29-EFT.WP.TBN.Measurement v1.0 | Chapter 8 | Instrument & Processing-Chain Metrology (Loopback / Triangle / Peer-to-Peer)

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Chapter 8 | Instrument & Processing-Chain Metrology (Loopback / Triangle / Peer-to-Peer)

• One-line objective: Using loopback / triangle / peer-to-peer fieldable schemes, isolate and measure instrument and processing-chain (Inst/Proc) delays and asymmetry terms, in lockstep with dual-form T_arr reconciliation and with uncertainty/manifest-based publication.
  (All path integrals are taken along gamma(ell) with measure d ell.)
• I. Scope & Objects
• Inputs
• Topology & ports: device/link under test D={Tx,Rx,port}, segmented path and interfaces {Σ_j}, probe probe∈{PPS,TWTT,PRBS,timestamp}.
• Timebase & triggering: tau_mono/ts, reference refclk with offset/skew/J (see Ch. 3).
• Path & environment: gamma(ell), n_eff(f,x) (see Chs. 2/7), measurement window W=[ts-Δt,ts], RBW/ENBW.
• Outputs
• Inst/Proc decomposition: ΔT_inst={frontend,codec,fpga,serdes,filter,connector}, ΔT_proc={buffer,queue,stack}, asymmetry ΔT_asym;
• Dual-form arrival & reconciliation: T_arr^{form1/form2}, reconciled T_arr*, and the Inst/Proc contribution to delta_form;
• Manifest: manifest.tbn.inst.*, including evidence URIs and uncertainties u/U.
• Boundary
• Focuses on in-device / processing-chain quantification. External media/environment corrections are in Ch. 7; network-layer switching/queuing decomposition is in Chs. 6/10.
• II. Terms & Variables
• Loopback/symmetry: round-trip τ_loop=τ_fwd+τ_rev, asymmetry ΔT_asym=(τ_fwd-τ_rev)/2.
• Component delays: ΔT_frontend, ΔT_codec, ΔT_fpga, ΔT_serdes, ΔT_filter, ΔT_conn; processing delays ΔT_buffer, ΔT_stack.
• Dual-form arrival: T_arr^{form1}=(1/c_ref)(∫ n_eff d ell), T_arr^{form2}=(∫ (n_eff/c_ref) d ell), delta_form=|…|.
• Dimensions: unit(T)= "[T]", unit(delta_form)="[T]"; check_dim(*) must pass.
• III. Postulates P508-*
• P508-1 (Dual-form pairing): Any instrument/processing-chain metrology or correction must co-publish T_arr^{form1/form2} with delta_form ≤ tol_Tarr.
• P508-2 (Identifiability): Decomposition parameters are solved only from observable invariants (loopback/triangle/peer). No “hard-coded” empirical constants; non-identifiable parts enter u/U as upper bounds.
• P508-3 (Explicit measures): Timestamp/correlation/pulse measurements explicitly declare ( ∫_{t∈W} · dt ) and the window/bandwidth; interface points and port directionality are persisted.
• P508-4 (Dimensions/RefCond): All fields pass check_dim( y - f(x) ); RefCond.hash and device firmware/config hashes are traceable.
• P508-5 (Asymmetry guard): If |ΔT_asym| > τ_asym_max is detected, flag it and trigger strategy cards (degrade/bypass/rollback).
• IV. Minimal Equations S508-*
• Loopback (single-ended round-trip)
• S508-1 (ideal symmetry)
  τ_loop ≈ 2( T_arr* + ΔT_inst + ΔT_proc ) ⇒
  ΔT_inst+ΔT_proc ≈ τ_loop/2 - T_arr*.
• S508-2 (with asymmetry & interfaces)
  τ_loop = (T_arr,fwd* + T_arr,rev*) + (ΔT_inst,fwd + ΔT_inst,rev) + (ΔT_proc,fwd + ΔT_proc,rev),
  ΔT_asym = [(ΔT_inst,fwd-ΔT_inst,rev)+(ΔT_proc,fwd-ΔT_proc,rev)]/2.
• Peer-to-Peer (A↔B)
• S508-3
  Given τ_AB, τ_BA,
  T_1way ≈ (τ_AB - ΔT_inst,A - ΔT_proc,A + τ_BA - ΔT_inst,B - ΔT_proc,B)/2,
  ΔT_asym ≈ (τ_AB - τ_BA)/2 + (ΔT_inst,B-ΔT_inst,A + ΔT_proc,B-ΔT_proc,A)/2.
• Triangle (A–B–C closed loop)
• S508-4
  τ_AB + τ_BC - τ_AC ≈ 2(ΔT_asym,ABC),
  using the third node to cancel common paths and amplify Inst/Proc asymmetry observability.
• Component modeling & superposition
• S508-5
  ΔT_inst = ΔT_frontend + ΔT_codec + ΔT_fpga + ΔT_serdes + ΔT_filter + ΔT_conn,
  ΔT_proc = ΔT_buffer + ΔT_stack;
  when only totals are identifiable, record component priors as bounds and include in u/U.
• Jitter & spectra
• S508-6
  σ_t^2 = ∫ S_t(f) df; device-internal jitter share
  σ_t,inst^2 ≈ σ_t,total^2 - σ_t,ref^2 - σ_t,path^2 (independence approximation);
  S_t(f) and RBW/ENBW are annotated for consistency with Chs. 4–5.
