36-EFT.WP.EDX.Current v1.0 | Chapter 9 — Metrology Chain & Experimentally Measurable Quantities (M10-*)

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Chapter 9 — Metrology Chain & Experimentally Measurable Quantities (M10-*)

EFT.WP.EDX.Current v1.0
Chapter 9 — Metrology Chain & Experimentally Measurable Quantities (M10-*)

I. Chapter Objectives & Structure

1. Objective: Define the measurables and a unified metrology chain for EDX.Current, fixing traceability, synchronization, de-embedding, and path correction; establish the uncertainty budget and publication gates so that S20-* / S40-* / S50-* / I30-* / Chapter 8 close the loop under one metrological framework.
2. Structure: M10-1 Traceability → M10-2 Synchronization & drift → M10-3 Uncertainty budget & gates → Data structure & records → Falsifiability → Compliance templates → Correspondence & degeneracy → Cross-chapter pointers & summary.
3. Shared dialect (time-of-arrival; path/measure explicit; record delta_form):
   • Constant-factored: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
   • General: T_arr = ( ∫ ( n_eff / c_ref ) d ell )

II. Measurables & Units (minimal list)

• I(t) (A), J(x,t) (A·m⁻²), V(t) (V), Z(omega) (Ω, complex), |Z(omega)| (Ω), arg Z(omega) (rad).
• T_arr (s), ΔT_arr (s, path differential), n_eff(x,t) (—), c_ref (m·s⁻¹).
• Energy & power: p = ( J · E ) (W·m⁻³), S (W·m⁻²), u (J·m⁻³).
• Sync-related: Δt_sync (s); environment variables (temperature/stress/bias) in SI.
• Constraints: All key equalities must pass check_dim; the linear phase–delay approximation is used only within the coherence window (see Chapter 8 and S20-5).

III. M10-1 Traceability Chain

• References & standards: Timebase (10 MHz / pulse trains), resistance/capacitance/coax/probe standards; include calibration certificates and traceability IDs in metadata.
• Fixtures & de-embedding: Apply deemb separately to measurement and simulation; fix baseline_id; align port definitions and order via anchors (see I30-3).
• Path correction: Using the layout ↔ gamma(ell) binding, map routing/return to {γ_p}, correct arg Z and T_arr, and record as in Chapter 8.
• n_eff calibration: Joint inversion of material/geometry/boundaries or comparison to reference fixtures; publish the interval and method summary for n_eff (mandatory).
• Consistency gates: Passivity (Re{Z} ≥ 0), K–K consistency, check_dim, and delta_form alignment.

IV. M10-2 Synchronization & Drift

• Timebase alignment: Record reference clock/trigger/sampling channels; estimate and compensate Δt_sync; phase equivalent: Δφ_sync(omega) = ( omega · Δt_sync ).
• Temperature/stress drift: Map environmental changes to smooth renormalization of n_eff and T_arr; exceeding the linear window triggers re-calibration.
• Alarms & gates: If |Δt_sync| > τ_gate or |d n_eff / dT| exceeds a threshold, mark the dataset as diagnostic-only; not eligible for publication.

V. M10-3 Uncertainty Budget & Publication Gates

1. Contributors: u_inst (instrumentation), u_deemb (de-embedding), u_sync (timebase), u_neff, u_path (discretization/geometry), u_env (environment).
2. Combination (examples):
   • T_arr:
     u^2(T_arr) ≈ Σ_i ( (Δell_i/c_ref)^2 · u^2(n_eff(i)) + ( n_eff(i)/c_ref )^2 · u^2(Δell_i) ) + u^2(Δt_sync)
   • arg Z:
     u^2(arg Z) ≈ u^2(arg Z)_inst + ( omega^2 · u^2(T_arr) ) + u^2(K–K_fit)
3. Publication gates (suggested):
   • u(T_arr) / T_arr ≤ 5% (engineering); ≤ 1% (benchmark/release).
   • Re{Z} ≥ 0, K–K passed, check_dim = pass, delta_form recorded.

VI. Data Structure & Records (minimal template)

metrology:

baseline_id: "BLSN-2025-EDX-001"

instruments: [{type:"VNA", model:"—", cal:"2025-08-01"}, {type:"scope", bw_GHz:—}]

standards: [{type:"thru"}, {type:"open"}, {type:"load"}, {type:"short"}]

deemb: {method:"TRL", version:"1.2", file:"/path/deemb.json"}

timebase: {ref:"10MHz", sync_scheme:"shared_ref+trigger", dt_sync_s: 2.0e-12}

env: {temp_C: 25.0, humidity_pct: 40.0, stress:"none"}

binding_ref: "LAY2PATH-xxxx"

arrival:

form: "n_over_c" # or "one_over_c_times_n"

gamma: "explicit"

measure: "d_ell"

c_ref: 299792458.0

Tarr_s: 1.234e-09

u_Tarr_s: 6.0e-12

n_eff:

method: "inversion"

value: [ ... ] # per segment or effective

u_rel_pct: 3.5

qa_gates: {check_dim:"pass", passivity:"pass", KK:"pass"}

VII. Falsifiability Criteria (metrology side)

• Multi-path switching: With netlist/materials fixed, switch layout → gamma(ell); within the coherence window, Δarg Z(omega) must translate linearly with ΔT_arr. Otherwise, reject the path model or the sync hypothesis.
• Medium perturbation: Under small perturbations of n_eff (temperature/bias), T_arr must vary smoothly without non-causal spikes; otherwise reject the kernel/weighting model (see S40-* / S50-*).
• Dialect agreement: On the same dataset, the two T_arr dialects must agree within u(T_arr); otherwise check units, paths, and delta_form.

VIII. Compliance Snippets (copy-ready)

• Sync correction: phi_corr(omega) = arg Z_raw(omega) - ( omega · Δt_sync )
• Arrival discrete estimate:
  T_arr = (1/c_ref) · Σ_i n_eff(i) Δell_i or T_arr = Σ_i (n_eff(i)/c_ref) Δell_i
• Publication QA:
  check_dim = pass ; Re{Z} ≥ 0 ; KK_consistency = pass ; delta_form ∈ {"n_over_c","one_over_c_times_n"} (recorded)

IX. Correspondence & Degeneracy to Classical Framework

X. Cross-Chapter Guidance & Summary

• Upstream/parallel: I30-3 (alignment API), Chapter 8 (paths/measure), S20-5 (phase–delay), S40-* / S50-* (kernels & mapping).
• Downstream: M20-* (experimental design & falsification) adopts this chapter’s u(T_arr), u(n_eff), and QA gates as acceptance criteria.
• Summary: This chapter fixes measurables, traceability, sync correction, and the uncertainty budget as the M10-* execution dialect, ensuring that tension landscape, paths, and impedance data are reproducible, comparable, and falsifiable under unified metrological gates.