate failure → Fix: block release; enter feedback calibration or [Restricted].

X. Release & Layout

PTN_EXPORT/

configs/

uq_coupling.yaml

feedback_plan.yaml

reports/

check_dim_report.json

uq_summary.json

validate_report.json

audit.jsonl

figs/

uq_intervals.pdf

cov_blocks.svg

feedback_flow.svg

report_manifest.yaml

SIGNATURE.asc

XI. Cross-References

• Architecture & computation graph: Ch. 3; stage specs: Ch. 6; resources & performance: Ch. 8; quality gates: Ch. 9.
• Error Budget: covariance & propagation (Ch. 5/Ch. 6), composition & intervals (Ch. 8), threshold mapping (Ch. 9).
• Parameter Card: versioning & freshness (Ch. 6), data contracts & interfaces (Ch. 9).

XII. Checklist

• Declared and consistent UQ methods (Delta/MC/Bootstrap) for stages and pipeline; unified coverage.
• For path stages: explicit gamma/measure/delta_form; I70-dim_check passed, p_dim = 1.0.
• cov_group/Σ aligned with Error Budget and PD; uq_summary.json passes gate comparisons.
• Feedback triggers, actions, and replay order are machine-readable; audit and signatures complete.
• Release includes configs/reports/figures and manifest; citation anchor coverage ≥ 90%.