36-EFT.WP.EDX.Current v1.0 | Chapter 10 — Experimental Design & Falsification (M20-*)

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

I. Chapter Objectives & Structure

1. Objective: Establish positive/negative criteria and power analysis that distinguish EDX.Current from classical frameworks; provide reproducible protocols and publication gates so that S20-* / S40-* / S50-* / I30-* / M10-* / Chapter 8 close the loop under one metrological and recording dialect.
2. Structure: M20-1 Criteria & sample size → M20-2 Observation geometry/path design → M20-3 Data cleaning & blinding → Reference experiments & workflow → Failure modes & troubleshooting → 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. Test Matrix & Controls (Overview)

1. Primary endpoints: slope and translation of arg Z(omega), smooth renormalization of |Z(omega)|, measurable changes in T_arr and ΔT_arr, and controllable drift of kernel weights w_p.
2. Experiment types:
   • Path-switching tests (alter layout → gamma(ell) via geometry/return/guards)
   • Medium-perturbation tests (small perturbations of n_eff via temperature/stress/bias)
   • Interface-binding tests (modify boundary treatments and I30-* binding parameters)
3. Controls: Classical RLC/telegrapher/effective-medium Z_ref(omega); EFT prediction Z_eft(omega)=Z_ref+ΔZ_T realized via S40-* / S50-*.

M20-1 Criteria & Sample Size (Criteria & Power)

A. Criteria (positive/negative)

1. P1 Linear phase-translation criterion (path switching): Within the coherence window, Δarg Z(omega) is linear in omega with slope k_φ satisfying
   k_φ ≈ ΔT_arr, and linear fit quality R^2 ≥ 0.98 with residuals |ε(omega)| ≤ 3·u(arg Z). Positive: all gates pass. Negative: any gate fails.
2. P2 Smooth renormalization criterion (medium perturbation): Under slow sweeps of temperature/stress, |Z| and arg Z vary smoothly with T_arr(n_eff) and show no non-causal spikes or negative real parts. Positive: passivity and K–K hold. Negative: any violation.
3. P3 Weight-response criterion (binding/boundary): Guard/ground adjustments that raise/lower target w_p produce arg Z shifts consistent with Σ_p (Δw_p · T_arr,p) (within u(T_arr)). Positive: consistent. Negative: significant deviation.
4. P4 Kernel-causality criterion (spectral form): Inverted kernels K_s(ω), K_t(ω) have no right-half-plane poles and Re{Z_eft} ≥ 0. Positive: pass. Negative: fail.

B. Effect Sizes & Sample Size

1. Primary effects: δ_T = |ΔT_arr|, δ_φ = |Δ(arg Z)/Δω|, δ_Z = ||Z_eft|-|Z_ref|| / |Z_ref|.
2. Power analysis (indicative): For slope testing with target power 1-β, significance α, phase-noise SD σ_φ, number of frequency points N_ω, bandwidth B_ω:
   N ≳ ((z_{1-α/2}+z_{1-β}) · σ_φ / (δ_φ · √S_ω))^2, where S_ω is the variance scale of frequency samples (set by B_ω and sampling).
3. Suggested gates: engineering validation 1-β ≥ 0.8, α ≤ 0.05; benchmark release 1-β ≥ 0.9, α ≤ 0.01.
4. Blocking & repeats: per configuration R ≥ 5 repeats; ≥2 cross-day repeats to separate u_env and u_sync.

M20-2 Observation Geometry & Path Design (Geometry & Paths)

A. Layout & Paths

1. Build layout ↔ gamma(ell) via I30-2, define a main path γ_main and 1–2 controlled side paths γ_side, and record segment-level {material, geometry, neighbor boundary, n_eff}.
2. Coherence-window selection: choose bands where arg Z is near-linear; narrow the band if needed to improve R^2 and power.

B. Control Knobs

1. Path switching: routing topology, guard on/off, ground-return path.
2. Medium perturbation: temperature T, stress/bias b, ensuring |Δn_eff| stays within the linear perturbation window.
3. Boundary treatment: plating/crimp/contact; all changes recorded in BC.

C. Records & Gates

• Mandatory: arrival{form,gamma,measure,c_ref,Tarr,u_Tarr}, delta_form, anchors, deemb, sync; pass check_dim and passivity gates.

