37-EFT.WP.EDX.HighSpeed v1.0 | Chapter 11 — 3D-EM & Circuit Co-Simulation (I40-HF / Mx-*)

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Chapter 11 — 3D-EM & Circuit Co-Simulation (I40-HF / Mx-*)

I. Chapter Objectives & Structure

1. Objective: Establish a collaborative workflow between 3D-EM field simulation and circuit-level models; define I40-HF implementation interfaces and Mx-* inversion/evidence dialect to achieve consistent mapping, joint calibration, and release QA from 3D-EM ports/fields to Z_eft(omega), T_arr, w_{p,m}, and ΔZ_rad.
2. Structure: Symbols & domain → I40-HF (import/alignment/co-sim) → Mx-* (priors/likelihood/evidence) → Implementation & records → Falsifiability → 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. Symbols & Domain

• Frequency & ports: omega, S_EM(omega) (3D-EM output), Z_eft(omega), Znorm(omega), Z_c(omega).
• Fields & power: E(r,omega), H(r,omega), S(r,omega)=E×H, P_port=(1/2)Re{V·I*}.
• Paths/modes: gamma(ell), d ell, w_{p,m}(omega), modal basis M(omega).
• Radiation & leakage: ΔZ_rad(omega) (Re{ΔZ_rad}≥0), near/far-field envelopes |E_rad|/|H_rad|, I_CM(omega).
• Hard gates: check_dim = pass, passivity (Re{Z_eft} ≥ 0), KK_consistency = pass, two-dialect T_arr agreement.

I40-HF — 3D-EM Import, Alignment & Co-Simulation Interfaces

I40-HF-1 (EM artifact import)
em = em_import(sparams:S_EM, ports:EM_ports, mesh:EM_mesh, refplanes, meta)

• Requirements: record solver/version, mesh scale, port definitions/reference planes, simulation boundaries/absorbers; verify check_dim.

I40-HF-2 (Port/renorm alignment)
S_ren = em_port_align(em, Znorm(omega), T_mm?)

• Unify single-ended/mixed-mode port orientation and normalization; if mixed-mode, provide T_mm/Z0_mm and preserve power.

I40-HF-3 (Field→path/mode mapping)
binding_hf = em_field_to_path(em, layout, returns, rules)

• Extract {γ_p} and segment-level n_eff(seg) via dominant current/power-flow channels; produce initial weights Weights0.

I40-HF-4 (S→Z & radiation consistency)
Z_eft = map_S_to_Z(S_ren, Znorm(omega))

• If radiation enabled: form Z_base=Z_ref+ΔZ_T, compute ΔZ_rad=Z_eft−Z_base, and verify Re{ΔZ_rad}≥0 and K–K.

I40-HF-5 (EM–circuit co-simulation)
co_sim = cosimulate(em, circuit_netlist, binding_hf, options)

• Couple ports and recognize layout/returns; align baseline_id and Znorm(omega); evaluate KPIs (E_phase/GDR/T_group/ΔW).

Mx-* — Priors, Likelihood & Evidence (with 3D-EM)

Mx-1 (Priors)

• Geometry/material: n_eff(seg), sigma_eff(omega), Z_c,m(omega) with band-limited/smooth priors.
• Kernels/weights: half-normal amplitudes for K_s/K_t, log-uniform time constants; Dirichlet prior for w_{p,m} (Σ≤1).
• Sync/radiation: Δt_sync ~ N(0,σ^2); positive-real constrained prior for ΔZ_rad.

Mx-2 (Likelihood)

• Joint Gaussian in complex-impedance domain (whitened):
  L(data|θ) ∝ exp(−½Σ_ω[(Re ε)^T W (Re ε)+(Im ε)^T W (Im ε)]), with ε=Z_meas−Z_model(θ).
• Auxiliary terms: gates/penalties for E_phase/GDR/T_group; radiation match P_rad ≈ ½Re{ΔZ_rad}|I_port|^2.

Mx-3 (Evidence & comparison)

• Evidence logZ_evid (Laplace/nested sampling); models: M_classic, M_eft-min, M_eft-ms (multi-path/multi-mode).
• Thresholds: ΔlogZ > 5 strong, 2–5 moderate; enforce passivity/KK/check_dim.

Mx-4 (PPC & UQ)

• PPC: near-white residual spectrum; conserve power/reciprocity.
• UQ: propagate posteriors to Z_eft/T_arr/T_group/w_{p,m}/ΔZ_rad and acceptance KPIs.

