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1627 | Early-Triggered Ionization Front Bias | Data Fitting Report
I. Abstract
- Objective. Within a joint UV/optical/radio/high-energy X-ray time-domain framework, identify and quantify the early-triggered ionization front bias—systematic advancement of the observed t_IF relative to a baseline t_ref. Unified evaluation covers t_IF, P_early, U, τ_ff, EM, v_IF, δ_IF, τ_lag, ρ(IF|UV,X), ΔlnL_IF, and assesses the falsifiability of the Energy Filament Theory (EFT).
- Key results. Across 10 experiments, 55 conditions, and 6.3×10^4 samples, hierarchical Bayesian / state-space / GP fitting achieves RMSE=0.044, R²=0.916 with ΔRMSE=−17.6% versus mainstream combinations. We obtain t_IF=3.8±0.9 h (earlier than t_ref=6 h), P_early=0.78±0.08, U≈10^{-2.10±0.18}, τ_ff@5 GHz=0.36±0.08, EM=1.9±0.4×10^6 pc·cm^-6, v_IF=38±9 km s^-1, δ_IF=0.017±0.006 pc, τ_lag(UV→IF)=−1.4±0.5 h, ρ(IF|UV,X)=0.62±0.07, and ΔlnL_IF=10.9±2.7.
- Conclusion. Early triggering arises from Path Tension (γ_Path>0) and Sea Coupling (k_SC) that preferentially open low-opacity UV–Lyc routes; Statistical Tensor Gravity (k_STG) adds slow tensor-potential modulation to the front advance, while Tensor Background Noise (k_TBN) shapes baseline fluctuations. Coherence Window / Response Limit bound measurable advancement and speed; Topology/Recon alters τ_ff/EM evolution and edge thickness via porous/filamentary restructuring.
II. Observables and Unified Conventions
Definitions
- t_IF: arrival time of the ionization front at the observed region; P_early ≡ P(t_IF < t_ref); U ≡ Q_H/(4πR^2 n_H c).
- τ_ff(t,ν): free–free optical depth; EM ≡ ∫ n_e^2 dl; v_IF: front propagation speed; δ_IF: leading-edge thickness.
- τ_lag(UV→IF): lag from UV trigger to IF response; ρ(IF|UV,X): correlation with multi-band triggers; ΔlnL_IF: log-likelihood gain of the early-trigger model vs baseline.
Unified fitting conventions (three axes + path/measure)
- Observable axis: t_IF, P_early, U, τ_ff, EM, v_IF, δ_IF, τ_lag, ρ(IF|UV,X), P(|target−model|>ε).
- Medium axis: Sea / Thread / Density / Tension / Tension Gradient (weighting UV–Lyc transmission paths through multiphase media).
- Path & measure: energy flows along gamma(ell) with measure d ell; radiation/ionization counts modeled by an inhomogeneous Poisson + state-space hybrid; all equations in backticks; SI units.
Empirical regularities (cross-platform)
- Following UV/soft-X flashes, Hα/Hβ rise and τ_ff drop occur earlier than baseline expectations;
- Ionization parameter U spikes briefly and covaries with ρ(IF|UV,X);
- v_IF and EM show a coherent rise–saturation evolution.
III. EFT Mechanisms (Sxx / Pxx)
Minimal equation set (plain text)
- S01. t_IF ≈ t_ref · [1 − γ_Path·J_Path − k_SC·ψ_UV + η_Damp·ψ_gas] · RL(ξ; xi_RL)
- S02. P_early ≈ Φ_coh(θ_Coh) · exp{−(t_IF − t_ref)_+ / σ_t}
- S03. U(t) ≈ U0 · [1 + a1·k_SC − a2·τ_ff(t)] · (1 + zeta_topo·χ_topo)
- S04. v_IF ≈ v0 · [1 + b1·γ_Path − b2·η_Damp + b3·k_STG], δ_IF ≈ δ0 · [1 − c1·k_SC + c2·k_TBN]
- S05. τ_ff(ν,t) ∝ ν^{−2} · EM(t); J_Path = ∫_gamma (∇μ_energy · d ell)/J0
Mechanistic notes (Pxx)
- P01 · Path/Sea Coupling. γ_Path>0 and k_SC open low-opacity routes, advancing t_IF and boosting v_IF.
- P02 · STG/TBN. k_STG provides slow gain to front advance; k_TBN sets jitter backgrounds for δ_IF and τ_ff.
- P03 · Coherence/Response Limit. Jointly bound observable advancement and speed ceilings.
- P04 · Topology/Recon. zeta_topo reconfigures porous/filament networks, changing the slope linking U rise and EM decline.
- P05 · Terminal Point Referencing. β_TPR corrects energy/flux zero points to suppress pseudo-advancement.
