36-EFT.WP.EDX.Current v1.0 | Chapter 14 — Simulation Stack & Benchmark Cases (Methods.SimStack)

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Chapter 14 — Simulation Stack & Benchmark Cases (Methods.SimStack)

I. Chapter Objectives & Structure

1. Objective: Build a multi-scale Simulation Stack (SimStack) that, under a unified dialect, executes the full forward → inversion → validation → release workflow from netlist/layout/binding to Z_eft(omega), T_arr, w_p, and kernels K_{·}; provide reproducible sim–meas alignment and a benchmark case library.
2. Structure: Stack layers → Shared dialect & records → Numerical methods & stability → Benchmark cases → Sim–meas alignment → Falsifiability → Data structure & export → Compliance templates → Correspondence & degeneracy → Cross-chapter pointers & summary.
3. Shared arrival dialect (two equivalent forms; 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. Simulation Stack Layers (bottom-up)

1. Physics Core (S20/S40/S50):
   • S20-*: continuity/power conservation & minimal effective conduction;
   • S40-*: causal kernel convolutions with path weighting;
   • S50-*: impedance mapping Z_eft = Z_ref + ΔZ_T (+ ΔZ_rad).
2. Path Engine (I30 / Chapter 8):
   layout ↔ gamma(ell) binding; discretization {Δell_i, n_eff(i)}; multi-path weights w_p(omega).
3. Boundary & Radiation:
   Positive-real radiation correction ΔZ_rad(omega) with Re{ΔZ_rad} ≥ 0 and K–K consistency.
4. Solvers:
   Frequency-domain solvers (sparse linear / FFT convolution) and optional time-domain convolution; robust ∂Z/∂θ and sensitivity.
5. UQ & Inversion (Mx-*):
   Prior/likelihood/evidence, HMC/NUTS or SMC, posterior predictive checks (PPC).
6. I/O & Cards:
   Data/model/pipeline cards with mandatory arrival and qa_gates; versioning and reproducible seeds.

III. Shared Dialect & Records (mandatory)

• Arrival time: choose one dialect; record gamma(ell), d ell, c_ref, and delta_form.
• Units & dimensions: SI; all key equalities must pass check_dim = pass.
• Passivity & causality: Re{Z_eft} ≥ 0; K–K consistency; no right-half-plane poles in kernel spectra.
• Path weights: w_p ≥ 0, Σ_p w_p ≤ 1; coherent sum inside the window, energy composition outside.
• Sync correction: arg Z_corr(omega) = arg Z(omega) − ( omega · Δt_sync ).

IV. Numerical Methods & Stability

1. Frequency-domain kernel convolution: J_T = ( K_s ⊛ ∇T_fil ) + ( K_t ⊛ ∂T_fil/∂t ) → multiplication in frequency with windowing/band-limits; apply smooth/band-limited priors to K_{·}(ω); forbid right-half-plane poles.
2. Discrete arrival time:
   • n_over_c: T_arr ≈ (1/c_ref) * Σ_i n_eff(i) · Δell_i
   • one_over_c_times_n: T_arr ≈ Σ_i ( n_eff(i) / c_ref ) · Δell_i
3. Grid & bandwidth: choose N_ω and B_ω by the coherence window and target phase linearity error E_phase; recommended numeric gate: small | d^2 (arg Z) / dω^2 | < κ_phase.
4. Stability tactics: whitened residual spectral flatness checks; regularize or re-parameterize ill-conditioned sensitivities (e.g., log σ_eff).
5. Parallelism & caching: parallelize over paths/frequencies; cache kernels/weights/geometry to avoid repeated convolutions.

V. Benchmark Case Library (minimal, reproducible)

• SIM-01 | Path switch A/B (P1/P3): equal-length pair; only guards/return differ. Target: linear Δarg Z(ω) shift consistent with ΔT_arr.
• SIM-02 | Small medium perturbation (P2): fixed layout; slow temperature sweep. Target: smooth renormalization of |Z| & arg Z; no non-causal spikes.
• SIM-03 | Boundary discontinuity / radiation gate (EMI): plane gap / long stub. Target: monotone non-negative Re{ΔZ_rad}; near/far-field drop with sealing.
• SIM-04 | HF via / plane transition (HF): via barrel length / reference switch. Target: rising w_side(ω) and degraded E_phase/GDR.
• SIM-05 | Connector/launch transition: suppress modal conversion. Target: reduced Z_c(ω) deviation and smaller ΔW.
• SIM-06 | Cable coupling (CM): return strategies for bundles. Target: I_CM and near-field hotspots track γ_side(cable) weights.

