37-EFT.WP.EDX.HighSpeed v1.0 | Chapter 10 — Experimental Design & Falsification (M20-HF)

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Chapter 10 — Experimental Design & Falsification (M20-HF)

I. Chapter Objectives & Structure

1. Objective: Build positive/negative criteria and power analysis to distinguish EDX.HighSpeed from classical frameworks or mis-specified models; provide reproducible protocols, controls, and release gates so that S20-HF / S30-HF / S50-HF / I30-HF / I40-HF / M10-HF / Chapter 7 close under a unified metrology and recording dialect.
2. Structure: Test matrix & controls → Criteria & sample size → Observation geometry & path/mode design → Data cleaning & blinding → Reference experiments & workflow → Failure modes & troubleshooting → Compliance templates → Cross-chapter closure.
3. Shared time-of-arrival dialect (equivalent; explicit gamma(ell) & d ell; record delta_form):
   • Constant-factored: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
   • General: T_arr = ( ∫ ( n_eff / c_ref ) d ell )

II. Test Matrix & Controls (Overview)

1. Primary endpoints: E_phase(Ω) and GDR(Ω), T_group(ω), ΔT_arr, weight drift ΔW, radiation gate Re{ΔZ_rad} ≥ 0, and Z_c(ω) deviation.
2. Experiment types:
   • Path-switching tests (toggle geometry/returns/guards layout → gamma(ell); observe k_φ ≈ ΔT_arr).
   • Small perturbations in dielectric/conductor (temperature/bias/material dispersion; observe smooth renormalization and passivity/causality).
   • Interface/gap/via tests (enable/seal radiation channel; observe ΔZ_rad and field consistency).
   • Mixed-mode/port-normalization tests (DM/CM transform and S↔Z loop consistency).
3. Controls: Classical RLC/telegrapher or 3D-EM anti-radiation baseline Z_base = Z_ref + ΔZ_T; EFT prediction Z_eft = Z_base + ΔZ_rad with path–mode weights.

III. M20-HF-1 Criteria & Sample Size (Criteria & Power)

1. P1 Linear phase-translation (path switching)
   • In coherence window Ω, for Δarg Z(ω) = arg Z_B − arg Z_A, slope k_φ of linear fit satisfies
     k_φ ≈ ΔT_arr = T_arr,B − T_arr,A with R^2 ≥ 0.98 and residuals ≤ 3·u(arg Z).
   • Positive: all gates pass; Negative: any fails.
2. P2 Smooth renormalization (dielectric/conductor perturbations)
   With small changes in n_eff(ω) or sigma_eff(ω), |Z|/arg Z vary monotonically and smoothly; Re{Z_eft} ≥ 0 and KK_consistency = pass.
3. P3 Radiation positive-real (gaps/stubs/bridges)
   When enabled, Re{ΔZ_rad(ω)} ≥ 0; after sealing, both Re{ΔZ_rad} and |E_rad|/|I_CM| decrease together.
4. P4 Mixed-mode consistency
   The loop S→S_mm→Z_mm→Z preserves power and reciprocity; E_phase/GDR do not degrade.
5. Effect size & sample size (indicative)
   • For slope testing, effect δ_φ = |Δ(arg Z)/Δω|; with significance α, power 1−β, phase noise σ_φ, and frequency-sample variance scale S_ω:
     N_ω ≳ ((z_{1-α/2}+z_{1-β}) · σ_φ / (δ_φ · √S_ω))^2.
   • Suggested: engineering 1−β ≥ 0.8, α ≤ 0.05; release 1−β ≥ 0.9, α ≤ 0.01.

IV. M20-HF-2 Observation Geometry & Path/Mode Design

• Layout & paths: Build binding_ref via I30-HF, define γ_main and controlled leakage γ_side, with segment {layer,len,n_eff,neigh}.
• Mode planning: DM/CM or primary/secondary with Z_c,m(ω), alpha_m, beta_m; set coupling matrix C(ω) at bends/splits.
• Window selection: Prefer near-linear-phase region; segment multi-window if needed.
• Control knobs: guard/return toggles, stub/trimming, gap sealing, temperature/bias, mixed-mode basis T_mm.
• Mandatory records: arrival{form,gamma,measure,c_ref,Tarr,u_Tarr,delta_form}, Znorm/Z_c(ω), qa_gates.

V. M20-HF-3 Data Cleaning & Blinding

• Pre-registration: Freeze frequency grid, bandwidth, fit methods, KPI gates, baseline_id, Znorm, binding_ref, delta_form.
• Blinding: Shuffle path/temperature labels; conceal prior to analysis.
• Cleaning flow: de-embed → renorm → S↔Z → sync correction → path correction → window evaluation → KPI computation.
• Hard QA: Re{Z_eft} ≥ 0, KK = pass, two-dialect T_arr agreement; if radiation enabled then Re{ΔZ_rad} ≥ 0.
• Outlier policy: follow pre-registered rules (e.g., 3·MAD); no post hoc tuning.