M20-3 Data Cleaning & Blinding (Cleaning & Blinding)

A. Pre-registration & Freeze

• Before measurement, freeze: frequency grid, bandwidth, fit method, criterion gates, baseline_id, delta_form, binding_ref.
• Blinding: shuffle labels for path configurations/temperature; do not reveal true labels before analysis.

B. Cleaning Workflow

• De-embedding/sync correction: apply_deemb, time_align; path correction: path_correct.
• QA gates: Re{Z} ≥ 0, K–K consistency, check_dim = pass; failing data are flagged diagnostic-only.
• Outliers & exclusion: detect via pre-registered rules (e.g., 3·MAD); post hoc tuning is prohibited.

III. Reference Experiments & Executable Workflow (Reproducible)

A. Path-Switching Test (validates P1/P3)

• Fabricate two equal-length layouts differing only in guards/return to realize {γ_A, γ_B}; calibrate n_eff.
• Measure Z_A(ω), Z_B(ω); compute Δarg Z = arg Z_B - arg Z_A.
• Fit Δarg Z = k_φ · ω + b; test k_φ against ΔT_arr = T_arr,B - T_arr,A; report R^2 and residuals.
• Decision: pass → positive; else negative, with deviation vector (amplitude/phase/frequency dependence).

B. Medium-Perturbation Test (validates P2)

• Fix γ_main; sweep temperature or bias; record Z(ω;T) and T_arr(T).
• Check smooth renormalization of |Z| and arg Z with passivity/K–K; fit a monotone curve for T_arr(T) and report u(T_arr).
• Decision: any non-causal spike or negative real part → negative.

C. Interface-Binding Test (validates P3/P4)

• Change contact/plating/crimp; record changes in BC; keep binding_ref unchanged.
• Invert K_s,K_t; test causality/stability; compare w_p changes with Δarg Z.
• Decision: non-causal kernels or weight–phase mismatch → negative.

IV. Failure Modes & Troubleshooting

• Out-of-window coherence: spurious oscillations from using coherent sums beyond the window → restrict to the window or switch to energy composition.
• Sync mismatch: uncompensated Δt_sync → run time_align and recheck standards.
• Unlogged path leakage: missing minor branches → update binding_ref and {γ_p}, re-estimate w_p.
• De-embedding error: fixture model mismatch → cross-check TRL/SSL and recalibrate.
• Overfit kernels: spurious right-half-plane poles → band-limit/smooth priors on K_s/K_t.

V. Compliance Template (copy-ready)

protocol:

prereg:

baseline_id: "BLSN-EDX-001"

delta_form: "n_over_c"

binding_ref: "LAY2PATH-xxxx"

criteria: ["P1","P2","P3","P4"]

alpha: 0.05

power: 0.8

configs:

- id: "path_A"

layout: "A"

- id: "path_B"

layout: "B"

acquisition:

freq_span_GHz: [f_min, f_max]

points: N_ω

repeats: 5

alignment:

deemb: {method:"TRL", version:"1.2"}

sync: {dt_sync_s: 2.0e-12}

arrival_record:

form: "n_over_c"

gamma: "explicit"

measure: "d_ell"

qa_gates: ["check_dim","passivity(Re{Z}≥0)","KK_consistency"]

analysis:

tests:

- P1: "linfit(ΔargZ vs ω) → k_φ ≈ ΔT_arr ; R2≥0.98 ; |ε|≤3·u(argZ)"

- P2: "smooth_renorm(|Z|, argZ) & passivity & K-K"

- P3: "Δw_p ↔ ΔargZ slope consistency"

- P4: "no RHP poles in K_s/K_t"

VI. Correspondence & Degeneracy to Classical Framework

VII. Cross-Chapter Pointers & Summary

• Dependencies: M10-* (metrology chain), I30-* (binding/alignment), S20-5 (phase–delay), S40-* / S50-* (kernels & mapping).
• Delivery: Publications must include pre-registration, raw records, and alignment/de-embedding artifacts, with u(T_arr), u(arg Z), and gate outcomes.
• Summary: This chapter fixes experimental design, power analysis, and falsification lines as the M20-* execution dialect, ensuring that EDX.Current predictions are tested against classical models in a reproducible, quantifiable, and falsifiable manner.