38-EFT.WP.EDX.EMI v1.0 | Chapter 3 — Axioms & Physical Picture (P10-EMI)

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Chapter 3 — Axioms & Physical Picture (P10-EMI)

I. Chapter Objectives & Prerequisites

1. Objective: Present the minimal axiom set P10-EMI-* for EDX.EMI, give a tension-landscape physical picture for emission/immunity, and unify port–path–field under ΔZ_rad(omega) into testable statements and engineering records, supporting S20-EMI / S30-EMI / S40-EMI / I40-EMI / M10-EMI.
2. Shared time-of-arrival dialect (equivalent; 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 )
3. Frequency variable omega; key equalities check_dim = pass; hard gates: passivity (Re{Z_eft} ≥ 0), KK_consistency = pass, two-dialect T_arr agreement.

II. Physical Picture (Port–Path–Field Coordination)

• Leakage-channel dominance: gaps/apertures, open returns, long stubs, and mismatched transitions activate leakage paths γ_side, raising w_{side}(omega) and adding a positive-real increment ΔZ_rad(omega) at the port.
• Power consistency: radiated power is represented by port quantities:
  P_rad(omega) ≈ (1/2) · Re{ΔZ_rad(omega)} · |I_port(omega)|^2 ,
  trending consistently with |E_rad|/|H_rad|.
• Immunity reverse mapping: external E_ext/H_ext or cable/port injection redistributes w_{p,m}(omega), producing calibrated shifts in Δarg Z and T_arr.

III. Axioms (P10-EMI-*)

• P10-EMI-1 (Positive-real radiation channel)
  Statement: When geometric/shielding discontinuities activate leakage γ_side,
  Z_eft(omega) = Z_ref(omega) + ΔZ_T(omega) + ΔZ_rad(omega),
  with Re{ΔZ_rad(omega)} ≥ 0 and K–K consistency; after sealing/closing, Re{ΔZ_rad} decreases monotonically.
  Domain/Constraints: Consistent port normalization (Znorm(omega)/mixed-mode); explicit path/measure.
  Falsifiability: If Re{ΔZ_rad} < 0 or no decrease after sealing, reject the channel classification or mapping.
• P10-EMI-2 (Port–field power equivalence)
  Statement:
  P_rad(omega) ≈ (1/2) · Re{ΔZ_rad(omega)} · |I_port(omega)|^2 ,
  monotonic with |E_rad|/|H_rad|.
  Domain/Constraints: detector ∈ {pk,qpk,avg}, IF bandwidth/time constants recorded; probe/antenna factors versioned.
  Falsifiability: If port-estimated P_rad diverges from field envelopes, reject the equivalence.
• P10-EMI-3 (Path–weight coupling)
  Statement: Leakage weights co-vary with radiation correction: w_{side}(omega) ↑ ⇒ Re{ΔZ_rad}(omega) ↑, raising
  ΔW = Σ_{p,m}|w_{p,m}(ω2)−w_{p,m}(ω1)|; closing returns/sealing reduces both.
  Domain/Constraints: Σ_{p,m} w_{p,m} ≤ 1; path/mode sets consistent with binding_ref.
  Falsifiability: If ΔW trends disagree with Re{ΔZ_rad}, reject the path–weight model or annotations.
• P10-EMI-4 (Immunity reverse consistency)
  Statement: Under fixed injection, slope shifts in Δarg Z and drifts in T_arr are explained linearly/monotonically by redistributions in w_{p,m}.
  Domain/Constraints: Mixed-mode normalization first; preserve power/reciprocity before back-projection to SE domain.
  Falsifiability: If Δarg Z/T_group shifts contradict weight predictions, reject injection records or normalization.
• P10-EMI-5 (Two-dialect agreement)
  Statement: For the same gamma(ell) and n_eff,
  |T_arr^{(n_over_c)} − T_arr^{(n_over_c_times_n)}| ≤ u(T_arr).
  Falsifiability: If exceeded, reject release or audit paths/units/records.

IV. Engineering Corollaries & Minimal Rules

• Seal-first strategy: prioritize high-sigma_seam, open returns, and long stubs to lower Re{ΔZ_rad} and ΔW.
• Mixed-mode first: normalize DM/CM before back-projection; ensure S↔Z loop passes passivity/K–K.
• In-window evaluation: compute KPIs (E_phase/GDR) and power equivalence inside the window; use energy composition outside.

V. Implementation & Records (snippets)

• Phase correction: arg Z_corr(omega) = arg Z_raw(omega) − ( omega · Δt_sync ).
• Record template:
• emi_record:
• band_GHz: [f_min, f_max]
• normalization: {Znorm_ohm:[50.0,50.0], mixed_mode:{enabled:true, T_mm:"/cfg/T_mm.yaml", Z0_mm_ohm:[100,25]}}
• arrival: {form:"n_over_c", gamma:"explicit", measure:"d_ell", c_ref:299792458.0, Tarr_s:..., u_Tarr_s:..., delta_form:"n_over_c"}
• geometry: {seams:{sigma_seam_S:0.12, locations:["J3_gap"]}, stubs:{max_len_mm:3.5}}
• impedance: {Z_eft:{real:[...], imag:[...]}, deltaZ_rad:{Re_ohm:[...], Im_ohm:[...]}} # Re ≥ 0
• fields: {E_rad_peak_dBuV_m:[...], H_rad_peak_dBA_m:[...], I_CM_A:[...]}
• weights: {w_main:[...], w_side:[...], ΔW: 0.19}
• qa_gates: {check_dim:"pass", passivity:"pass", KK:"pass"}

VI. Baselines & Reference Fixtures (reproducible)

• Seam/aperture board (sealable): verify Re{ΔZ_rad} ≥ 0 and its decrease after sealing; fields and I_CM decrease together.
• Return bridge/stub board: verify w_side↑ → ΔZ_rad↑ → fields↑ and inverse after closing.
• Mixed-mode/cable jigs: verify DM/CM normalization and consistency of I_CM with ΔZ_rad/ΔW trends.
• Ship with dataset_card/pipeline_card/env_lock and reference outputs for regression and release gates.

VII. Falsifiability (chapter-specific)

• J-EMI-1: Re{ΔZ_rad} < 0 or K–K fails → reject P10-EMI-1 or normalization/mapping.
• J-EMI-2: After sealing, if Re{ΔZ_rad} and |E_rad|/|I_CM| don’t drop together → reject channel/geometry records.
• J-EMI-3: If ΔW trend mismatches Re{ΔZ_rad} → reject path–weight model.
• J-EMI-4: Under injection, if Δarg Z/T_group shifts contradict weight predictions → reject immunity consistency.
• J-EMI-5: Two-dialect T_arr difference beyond u(T_arr) → reject release.

VIII. Cross-Chapter Links & Closure

• Dependencies: Chapter 2 (Terms & Symbols), EDX.HighSpeed Chapter 13 (EMI/EMC Coordination), Chapter 8 (S↔Z Mapping), Chapter 7 (KPIs).
• Downstream: Chapter 4 (Minimal Equations & Equivalents), Chapter 5 (Seams & Shielding Continuity), Chapters 6–8 (Cables/Injection & Mapping), Chapter 9 (Metrology Chain), Chapter 10 (Falsification).