20-EFT.WP.Metrology.TimeBase v1.0 | Chapter 1 — Definition & Scope of the Time-Base Domain

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Chapter 1 — Definition & Scope of the Time-Base Domain

One-line objective: Define a consistent time-base semantics and metrological boundary across devices / networks / applications, specifying the minimal loop for inputs/outputs, gauges, and the release manifest.

I. Scope & Objects

1. Inputs
   • Device & system time sources: osc(local), GNSS, NTP/PTP/SyncE observation logs, PPS/1PPS captures.
   • Data-layer timestamps: tau_mono (monotonic base), ts (published base), packet delay and queue statistics.
   • Path & arrival parameters: gamma(ell), n_eff, c_ref, mandatory dual-form T_arr fields.
2. Outputs
   • Time-base mapping params: offset, skew, residual term epsilon(tau_mono) and jitter J.
   • Stability curves: sigma_y(tau), TDEV(tau), MDEV(tau).
   • Arrival-time harmonization: dual-form T_arr and difference delta_form, path length L_gamma.
   • manifest.time and associated compliance contract results.
3. Boundary conditions & constraints
   • tau_mono must be monotonic (no rollback); ts is public-facing and may be non-monotonic due to leap seconds or timezone policy.
   • Network paths may be asymmetric; path_asym must be estimated or upper-bounded.
   • Business-side SLA decomposition is out of scope here; we define only metrology-layer SLI/SLO gauges.

II. Terms & Variables

1. Time bases & mapping
   • tau_mono (internal monotonic), ts (external published), t_ref, tau_ref (reference anchors).
   • offset (phase offset), skew (frequency offset, ppm/ppb), drift (long-term rate).
   • Residual & jitter: epsilon(tau_mono), J (jitter, J_rms, J_pp).
2. Stability & noise
   Allan family: sigma_y(tau), TDEV(tau), MDEV(tau); the mapping from phase noise to time domain is not expanded here.
3. Path & arrival
   • gamma(ell) (path parameterization), d ell (measure), path length L_gamma = ( ∫_gamma 1 d ell ).
   • Dual arrival-time forms: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )；T_arr = ( ∫ ( n_eff / c_ref ) d ell )。
   • Difference gauge: delta_form = | ( 1 / c_ref ) * ( ∫ n_eff d ell ) - ( ∫ ( n_eff / c_ref ) d ell ) |。
4. Units & dimensions
   unit(ts)="s", dim(ts)="[T]"; unit(skew)="ppm"; unit(n_eff)="1"; run check_dim(expr) before publication.

III. Axioms P501- **

• P501-1 (Monotonic Baseline): non_decreasing(tau_mono) is a mandatory contract; rollback or back-stepping is forbidden.
• P501-2 (Explicit Mapping): The published time base must be defined and auditable via
  ts = t_ref + offset + skew * ( tau_mono - tau_ref ) + epsilon(tau_mono)。
• P501-3 (Window Consistency): All statistics are evaluated on the declared Delta_t and tau and aligned with manifest.time.window.
• P501-4 (Dual Arrival Forms): Whenever arrival time is involved, compute both forms and record delta_form.
• P501-5 (Dimensional Conservation): All physical quantities entering equations must pass unit/dimension checks via check_dim.
• P501-6 (Path Monotonicity): non_decreasing(ell) is mandatory; missing/imputed data must be flagged m ∈ {0,1} (see Cleaning volume).

*IV. Minimal Equations S501- **

• S501-1 (Time-Base Mapping)
  ts = t_ref + offset + skew * ( tau_mono - tau_ref ) + epsilon(tau_mono)。
• S501-2 (Offset/Frequency-Offset Estimation)
  hat{offset}, hat{skew} = argmin_{a,b} ( ∑ w_i * ( ts_i - ( a + b * ( tau_i - tau_ref ) ) )^2 )，w_i ≥ 0, ( ∑ w_i ) / N ≈ 1。
• S501-3 (Jitter Gauges)
  J_rms = ( E[ epsilon^2 ] )^(1/2 )；publish J_pp = max(epsilon) - min(epsilon)。
• S501-4 (Stability)
  sigma_y(tau) = ( 1 / sqrt(2) ) * std( y_{k+1} - y_k )，with explicit construction of y_k and tau。
• S501-5 (Dual Arrival Forms & Difference)
  As above; assert delta_form ≤ tol_Tarr。
• S501-6 (Path Length)
  L_gamma = ( ∫_gamma 1 d ell )—used to harmonize arrival and propagation budgets.
• S501-7 (Upper Bound on Path Asymmetry)
  | path_asym | ≤ tol_asym; if unknown, include a conservative upper bound in U.