• Dual forms & reconciliation
• S508-7
  T_arr* = T_arr^{form2} + ΔT_geom + ΔT_med + (ΔT_inst + ΔT_proc) + ΔT_sync,
  while loopback/peer/triangle solutions act only on ΔT_inst/ΔT_proc; delta_form remains an independent constraint.
• V. Metrology Flow M50-8 (Ready → Measure → Solve → Check → Persist)
• Ready: Freeze device/firmware/config hashes and port topology; bind RefCond and tau_mono/ts; set W,w(t),RBW/ENBW; choose {loop|peer|triangle} and thresholds.
• Measure: Acquire timestamps/correlation/pulse round-trip data {t1..t4} or {τ_AB, τ_BA, τ_BC, τ_CA}; align to the unified timebase.
• Solve: Apply S508-1…4 to solve ΔT_inst, ΔT_proc, ΔT_asym; decompose components when identifiable; estimate jitter spectrum S_t(f) and σ_t.
• Check:
• check_dim(T)=[T], delta_form ≤ tol_Tarr;
• Consistency with Ch. 6 one-way/round-trip delays; |ΔT_asym| ≤ τ_asym_max or flag exception;
• Build u/U incorporating echo/timestamp quantization/trigger/PLL/correlation-window contributors.
• Persist:
  manifest.tbn.inst = {scheme:{loop|peer|triangle}, topo:{ports,Σ}, timestamps:{…}|pairs:{…}, results:{ΔT_inst,ΔT_proc,ΔT_asym,σ_t,S_t}, Tarr:{form1,form2,delta_form,T_arr*}, components:{frontend,codec,fpga,serdes,filter,connector,buffer,stack}, u/U, RefCond, contracts.*, signature}.
• VI. Contracts & Assertions C50-8x (Suggested thresholds)
• C50-801 (Dual-form difference): delta_form_p95 ≤ tol_Tarr.
• C50-802 (Asymmetry bound): |ΔT_asym|_p95 ≤ τ_asym_max; if exceeded, annotate and trigger strategy cards.
• C50-803 (Evidence completeness): Loopback/peer/triangle timestamp sets or correlation evidence URIs must be persisted; ports/directions explicit.
• C50-804 (Spectra/jitter): σ_t_p95 ≤ σ_t,max, in-band S_t(f) within spectral gates; RBW/ENBW consistent with the window.
• C50-805 (Dimensions/freshness): check_dim(*) passes; device/firmware/config and RefCond meet age ≤ Δt_max, coverage ≥ cov_min.
• VII. Implementation Bindings I50-8* (Interface prototypes, I/O, invariants)
• I50-81 loopback_delay(stamps|correl, cfg) -> {τ_loop, ΔT_inst+ΔT_proc, ΔT_asym?, u, meta}
• I50-82 peer_delays(pairs:{τ_AB,τ_BA}, cfg) -> {T_1way, ΔT_asym, u, meta}
• I50-83 triangle_delays(pairs:{τ_AB,τ_BC,τ_CA}, cfg) -> {ΔT_asym, u, meta}
• I50-84 inst_decompose(total, priors) -> {components:{frontend,…,stack}, u, meta}
• I50-85 jitter_psd(traces, RBW, ENBW) -> {S_t(f), σ_t, meta}
• I50-86 inst_to_twoform_consistency(n_eff, gamma, c_ref) -> {T_arr_form1, T_arr_form2, delta_form}
• I50-87 assert_inst_contracts(ds, rules) -> {report, pass}
• I50-88 emit_inst_manifest(results, policy) -> {uri, status}
• Invariants: two_forms_present=true; check_dim(*) passes; port topology / firmware / config hashes and RefCond are traceable; evidence URIs are replayable.
• VIII. Cross-References
• Mathematical baseline & dual forms: Ch. 2.
• Acquisition & timebase: Ch. 3.
• Estimators/statistics: Chs. 4–5.
• Link delay: Ch. 6.
• Environmental corrections: Ch. 7.
• Network-layer reconciliation & anchors: Ch. 10.
• Uncertainty/contracts: Chs. 11–12.
• IX. Quality & Risk Control
• SLIs/SLOs: delta_form_p95, |ΔT_asym|_p95, σ_t_p95, var_emp/CRLB, age(RefCond), coverage.
• Fallback strategies: rising asymmetry → combine peer/triangle/loopback calibration; rising jitter → reduce bandwidth/average/clean clocks; insufficient evidence → re-measure or reject; growing dual-form gap → unify on form2 and widen guardband.
• Audit: timestamp/correlation evidence, port topology & firmware/config hashes, decomposition results & uncertainties, manifest signature chain & replay scripts.
• Summary
• This chapter delivers three practical schemes—loopback, triangle, and peer—to measure instrument and processing-chain delays and asymmetries, rigorously paired with the dual-form T_arr and uncertainties.
• Anchored by M50-8 / C50-8x / I50-8* and manifest.tbn.inst, device-side metrology becomes measurable, traceable, and rollback-ready, laying the groundwork for the upcoming “spectrum–time consistency” and “analytics vs. anchors & replay” (Chs. 9–10).