21-EFT.WP.Metrology.Sync v1.0 | Appendix D — Metrics & Drift Measures (Synchronization-Specific)

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Appendix D — Metrics & Drift Measures (Synchronization-Specific)

I. Purpose & Scope

• Define a synchronization-domain metric family with unit conventions and windowing, specify drift measures and alert rules, and align these with manifests, contracts, and SLOs.
• All statistics are computed on tau_mono and published on ts. Any arrival-time metric must record both forms alongside delta_form.

II. Metric Families & Unit Conventions

1. Time error & derivative
   • offset(t): time error w.r.t. reference, unit s, dim="[T]".
   • skew(t) = d offset(t) / dt: frequency error, unit s/s, dim="1".
2. Jitter & delay
   • J_rms, J_pp: RMS and peak-to-peak time/phase jitter, unit s.
   • latency: one-way or round-trip quantiles, unit s.
   • PDV: packet delay variation (e.g., p99), unit s.
   • asym: link asymmetry estimate, unit s.
3. Allan family & time-domain stability
   • ADEV(tau), MDEV(tau), HDEV(tau): unit 1.
   • TIE(t), MTIE(tau), TDEV(tau): unit s.
4. Dual-form arrival time
   • T_arr.form1 = ( 1 / c_ref ) * ( ∫ n_eff d ell )
   • T_arr.form2 = ( ∫ ( n_eff / c_ref ) d ell )
   • delta_form = | T_arr.form1 - T_arr.form2 | (unit s).
5. Drift measures
   • Distributional distances: W1 (discrete approximation), KL, PSI (dimensionless).
   • Trends: drift_slope (robust slope of offset or skew, unit s/s or s/s²), drift_level ∈ {none, soft, hard}.

III. Sampling, Windows & Publication Rules

1. Sampling & denoising
   • Raw timestamp period tau0; statistical window Delta_t = m * tau0.
   • Sliding aggregation: hop size hop ∈ [0.1, 0.5] * Delta_t.
2. Effective samples & weights
   • For weighted statistics, publish n_eff = ( ( ∑ w_i )^2 ) / ( ∑ w_i^2 ).
   • Publish unit(x), dim(x), and u(x) (standard uncertainty).
3. Publication
   Compute internally on tau_mono; publish on ts, recording the mapping for offset/skew/J and window.

IV. Minimal Equations S60D- (Definitions & Computables)*

1. S60D-1 (offset/skew)
   offset_k = ts_node_k - ts_ref_k；skew_k = ( offset_k - offset_{k-1} ) / tau0。
2. S60D-2 (J_rms/J_pp)
   J_rms = sqrt( mean( ( offset_k - mean(offset) )^2 ) )；J_pp = max(offset) - min(offset)。
3. S60D-3 (PDV)
   PDV_pq = percentile(delay, q) - percentile(delay, p)（commonly p=0.01, q=0.99; or publish pdv.p99 directly）。
4. S60D-4 (ADEV) (discrete, tau = m * tau0)
   ADEV(tau) = sqrt( ( 1 / ( 2 * (N - 2m) ) ) * ∑_{k=1}^{N-2m} ( y_{k+2m} - 2*y_{k+m} + y_k )^2 ) where y_k is window-averaged fractional frequency.
5. S60D-5 (TIE/MTIE/TDEV)
   • TIE(t_k) = offset_k - offset_0；
   • MTIE(tau) = max_{u,v: v-u=tau} | offset_v - offset_u |；
   • TDEV(tau) = sqrt( (1/2) * mean( ( offset_{k+2m} - 2*offset_{k+m} + offset_k )^2 ) ) / tau。
6. S60D-6 (W1/KL/PSI) (histogram with bins=b, smoothing eps>0)
   • W1 = ∑_{b} | CDF_ref(b) - CDF_cur(b) | * Δb；
   • KL = ∑_{b} p_ref(b) * log( p_ref(b) / ( p_cur(b) + eps ) )；
   • PSI = ∑_{b} ( p_ref(b) - p_cur(b) ) * log( p_ref(b) / ( p_cur(b) + eps ) )。
7. S60D-7 (delta_form)
   delta_form = | ( 1 / c_ref ) * ( ∫ n_eff d ell ) - ( ∫ ( n_eff / c_ref ) d ell ) |。

V. Drift Detection Flow M60-D1 (Ready → Detect → Classify → Act)

1. Ready
   • Align tau_mono; select Delta_t; choose ref (prior stable window or golden period).
   • Build histograms & quantiles for ref and cur.
2. Measure
   • Compute W1/KL/PSI for {offset, skew, delay, pdv}.
   • Compute drift_slope (Theil–Sen or Huber—robust to outliers).
   • Evaluate delta_form, ADEV/MDEV/HDEV at key tau.
3. Classify
   • Map thresholds to drift_level ∈ {none, soft, hard}.
   • Enforce temporal consistency: promote only after k consecutive breaches to avoid jittery false alarms.
4. Act
   • soft: de-weight PTP samples, tighten servo bandwidth, increase message rate.
   • hard: trigger holdover/failover, switch GM, lock audit & replay artifacts.
5. Persist
   Write to manifest.sync.metrics.* and contracts.*; sign & freeze (Appendix C).

VI. Contracts & Threshold Suggestions C60- (Baseline; tune per domain)*

• C60-sync-31: metrics.offset.p99 ≤ 1e-6 s, window Delta_t=300 s.
• C60-link-01: link.pdv.p99 ≤ 1e-4 s.
• C60-arr-71: arrival.delta_form ≤ tol_Tarr (site-calibrated).
• C60-drift-11: W1(offset) ≤ 0.2 * Δb_count or PSI(offset) ≤ 0.1.
• C60-drift-12: |drift_slope(offset)| ≤ 1e-10 s/s (rolling 1 h).
• C60-adev-21: for tau ∈ {1,10,100}s, ADEV(tau) does not exceed the site envelope.
• C60-mtie-31: MTIE(900s) ≤ 5e-6 s.
• Map failures to contracts[*].status ∈ {pass, soft, hard} and attach runbook IDs.

VII. Implementation Bindings I60- (Measurement & Monitoring)*

• compute_allan(y, tau0, taus, mode) -> {ADEV,MDEV,HDEV}
• compute_tie(offset, tau0) -> {TIE, MTIE, TDEV}
• measure_pdv(delays, quantiles) -> pdv_report
• dist_shift(ref_hist, cur_hist, bins, eps) -> {W1, KL, PSI}
• robust_slope(series, method) -> drift_slope with method ∈ {theil_sen, huber}
• detect_sync_drift(metrics_ref, metrics_cur, rules) -> {level, causes, actions}
• emit_sync_metrics_panel(metrics) -> panel_spec
• Invariants: check_dim(all); consistent windows; n_eff ≥ n_min; delta_form ≤ tol_Tarr.

VIII. Cross-References

• Allan family definitions & noise typing: Chapter 9.
• Dual-form arrivals & path harmonization: EFT.WP.Metrology.TimeBase v1.0 Chapter 9.
• Contract persistence & manifest fields: this volume Appendix B and Appendix C.
• Statistical drift & distance measures (broader scope): Methods.CrossStats v1.0 Chapter 7 and Appendix D.

IX. Panel Mapping & Publication Fields

• Core dashboard SLIs: offset.p99, pdv.p99, J_rms, ADEV(tau=1,10,100)s, MTIE(900s), W1(offset), PSI(offset), delta_form.
• manifest.sync.metrics.* maps 1:1 to dashboard fields; each value carries unit, u(x), and window.
• Alerting policy: soft → yellow; hard → red with automatic rollback/switch playbooks.

Summary