V. Metrology Flow M50-1 (Master Workflow)

1. Readiness
   • Inputs contain tau_mono, ts or an alignment reference sync_ref, and the arrival-time path fields gamma(ell), n_eff, c_ref.
   • Run repair_units for unit normalization and check_dim.
2. Acquisition & Screening
   Collect PPS/PTP/NTP observations; cull packet loss and step anomalies; mark missingness m.
3. Offset/Skew Fitting
   Within window Delta_t, estimate hat{offset}, hat{skew} via weighted robust regression; output residual epsilon(tau_mono).
4. Jitter & Stability
   Compute J_rms/J_pp and sigma_y(tau_set); persist under time.stability.*.
5. Parallel Arrival Forms
   Compute both T_arr forms and delta_form; verify non_decreasing(ell) and L_gamma.
6. Checks & Assertions
   Execute C50-1x contracts (next section); map failures to severity and actions.
7. Persistence & Signature
   Emit manifest.time: offset/skew/J, sigma_y, T_arr.*, contracts, TraceID, signature.

VI. Contracts & Assertions

• C50-11: non_decreasing(tau_mono).
• C50-12: offset_p99 ≤ tol_offset (units µs/ns).
• C50-13: |skew| ≤ tol_skew (ppm/ppb).
• C50-14: J_rms ≤ tol_jitter, J_pp ≤ tol_jitter_pp.
• C50-15: delta_form ≤ tol_Tarr; non_decreasing(ell).
• C50-16: |path_asym| ≤ tol_asym (if unknown: include upper bound in U and annotate).
• C50-17: check_dim(expr)=pass; all fields entering S501-* are dimensionally consistent.

VII. Implementation Bindings I50- **

• time_source_probe(dev, proto) -> samples: acquire raw PPS/PTP/NTP observations.
• estimate_offset_skew(samples, method, window) -> {offset, skew, epsilon} (method ∈ {robust_ols, huber, ransac}).
• compute_allan(freq_series, tau_set) -> {sigma_y, TDEV, MDEV}.
• align_timebase(ds, sync_ref) -> ds': map to ts with offset/skew/J and uncertainty.
• enforce_arrival_time_convention(ds) -> ds': compute dual-form T_arr, delta_form, and path checks.
• emit_time_manifest(ds, policy) -> manifest.time.
• Invariants: unique(TraceID); sum(w_i)/N ≈ 1; delta_form ≤ tol_Tarr; non_decreasing(tau_mono, ell).

VIII. Cross-References

• Cleaning: Methods.Cleaning v1.0 Chapter 5 (timeline & sync cleaning), Chapter 6 (paths & arrival time).
• Imaging: Methods.Imaging v1.0 Chapter 13 (time/path gating & arrival consistency).
• Statistics: Methods.CrossStats v1.0 Chapter 11 (time series) and Appendix E (error & uncertainty propagation).
• Core: EFT.WP.Core.DataSpec v1.0 (fields & units), EFT.WP.Core.Threads v1.0 (streaming & backpressure).

IX. Quality Gauges & Risk Control

1. Suggested SLI/SLOs
   • offset_p99, |skew|_p95, J_rms, sigma_y(tau_grid);
   • Arrival-time consistency: delta_form_p99.
2. Drift & Alerting
   Trend bands for offset/skew; out-of-band alerts on sigma_y; if path_asym spikes, roll back to conservative upper bounds.
3. Rollback strategy
   Degrade (weight time-derived signals) → rate-limit sync updates → fallback reference source → freeze_release to pause publication.

Summary