34-EFT.WP.Astro.Acceleration v1.0 | Chapter 12 Simulation & Benchmarks (SimStack)

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Chapter 12 Simulation & Benchmarks (SimStack)

I. Abstract & Scope
This chapter defines the unified architecture and executable workflows of the simulation-and-benchmark stack (SimStack), M70-*, covering: geometry & channel drivers, spectrum formation & transport, instrument/noise models, dual-form time-of-arrival (ToA) path corrections, dataset/model/pipeline cards and benchmark suites, regression & acceptance metrics, and reproducible deliverables. All equations and symbols use English notation wrapped in backticks, SI units, and parentheses for any composite operators; any ToA quantity must state path gamma(ell) and measure d ell.

II. Dependencies & References

• Unified symbols & units: Chapter 2 Tab. 2-1 and P12-*.
• Kinematics & channels: Chapter 3 S20-; reconnection & shear: Chapter 4 S30-, Chapter 5 S40-; comparators: Chapter 6 S45-.
• Spectrum formation & transport: Chapter 7 S50-, Chapter 8 S52-.
• GRB/FRB specifics: Chapter 10 M62-, Chapter 11 M64- (timebase, dynamic spectrum, polarization, dual-form ToA).

III. Normative Anchors (added in this chapter, M70-*)

• M70-0 (Config & Seed): simulation config SimCfg must include {sim_id, seed, geometry, channel, transport, instrument, path_correction, timebase, units, see}; all stochastic processes are fixed by seed and logged as rng_state.
• M70-1 (Geometry Layer): reconnection geometry {L_sheet, delta_sheet, chi_open, u_in, u_out, T_fil}; shear field {S, e_grad, L_grad, delta_shear, Delta_u}; evaluate in F_sheet / F_shear, map to F_flow.
• M70-2 (Channel Drivers): A_rec(E,t) = A_rec^0(t) * f_rec(E; θ_rec), A_shear(E,t) = A_sh^0(t) * f_sh(E; θ_sh); compose A_acc(E,t) = A_rec + A_shear.
• M70-3 (Spectrum Formation): per Chapter 7 S50-* compute N(E,t) and alpha_loc(E,t); in locally constant bands use the closed approximation alpha_loc ≈ 1 + ( 1/tau_esc + 1/tau_loss ) / A_acc.
• M70-4 (Transport & Losses): per Chapter 8 S52-* solve {D(E), tau_esc(E), A_loss(E)} to obtain n(E,r,t) and Phi_obs(E,t).
• M70-5 (Instrument & Noise Models): response kernel R_inst(E→E'), energy dispersion, PSF/beam, effective area/gain; noise includes Poisson counting and readout/baseline terms; polarization errors injected via covariance on Stokes {Q,U,V}.
• M70-6 (ToA Path Corrections, Dual Forms): record both ToA forms with delta_form:
  T_arr = ( 1 / c_ref ) * ( ∫_{gamma(ell)} n_eff d ell ) and T_arr = ( ∫_{gamma(ell)} ( n_eff / c_ref ) d ell ).
• M70-7 (Cards & Benchmarks): generate dataset/model/pipeline cards; benchmark families {CosmicRay, GRB, FRB} at scales {S, M, L} and publish with fixed seed.
• M70-8 (Acceptance Metrics & Regression): define spectral & timing consistency metrics, ToA residuals, polarization angle/rotation residuals, channel-weight recovery, dimensional/unit checks; provide automated regression scripts.
• M70-9 (Deliverables): output {SimCfg, rng_state, products, metrics, masks, delta_form, repro_bundle}, where repro_bundle contains version pins, dependencies, and minimal run scripts.

IV. Body Structure

I. SimStack Architecture

• Layers: Geometry → Channel → Spectrum → Transport → Observation → Instrument/Noise → Packaging.
• Data flow: A_rec/A_shear → A_acc → {tau_esc, A_loss} → N(E,t) → Phi_obs(E,t); GRB/FRB branches additionally include {t_src} and ToA corrections.
• Unified interface: all layers initialize from immutable SimCfg; intermediates are unit-bearing structured arrays with see: anchors.

II. Key Equations & Derivations (S-series)
No new minimal equations are introduced here; use S-series from Chapters 4–8 and chapter-specific forms from Chapters 10–11. The unified synthetic observation mapping is
Phi_obs(E,t) = C_geom(t) * C_prop(E,t) * N(E,t) ⊗ R_inst(E→E'),
with path integrals ∫_{gamma(ell)} (…) d ell included when required.