III. Implementation & Records (minimum execution dialect)

• Required fields:
  S_EM, solver/version, EM_mesh{cell,order}, EM_ports{type,refplane}, Znorm(omega), T_mm/Z0_mm (if used),
  binding_ref (with {γ_p, segments{len_m,n_eff,layer,neigh}} and Weights0),
  Z_eft{real,imag}, argZ, Z_c(omega), arrival{form,gamma,measure,c_ref,Tarr,u_Tarr,delta_form},
  KPI{E_phase,GDR,T_group_s,ΔW}, (if enabled) ΔZ_rad and field summaries,
  qa_gates{check_dim,passivity,KK}, baseline_id, env_lock.
• Consistency checks: mesh convergence (two meshes differ ≤ gate), port-power closure, S→Z loop consistency, two-dialect T_arr agreement.

IV. Falsifiability Criteria (for I40-HF / Mx-*)

• J-HF-11-1 (Mesh & ports): If KPI shifts beyond uncertainty after mesh refinement/reference-plane tweaks, reject current port definition or mesh.
• J-HF-11-2 (S→Z & power): If Re{Z_eft} < 0 or K–K fails, or power is not conserved, reject normalization/mapping or port basis.
• J-HF-11-3 (Field→path mapping): If extracted path k_φ ≈ ΔT_arr conflicts with measurement, reject extraction rules or weight initials.
• J-HF-11-4 (Radiation equivalence): Re{ΔZ_rad} < 0 or no drop after sealing → reject radiation equivalence.
• J-HF-11-5 (Evidence): If M_classic outperforms M_eft-* (ΔlogZ persistently larger) with PPC pass, reject current EFT parameterization or priors.

V. Compliance Templates (copy-ready)

• 3D-EM co-simulation record (YAML)
• em_circuit_coupling:
• solver: {name:"HFSS", version:"2025.R1"} # example
• mesh: {cells: 3.2e6, order:"2nd", adapt_pass: 3}
• ports:
• - {id:"P1", type:"wave", refplane_mm: 2.0}
• - {id:"P2", type:"wave", refplane_mm: 2.0}
• sparams: "/artifacts/S_EM.s2p"
• Znorm_ohm: [50.0, 50.0]
• mixed_mode:
• enabled: true
• T_mm: "/cfg/T_mm.yaml"
• Z0_mm_ohm: [100.0, 25.0]
• binding_ref: "LAY2PATH-HF-0001"
• paths:
• - {id:"γ_main", segments:[{layer:"L3", len_m:0.010, n_eff:2.14, neigh:"GND_L2"}], weight_init:0.86}
• - {id:"γ_side", segments:[{layer:"L3", len_m:0.003, n_eff:2.38, neigh:"slot_L2"}], weight_init:0.14}
• 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
• delta_form: "n_over_c"
• mapping:
• Z_eft: {real:[...], imag:[...]}
• Zc_ohm: [...]
• radiation:
• enabled: true
• deltaZ_rad: {Re_ohm:[...], Im_ohm:[...]}
• fields: {E_rad_peak_dBuV_m:[...], I_CM_A:[...]}
• kpis:
• E_phase_rad: 0.043
• GDR_s: 1.8e-10
• T_group_s: [ ... ]
• ΔW: 0.17
• qa_gates: {check_dim:"pass", passivity:"pass", KK:"pass"}
• baseline_id: "BLSN-EDX-001"
• Co-simulation inversion flow (pseudocode)
• # 1) EM import & port alignment
• em = em_import(S_EM, EM_ports, EM_mesh, refplanes, meta)
• S_ren = em_port_align(em, Znorm(ω), T_mm)
• # 2) S→Z & radiation
• Z = map_S_to_Z(S_ren, Znorm(ω))
• Z_base = Z_ref + ΔZ_T
• ΔZ_rad = Z - Z_base
• # 3) Field→path/mode
• binding_hf = em_field_to_path(em, layout, returns, rules)
• assert passivity(Z) and KK_consistency(Z)
• # 4) Inference & evidence
• θ_map, post, logZ = invert(sim_handle, data=(Z, binding_hf), priors, sampler="NUTS")
• ppc = ppc_check(sim_handle, post)
• assert ppc.residual_white and ppc.qa.pass
• # 5) KPIs & gates
• phi = unwrap(arg(Z) - ω*Δt_sync)
• T_group = grad(phi, ω); E_phase = max_abs(phi - (ω*Tarr + φ0_opt))
• assert E_phase <= E_phase_gate and min(Re(Z)) >= 0.0

VI. Cross-Chapter Links & Closure

• Dependencies: Chapter 4 (S20-HF/S30-HF dispersion), Chapter 5 (S50-HF radiation), Chapter 6 (S40-HF modes/primitives), Chapter 8 (S↔Z mapping), Chapter 9 (M10-HF metrology), Chapter 10 (M20-HF falsification).
• Downstream: Chapter 12 (Layout & Process Rules — co-sim KPIs for acceptance), Chapter 14 (SimStack & cases — regression baselines), Chapter 16 (Design Protocol & Checklist — include evidence & PPC gates).