29-EFT.WP.TBN.Measurement v1.0 | Chapter 1 | TBN Metrology Domain: Definitions & Scope

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Chapter 1 | TBN Metrology Domain: Definitions & Scope

• One-line objective: Delimit the objects, inputs/outputs, and engineering boundaries of Time-Base Backbone Network (TBN) metrology; establish a unified publication convention—traceable to RefCond—with dual-form arrival-time handling and manifest key fields.
  (All path integrals are taken along gamma(ell) with measure d ell.)
• I. Scope & Objects
• Objects (systems & links under test)
• Nodes/links/switching equipment: local oscillators and distribution, optical/electrical spans, switching/queuing stages, measurement probes and front-ends.
• Propagation path: gamma(ell) = ⊕_{seg∈{fiber,fso,device}} gamma_seg(ell), with path length L_gamma = ( ∫_gamma 1 d ell ).
• Timebase & references: unified computed time tag tau_mono and publication time ts; local clock parameters offset/skew/J.
• Objects (measurands)
• Phase/frequency: phi(t), y(t) (instantaneous frequency deviation), phase-noise spectrum S_phi(f), frequency-noise spectrum S_y(f), Allan-family sigma_y(τ).
• Arrival time (dual forms in parallel): T_arr^{form1} = ( 1 / c_ref ) * ( ∫_{gamma} n_eff d ell ); T_arr^{form2} = ( ∫_{gamma} ( n_eff / c_ref ) d ell ); difference delta_form.
• Link/node metrics: lat_total = lat_prop + lat_ser + lat_sw + lat_q + lat_proc, plus SNR/RBW/ENBW, quantization noise, and trigger jitter.
• Inputs
• Observations & front-end: I/Q/pulses/timestamps; ADC/trigger/reference inputs; analysis window W=[ts-Δt, ts] and window function.
• Path/environment: n_eff(f,x), meteorology/TEC; device/span inventories with hash/id/validity.
• Synchronization/bases: PPS/Two-Way/ratio chains/loopback anchors; priors for offset/skew/J; RefCond sources (ephemerides/potential fields/media/instruments/timebase).
• Outputs
• Estimates & statistics: phi/y, S_phi/S_y/sigma_y, T_arr^{form1/2}, delta_form, lat_*.
• Corrections & reconciliation: corr_env(x; RefCond), reconciled T_arr*, and release thresholds/guardbands.
• Manifests: manifest.tbn.* (evidence/thresholds/uncertainty/signature).
• Out-of-scope boundaries
• Textbook derivations of fundamental constants/principles; higher-order RF/fiber/FSO propagation models are deferred to the Packets/PathCorrection/PathRedshift volumes; security policy and governance are handled in the companion Security volume.
• II. Terms & Variables
• Time–frequency & phase: f, omega=2*pi*f, phi(t), y(t) = (f(t)-f_ref)/f_ref, S_phi(f), S_y(f), sigma_y(τ).
• Path & media: gamma(ell), L_gamma, n_eff(f,x), n_phi(f), n_g(f) = n_phi - f * ( d n_phi / d f ).
• Arrival time & dual forms: T_arr^{form1}, T_arr^{form2}, delta_form, tol_Tarr, c_ref.
• Windowing & bandwidth: W=[ts-Δt,ts], RBW, ENBW, BW.
• Sync & clocks: offset, skew, J; refclk, PLL.
• Dimension exemplars: unit(T_arr) = "[T]", unit(S_phi) = "rad^2/Hz", unit(S_y) = "1/Hz", unit(sigma_y)= "1", unit(delta_form)="[T]".
• III. Postulates P501-*
• P501-1 (Dual-form parallelism): Any published arrival-time result must provide T_arr^{form1/form2} and delta_form in parallel, with the contract assertion delta_form ≤ tol_Tarr.
• P501-2 (Explicit measures): All integrals/averages/statistics must declare domain and measure: ( ∫_{gamma(ell)} · d ell ), ( ∫_{t∈W} · dt ), ( ∫_{f∈B} · df ).
• P501-3 (Dimensional compliance): Any field entering equations must pass check_dim( y - f(x) ); log↔linear conversions (dB↔linear, rad↔cycle) are persisted in scale.note.
• P501-4 (RefCond traceability): Reference conditions across path/environment/instruments/timebase are persisted as RefCond with hash/validity/coverage/Δt/Δx.
• P501-5 (Front-end coherence): Coherence of sampling/trigger/reference timebases must be recorded in the manifest; violations lead to rejection or degraded publication.
• IV. Minimal Equations S501-*
• Phase–frequency–statistics transforms
• S501-1: S_y(f) = (f/2π)^2 S_phi(f); sigma_y^2(τ) = 2 ∫_0^∞ S_y(f) |H_τ(f)|^2 df (where H_τ is the Allan filter).