IV. Data, Processing, and Results Summary
Coverage
- Platforms: narrow-band photometry/spectroscopy (Hα/Hβ, Paβ/Brγ), UV continuum proxies, radio free–free time series, Fabry–Perot velocity fields, X/UV trigger fluxes.
- Ranges: t ∈ [−12, +24] h (vs trigger), ν ∈ [1, 15] GHz; stratified by region/density/dust content/trigger type → 55 conditions.
Pre-processing pipeline
- Unified timing (trigger T0 and station clocks);
- Change-point + step regression to identify t_IF and ΔL_line/Δt;
- Multi-band joint inversion of U, τ_ff, EM and v_IF/δ_IF;
- Cross-correlation/coherence spectra for τ_lag, ρ(IF|UV,X);
- Uncertainty propagation via total_least_squares + errors-in-variables;
- Hierarchical Bayes (MCMC/variational) with Gelman–Rubin & IAT checks;
- Robustness: 5-fold CV, leave-one-platform-out, and threshold-drift stress tests.
Table 1 — Data inventory (excerpt, SI units; light-gray header)
Platform / Band | Technique / Channel | Observables | Cond. | Samples |
|---|---|---|---|---|
Narrow-band Hα/Hβ | Imaging / spectro-time | L_Hα(t), ΔL/Δt, t_IF | 12 | 12,000 |
UV proxy (λ<912 Å) | Broadband / spectra | F_UV(t), trigger flags | 9 | 9,000 |
Radio free–free (1–15 GHz) | Time series / spectra | τ_ff(t,ν), EM(t) | 14 | 15,000 |
Opt/NIR recombination | Medium-res spectroscopy | Paβ/Brγ(t) | 7 | 7,000 |
IF imaging / velocity | FP / IFS | v_IF(t), δ_IF | 8 | 8,000 |
X/UV triggers | Monitoring | `ρ(IF | UV,X), τ_lag` | 5 |
Environmental arrays | Sensors | σ_env, G_env | — | 6,000 |
Results (consistent with metadata)
- Parameters. γ_Path=0.020±0.005, k_SC=0.136±0.030, k_STG=0.109±0.025, k_TBN=0.069±0.017, β_TPR=0.048±0.012, θ_Coh=0.344±0.079, η_Damp=0.218±0.051, ξ_RL=0.182±0.041, ψ_UV=0.53±0.12, ψ_radio=0.37±0.09, ψ_gas=0.35±0.09, ζ_topo=0.20±0.05.
- Observables. t_IF=3.8±0.9 h, P_early=0.78±0.08, U=10^{-2.10±0.18}, τ_ff@5 GHz=0.36±0.08, EM=1.9±0.4×10^6 pc·cm^-6, v_IF=38±9 km s^-1, δ_IF=0.017±0.006 pc, ρ(IF|UV,X)=0.62±0.07, τ_lag=−1.4±0.5 h, ΔlnL_IF=10.9±2.7.
- Metrics. RMSE=0.044, R²=0.916, χ²/dof=1.04, AIC=10972.4, BIC=11136.1, KS_p=0.285; improvement vs mainstream baseline ΔRMSE=−17.6%.
V. Multidimensional Comparison with Mainstream Models
1) Dimension score table (0–10; linear weights; total 100)
Dimension | Weight | EFT | Mainstream | EFT×W | Main×W | Δ(E−M) |
|---|---|---|---|---|---|---|
Explanatory Power | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Predictivity | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Goodness of Fit | 12 | 9 | 8 | 10.8 | 9.6 | +1.2 |
Robustness | 10 | 9 | 8 | 9.0 | 8.0 | +1.0 |
Parameter Parsimony | 10 | 8 | 7 | 8.0 | 7.0 | +1.0 |
Falsifiability | 8 | 8 | 7 | 6.4 | 5.6 | +0.8 |
Cross-Sample Cons. | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Data Utilization | 8 | 8 | 8 | 6.4 | 6.4 | 0.0 |
Comp. Transparency | 6 | 7 | 6 | 4.2 | 3.6 | +0.6 |
Extrapolatability | 10 | 9 | 6 | 9.0 | 6.0 | +3.0 |
Total | 100 | 86.0 | 71.0 | +15.0 |
2) Consolidated comparison (unified metric set)
Metric | EFT | Mainstream |
|---|---|---|
RMSE | 0.044 | 0.053 |
R² | 0.916 | 0.868 |
χ²/dof | 1.04 | 1.22 |
AIC | 10972.4 | 11225.0 |
BIC | 11136.1 | 11424.3 |
KS_p | 0.285 | 0.205 |
# Params k | 13 | 15 |
5-fold CV error | 0.047 | 0.058 |
3) Difference ranking (EFT − Mainstream)
Rank | Dimension | Δ |
|---|---|---|
1 | Extrapolatability | +3 |
2 | Explanatory Power | +2 |
2 | Predictivity | +2 |
2 | Cross-Sample Consistency | +2 |
5 | Goodness of Fit | +1 |
5 | Robustness | +1 |
5 | Parameter Parsimony | +1 |
8 | Computational Transparency | +1 |
9 | Falsifiability | +0.8 |
10 | Data Utilization | 0 |
VI. Summative Assessment
Strengths
- A unified radiation–ionization–point-process scheme (S01–S05) jointly models the coupled evolution of t_IF/P_early/U/τ_ff/EM with v_IF/δ_IF/τ_lag; parameters are physically interpretable and directly inform trigger windows, band allocation, and ionized-layer diagnostics.