Each case ships netlist/layout/binding, arrival, qa_gates, target gates, and reference outputs for regression.

VI. Simulation–Measurement Alignment Workflow (I30-3 / M10)

• Port harmonization: map_ports(ports_sim, anchors)
• De-embedding: apply_deemb(dataset, deemb, baseline_id)
• Timebase: time_align(dataset, sync)
• Path correction: path_correct(dataset, binding)
• QA gates: check_dim, passivity, K–K
  Output: Z_eft(ω), T_arr, w_p—directly consumable by S40/S50 for kernel inversion and design acceptance.

VII. Falsifiability Criteria (simulation side)

• F1: For SIM-01, slope mismatch |k_φ^{sim} − k_φ^{meas}| ≤ 3·u(k_φ); failure rejects path/weighting or kernel settings.
• F2: For SIM-02, T_arr(T) is monotone and differentiable; Re{Z_eft} ≥ 0, K–K passed; else reject n_eff(ω,T) priors.
• F3: For SIM-03, after sealing gaps, min(Re{ΔZ_rad}) staying same or rising counts as failure (should fall or remain non-negative while converging).
• F4: PPC residuals must be near-white within the pre-registered band; structured spectra reject the current model.
• F5: Key derived quantities from the two T_arr dialects (phase slope / effective T_arr) must agree within u(T_arr).

VIII. Data Structure & Export (minimal template)

simstack:

case_id: "SIM-01"

model_id: "EDX-Current-eft-ms"

freq_grid_Hz: [...]

layout_ref: "LAY-2025-001"

binding_ref: "LAY2PATH-xxxx"

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

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

Tarr_s: 1.234e-09

u_Tarr_s: 6.0e-12

outputs:

Z_eft: {real: [...], imag: [...]}

argZ: [...]

weights: {w_main: [...], w_side: [...]}

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

seed: 20250915

IX. Compliance Templates (copy-ready)

• API prototypes

api:

- id: "SimStack.build"

proto: "build(netlist, layout, binding, options) -> sim_handle"

- id: "SimStack.forward"

proto: "forward(sim_handle, theta, freq_grid) -> {Z_eft, T_arr_p, w_p}"

- id: "SimStack.invert"

proto: "invert(sim_handle, data, priors) -> posterior, logZ"

- id: "SimStack.ppc"

proto: "ppc(sim_handle, posterior) -> residual_spectrum, gates"

- id: "SimStack.export"

proto: "export(sim_handle, format:'cards|json') -> artifact"

• HF group delay & phase linearity

phi = argZ[ω1:ω2] # coherence window

T_group = grad(phi, omega)

E_phase = max_abs(phi - (omega*Tarr + phi0_opt))

GDR = max_abs(T_group - median(T_group))

assert E_phase <= E_phase_gate and GDR <= GDR_gate

X. Correspondence & Degeneracy to the Classical Framework
With K_s = K_t = 0, w_p = 1, and ΔZ_rad = 0, the stack reduces to classical RLC/telegrapher solutions; the added value here is explicit paths/arrival/weights/positive-real radiation plus a unified metrology → inversion → evidence → release chain.

XI. Cross-Chapter Pointers & Summary

• Dependencies: S20-*, S40-*, S50-*, Chapter 8, Chapter 12, Chapter 13, I30-*, M10-*, M20-*.
• Summary: This chapter integrates multi-scale simulation, explicit paths, kernel convolution, weight evolution, radiation correction, and statistical inversion into a single SimStack. With standard cases and mandatory record fields, it guarantees reproducibility, alignment, and falsifiability, closing design, measurement, and modeling under a common semantic and metrological layer.