• S501-2: y(t) = (1/2π f_ref) d phi/dt; CRLB (pure sinusoid + AWGN): var(f̂) ≥ 6 / ( (2π)^2 · SNR · T_obs^3 ) (calibration constants are persisted).
• Arrival-time dual forms & difference
• S501-3: T_arr^{form1} = ( 1 / c_ref ) ( ∫_{gamma} n_eff d ell ); T_arr^{form2} = ( ∫_{gamma} ( n_eff / c_ref ) d ell ).
• S501-4: delta_form = | T_arr^{form1} - T_arr^{form2} |, with release gate delta_form ≤ tol_Tarr.
• Link-latency decomposition & reconciliation
• S501-5: lat_total = lat_prop + lat_ser + lat_sw + lat_q + lat_proc;
  reconciliation: T_arr* = T_arr^{form2} + ΔT_geom + ΔT_med + ΔT_inst + ΔT_proc + ΔT_sync.
• Windowing & bandwidth
• S501-6: Spectral metrics use RBW/ENBW with window w(t); ENBW = ( ∫ w^2 / (∫ w)^2 ) Fs. Publication must record window_fn/RBW/ENBW.
• V. Metrology Flow M50-1 (Ready → Acquire → Model/Estimate → Check → Persist)
• Ready: Align tau_mono/ts; freeze RefCond and device/span inventories; set W, RBW/ENBW, and thresholds.
• Acquire: Collect I/Q/pulses/timestamps; record trigger/reference coherence and SNR; capture sync state offset/skew/J.
• Model/Estimate:
• Phase & frequency: phi/y/S_phi/S_y/sigma_y (Chs. 4–5).
• Arrival time: T_arr^{form1/form2}, lat_* decomposition (Ch. 6).
• Environment/path/instrument corrections corr_env(x; RefCond) (Chs. 7–8/companion volumes).
• Check: check_dim(*), evaluate delta_form, assess analytic vs. observed residuals; propagate u/U (Ch. 11).
• Persist:
  manifest.tbn = {RefCond.hash, S_phi/S_y/sigma_y, T_arr_forms, lat_*, corr_env, u/U, contracts.*, signature}.
• VI. Contracts & Assertions C50-1x (Suggested thresholds)
• C50-101 (Dual-form difference): delta_form_p95 ≤ tol_Tarr (suggest tol_Tarr = 1e-3·T_arr or link-specific).
• C50-102 (Window/bandwidth compliance): Persisted RBW/ENBW consistent with the recorded window; leakage/resolution gates met.
• C50-103 (SNR/CRLB): Estimators satisfy SNR ≥ SNR_min and T_obs ≥ T_min; otherwise reject or downgrade.
• C50-104 (Dimensions & freshness): check_dim(*) passes; age(RefCond) ≤ Δt_max, coverage ≥ cov_min.
• C50-105 (Front-end coherence): Trigger/reference-coherence metrics pass; otherwise no publication.
• VII. Implementation Bindings I50-1* (Interface prototypes, I/O, invariants)
• I50-11 acquire_timing(frontends, refs) -> {raw, meta}
• I50-12 estimate_phase_freq(raw, method) -> {phi, y, S_phi, S_y, sigma_y, meta}
• I50-13 measure_latency(link, probe) -> {T_arr_form1, T_arr_form2, delta_form}
• I50-14 compose_corr_env(sources, RefCond) -> {corr_env, meta}
• I50-15 assert_measurement_contracts(ds, rules) -> {report, pass}
• I50-16 emit_tbn_manifest(results, policy) -> {uri, status}
• Invariants: two_forms_present=true; check_dim(*) passes; method/RefCond/hash traceable; window/bandwidth/window function persisted.
• VIII. Cross-References
• PathCorrection/Packets/PathRedshift: path corrections, dispersion mapping, FSO/fiber propagation.
• TimeBase/Sync: tau_mono/ts/offset/skew/J and synchronization conventions.
• Instrument: loopback/two-way/peer calibrations.
• Methods.Cleaning: dual-form and contract-persistence conventions.
• IX. Quality & Risk Control
• SLIs/SLOs: delta_form_p95, sigma_y(τ) quantiles, S_phi@f thresholds, ΔT_obs_p95, age(source), coverage, hit/stale_ratio.
• Fallback strategies: high dual-form difference → unify on form2 and widen guardband; insufficient SNR → extend window/swap estimator; expired RefCond → downgrade/reject; trigger incoherence → reset/re-align.
• Audit: manifest signature chain, source hashes, replay scripts, and dual-environment recomputation.
• Summary
• This chapter fixes the domain-level baseline for TBN metrology: measurand set and I/O, dual-form rigor with dimensional checks, RefCond traceability, and manifest-based publication.
• It delivers an executable scaffold across P501/S501/M50-1/C50-1x/I50-1*, serving as the engineering anchor for this volume and for cross-volume alignment (paths/sync/instruments).