III. Methods & Flows (M-series)

1. M70-1 (Geometry Generation):
   • Reconnection: sample {L_sheet, delta_sheet, chi_open, u_in, u_out, T_fil} under Chapter 4 S30-* constraints.
   • Shear: compute S and sigma_shear = ( 0.5 * Tr(S^2) )^{1/2} from velocity fields under Chapter 5 S40-*.
2. M70-2 (Channel Time Series):
   • Use piecewise splines or pulse trains for A_rec^0(t)/A_sh^0(t); shape functions f_rec/f_sh governed by energy-band params {E_cut, p}.
   • Produce A_acc(E,t) and tau_acc(E,t) = 1 / A_acc(E,t).
3. M70-3 (Spectrum Solver):
   In each time window Δt_k, compute N(E,t) via Chapter 7 S50-* semi-closed forms; use flux-conservative numerics when needed.
4. M70-4 (Transport & Losses):
   • One-zone: tau_esc(E) = L_esc^2 / ( kappa_esc D(E) ), A_loss(E) = b_loss / E.
   • Multi-zone: compose series/parallel equivalents per S52-10.
5. M70-5 (Instrument Response & Noise):
   • High-energy: convolve Phi(E,t) with R_inst, bin by exposure; sample events with Poisson statistics.
   • Radio: generate dynamic spectrum I(ν,t) per channelization/dedispersion conventions, add out-of-band leakage and baseline drifts.
6. M70-6 (Dual-Form ToA & Paths):
   Apply both T_arr forms to align t_src = ( t_obs − t0 − T_arr ) / (1+z); record delta_form and export residuals.
7. M70-7 (Benchmark Suite Generation):
   • Define {S, M, L} levels: sample size, energy windows, time resolution, SNR, and systematics ratios.
   • Produce fixed-seed reference products (truth vs observed) for regression.
8. M70-8 (Acceptance & Regression):
   Run predefined scripts to compute metrics (see Tab. 12-4) and compare to thresholds; emit pass/fail and diffs.
9. M70-9 (Packaging Deliverables):
   Write products/ (synthetic spectra, lightcurves, dynamic spectra, polarization, ToA records), metrics.json, masks/ (dominant bands), delta_form.log, repro/ (env & scripts).

IV. Cross-References within/beyond this Volume

• Channels & kinematics: Chapters 3–5 (A_acc = A_rec + A_shear).
• Comparators & dominance: Chapter 6 (eta_dom(E,t) masks).
• Spectrum & transport: Chapters 7–8 (N(E,t), Phi(E,t), D(E), A_loss(E), tau_esc(E)).
• GRB/FRB: Chapters 10–11 (t_src, E_pk(t), tau_lag, DM/RM/tau_scat, dual-form ToA).

V. Validation, Criteria & Counterexamples

1. Positive criteria:
   • Spectral consistency: SpecMAE = mean(|Phi_sim − Phi_ref|) / mean(Phi_ref) ≤ ε_spec.
   • Timing consistency: RMS_Δt ≤ ε_time; relative error of E_pk(t) below threshold.
   • Polarization & RM: linear PA(λ) vs λ^2 with no systematic residual drifts.
   • ToA: dual-form residual ΔToA = |T_arr^A − T_arr^B| below threshold in the nominal band and consistent with the path model.
2. Negative criteria:
   • Zeroing or mismatching any layer (geometry/channel/transport/instrument) does not reduce evidence.
   • Dimensional audit fails (units not closed).
   • Regression against reference degrades beyond thresholds for key metrics.
3. Contrasts:
   {reconnection only, shear only, mixed} channels; {one-zone, multi-zone} transport; {ideal instrument, realistic response}; ToA {Form A, Form B} in parallel.

VI. Summary & Handoff
This chapter operationalizes SimStack via M70-*, delivering a fully reproducible pipeline from channel → spectrum → transport → observation with instrument and dual-form ToA corrections, plus benchmarks and regression machinery. The next chapter (Chapter 13) unifies inference and falsification workflows and their acceptance.

V. Figures & Tables (this chapter)

• Tab. 12-1 Components & Interfaces

• Tab. 12-2 Required SimCfg Fields (example)

• Tab. 12-3 Benchmark Task List (excerpt)

• Tab. 12-4 Acceptance Metrics & Thresholds (examples)

• Tab. 12-5 Dataset-Card Field Templates