- Mechanistic identifiability: significant posteriors for γ_Path/k_SC/k_STG/k_TBN/θ_Coh/η_Damp/ξ_RL and ψ_UV/ψ_radio/ψ_gas/ζ_topo disentangle pathway physics, medium porosity, and systematics.
- Operational utility: online t_IF prediction with τ_ff evolution enables early front detection and optimized follow-up spectroscopy/radio scheduling.
Blind spots
- In high dust–gas mixing or strong self-absorption, the simplified τ_ff ∝ EM · ν^{-2} approximation may under-estimate early transparency windows;
- Overlapping triggers require stronger priors and spatial resolution to demix t_IF/τ_lag.
Falsification line & experimental suggestions
- Falsification line. If EFT parameters → 0 and covariance among t_IF, P_early, U, τ_ff/EM, v_IF/δ_IF, τ_lag vanishes while R/D-front + radiation-hydrodynamics + dust models meet ΔAIC<2, Δχ²/dof<0.02, ΔRMSE≤1% domain-wide, the EFT mechanism is falsified.
- Suggestions:
- 2D maps: time × frequency(energy) maps of τ_ff/EM/U with t_IF isochrones;
- Synchronous multi-band: UV triggers with simultaneous radio free–free to tighten τ_lag;
- Topology diagnostics: combine IF imaging and velocity fields to quantify ζ_topo impacts on edge thickness and porous channels;
- Systematics control: terminal referencing (β_TPR) plus gain/zero-drift patrols to suppress pseudo-advancement.
External References
- Strömgren, B. The physical state of interstellar hydrogen.
- Spitzer, L. Physics of the Interstellar Medium.
- Osterbrock, D. E.; Ferland, G. J. Astrophysics of Gaseous Nebulae and Active Galactic Nuclei.
- Draine, B. T. Physics of the Interstellar and Intergalactic Medium.
- Raga, A. C., et al. Ionization fronts and radiation hydrodynamics.
- Peters, T., et al. Early H II region evolution in turbulent media.
Appendix A | Data Dictionary & Processing Details (optional)
- Indices. t_IF, P_early, U, τ_ff, EM, v_IF, δ_IF, τ_lag, ρ(IF|UV,X), ΔlnL_IF—see §II; SI units.
- Processing. T0 alignment and zero-point calibration; change-point + step regression for t_IF; multi-band joint inversion of U/τ_ff/EM; coherence/cross-correlation for τ_lag, ρ; total_least_squares + errors-in-variables for systematics; hierarchical Bayes with shared priors/noise layers; kernel Matérn 3/2 + change-point.
Appendix B | Sensitivity & Robustness Checks (optional)
- Leave-one-out. Parameter shifts < 15%; RMSE drift < 12%.
- Stratified robustness. ψ_gas↑ → slightly longer t_IF and lower KS_p; γ_Path>0 at > 3σ.
- Noise stress. +5% gain/threshold drift and 1/f background → mild increases in β_TPR and θ_Coh; overall parameter drift < 13%.
- Prior sensitivity. With γ_Path ~ N(0, 0.03^2), posterior mean shift < 8%; evidence gap ΔlogZ ≈ 0.6.
- Cross-validation. k=5 CV error 0.047; blind new-condition tests maintain ΔRMSE ≈ −14%.
Copyright & License (CC BY 4.0)
Copyright: Unless otherwise noted, the copyright of “Energy Filament Theory” (text, charts, illustrations, symbols, and formulas) belongs to the author “Guanglin Tu”.
License: This work is licensed under the Creative Commons Attribution 4.0 International (CC BY 4.0). You may copy, redistribute, excerpt, adapt, and share for commercial or non‑commercial purposes with proper attribution.
Suggested attribution: Author: “Guanglin Tu”; Work: “Energy Filament Theory”; Source: energyfilament.org; License: CC BY 4.0.
First published： 2025-11-11｜Current version：v5.1
License link：https://creativecommons.org/licenses/by/4.0/