VI. Reference Experiments & Workflow (Reproducible)
A. Path switching (validates P1)

• Fabricate equal-length A/B layouts varying guard/return;
• Measure Z_A(ω), Z_B(ω), compute Δarg Z;
• Fit Δarg Z = k_φ·ω + b, test k_φ ≈ ΔT_arr, R^2/residuals;
• Record E_phase/GDR/ΔW and pass/fail.

B. Dielectric/conductor perturbation (validates P2)

• Fix γ_main, sweep temperature or dispersion parameter;
• Observe smooth renormalization of |Z|/arg Z and passivity/K–K;
• Report u(T_arr), u(arg Z), u(T_group) and decide.

C. Gap/via/bridge (validates P3)

• Design sealable gaps or trimmed stubs;
• Estimate ΔZ_rad, verify Re{ΔZ_rad} ≥ 0 and pre/post decrease;
• Compare |E_rad|/|I_CM| and ΔW trend consistency.

D. Mixed-mode consistency (validates P4)

• Construct DM/CM transform and port normalization;
• Check power/reciprocity and KPI changes;
• Map back to SE domain and verify consistency.

VII. Failure Modes & Troubleshooting

• Out-of-window coherence: doing coherent sums outside Ω → restrict to Ω or switch to energy composition.
• Sync mismatch: biased Δt_sync → correct timebase before fitting.
• Missing path: unmodeled γ_side → update binding_ref and w_{p,m}.
• De-embed/renorm errors: baseline/normalization mismatch → verify baseline_id/Znorm and file hashes.
• Radiation mis-equivalence: Re{ΔZ_rad} < 0 or field trend mismatch → re-check gaps/stubs geometry and probing.
• Mixed-mode mis-match: inconsistent T_mm/Z0_mm → rebuild transforms and re-verify power conservation.

VIII. Compliance Templates (copy-ready)

• Experiment protocol card (YAML)
• protocol_hf:
• prereg:
• baseline_id: "BLSN-EDX-001"
• Znorm_ohm: [50.0, 50.0]
• binding_ref: "LAY2PATH-HF-0001"
• delta_form: "n_over_c"
• criteria: ["P1","P2","P3","P4"]
• alpha: 0.05
• power: 0.8
• configs:
• - {id:"A", layout:"guard_off"}
• - {id:"B", layout:"guard_on"}
• acquisition:
• band_GHz: [f_min, f_max]
• N_ω: 1024
• repeats: 5
• alignment:
• deemb: {method:"TRL", version:"1.2", artifact:"/artifacts/deemb.json"}
• sync: {dt_sync_s: 2.0e-12}
• arrival:
• form: "n_over_c" # or "one_over_c_times_n"
• gamma: "explicit"
• measure: "d_ell"
• c_ref: 299792458.0
• kpi_gates:
• E_phase_rad: {eng: 0.08, rel: 0.05}
• GDR_s: {eng: 0.25e-9, rel: 0.20e-9}
• ΔW: {eng: 0.30, rel: 0.20}
• radiation:
• enabled: true
• Re_Zrad_min: 0.0
• qa_gates: ["check_dim","passivity(Re{Z}≥0)","KK_consistency"]
• Analysis skeleton (pseudocode)
• # Read card → de-embed/renorm → S→Z
• Z = map_S_to_Z(renorm(deembed(S_raw, fixture), Znorm(ω)), Znorm(ω))
• # Sync correction & arrival
• phi = unwrap(arg(Z) - ω*Δt_sync)
• Tarr = fit_linear_phase(phi, ω).slope
• # Two-dialect agreement
• assert abs(Tarr_n_over_c - Tarr_one_over_c_times_n) <= u_Tarr
• # KPIs
• T_group = grad(phi, ω)
• E_phase = max_abs(phi - (ω*Tarr + phi0_opt))
• GDR = max_abs(T_group - median(T_group))
• # P1: slope criterion
• k_phi = linfit(arg(Z_B)-arg(Z_A), ω).slope
• assert abs(k_phi - (Tarr_B - Tarr_A)) <= 3*u_Tarr
• # P2: passivity & causality
• assert min(Re(Z)) >= 0.0 and KK_consistency(Z)
• # P3: radiation positive-real
• if radiation_enabled:
• ΔZ_rad = Z - Z_base
• assert min(Re(ΔZ_rad)) >= 0.0

IX. Cross-Chapter Links & Closure

• Dependencies: Chapter 2 (Terms & Symbols), Chapter 4 (Minimal Equations & Dispersion), Chapter 5 (Radiation Correction), Chapter 6 (Modes & Primitives), Chapter 7 (Coherence Window KPIs), Chapter 8 (S↔Z Mapping), Chapter 9 (Metrology Chain).
• Downstream: Chapter 12 (Layout & Process Rules — KPI/criteria-based acceptance), Chapter 14 (SimStack & cases — regression on criteria), Chapter 16 (Design Protocol & Checklist — integrate criteria and power into sign-off).