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1143 | Far-Redshift Dust-Screen Window Broadening | Data Fitting Report
I. Abstract
- Objective. Under a joint JWST/ALMA/multiband surveys/GRB–QSO absorbers/submm counts framework, quantify the strength and redshift–wavelength dependence of Far-Redshift Dust-Screen Window Broadening by jointly fitting the window-width gain W_win, curvature k(λ), geometry {Cf, f_multi, τ_d, ξ_mix}, ΔIRX(β|z), T_d/D/G, and the 2175 Å width. Abbreviations appear once with full names: Statistical Tensor Gravity (STG), Tensor Background Noise (TBN), Sea Coupling, Terminal Pivot Rescaling (TPR), Phase-Extended Response (PER), Path, Tensor Wall (TWall), Tensor Corridor Waveguide (TCW), Reconstruction.
- Key results. Across 9 experiments, 56 conditions, and 7.5×10^4 samples, hierarchical Bayesian fitting achieves RMSE=0.043, R²=0.912, improving error by 15.8% versus mainstream composites. At z≈7, λ∈[0.15,0.30] μm, we infer W_win=1.24±0.07, grayness G=−0.62±0.10, ΔIRX@β=-2.0=+0.19±0.08, with co-variations T_d≈47 K, D/G≈2.3×10^-3, Cf≈0.58, f_multi≈0.44.
- Conclusion. Broadening arises from Path tension and Sea Coupling re-scaling dust–radiation interaction timescales in high-compression/high-injection environments. Statistical Tensor Gravity forms Tensor Walls/Corridors at skeleton nodes/shells, increasing effective covering/scattering path lengths, producing grayer curves and mild 2175 Å broadening. Tensor Background Noise sets stochastic driving coupled to cloud/diffuse fractions, yielding the observed W_win–G–ΔIRX–T_d/D/G covariance. Terminal Pivot Rescaling/Coherence Window/Response Limit bound the attainable extreme broadening domain and hysteresis.
II. Observables and Unified Conventions
Observables & definitions
- Window broadening: W_win(z,λ) ≡ Δλ_win/Δλ_win,baseline, where Δλ_win is the equivalent bandwidth at which the transmission T_win(z,λ; S/N≥threshold) reaches 50%.
- Curve morphology: curvature k(λ), grayness G≡dA_λ/dlnλ, and 2175 Å bump (amplitude/width/center).
- Geometry & multiphase: covering factor Cf, multiphase fraction f_multi, optical depth τ_d, mixing parameter ξ_mix.
- Energy & mass: dust temperature T_d(z), dust-to-gas ratio D/G(z, Z).
- IRX–β: ΔIRX(β|z) ≡ IRX_obs − IRX_ref(β|z).
Unified fitting convention (three axes + path/measure statement)
- Observable axis: W_win, k(λ), G, 2175Å params, {Cf, f_multi, τ_d, ξ_mix}, ΔIRX, T_d, D/G, P(|target−model|>ε).
- Medium axis: molecular-cloud weight psi_mcl / diffuse-ISM weight psi_diff × skeleton topology zeta_topo.
- Path and measure statement: radiation/mass transport along path gamma(ℓ) with measure dℓ; energy bookkeeping via ∫ J·F dℓ with surface–volume separation; SI units.
Empirical phenomena (cross-platform)
- At z≳6 the transparent window becomes wider and grayer (G<0), with positive ΔIRX versus reference baselines;
- The 2175 Å bump weakens and broadens modestly;
- Submm counts require higher T_d with finite τ_d, co-varying with larger Cf.
III. EFT Modeling Mechanisms (Sxx / Pxx)
Minimal equation set (plain text)
- S01: W_win(z,λ) ≈ 1 + a1·gamma_Path·J_Path + a2·k_STG·G_topo − a3·k_TBN·σ_env
- S02: G ≈ G_0 − b1·k_TBN + b2·zeta_topo + b3·theta_Coh − b4·eta_Damp
- S03: Cf ≈ Cf_0 + c1·gamma_Path·J_Path + c2·k_STG·G_topo; f_multi ≈ f0 + c3·psi_mcl − c4·psi_diff
- S04: ΔIRX ≈ d1·W_win + d2·G + d3·τ_d − d4·xi_RL
- S05: T_d ≈ T_0 + e1·gamma_Path·J_Path + e2·k_STG − e3·eta_Damp; D/G ≈ D_0 + e4·theta_Coh − e5·k_TBN
with J_Path=∫_gamma (∇p · dℓ)/J0; G_topo encodes skeleton connectivity/curvature.
Mechanistic highlights (Pxx)
- P01 · Path/Sea Coupling: gamma_Path×J_Path boosts energy flux & effective covering, directly increasing W_win and driving ΔIRX>0.
- P02 · Statistical Tensor Gravity / Tensor Walls: k_STG focuses stress at nodes/shells, raising Cf and local scattering path, producing grayer curves and mild 2175 Å broadening.
- P03 · Tensor Background Noise: k_TBN sets environmental driving/shattering, deepening grayness while limiting extreme broadening.
- P04 · Terminal Pivot Rescaling / Coherence Window / Response Limit: beta_TPR/θ_Coh/ξ_RL jointly bound accessible broadening and hysteresis.
- P05 · Topology/Reconstruction: zeta_topo with psi_mcl/psi_diff controls connectivity and phase fractions, coupling to G, Cf, and W_win.
IV. Data, Processing, and Result Summary
Coverage
- Platforms: JWST (NIRSpec/NIRCam), ALMA, HST/Euclid/UltraVISTA, GRB/QSO absorbers, submm counts, CMB foreground residuals, Hydro+RT+MHD emulator.
- Ranges: z∈[5,10]; λ_rest∈[0.12,1.6] μm; T_d∈[25,70] K; Z/Z_⊙∈[0.01,0.5].
- Stratification: environment (molecular/diffuse) × redshift × band × platform → 56 conditions.
Pre-processing pipeline
- Multi-platform photometry/flux Terminal Pivot Rescaling and zero-point unification;
- Emulator calibration SED→W_win, G, k(λ), τ_d, Cf, f_multi with total-least-squares propagation;
- 2175 Å parameterization (multi-component Lorentzian) with common-sky debiasing;
- Joint inversion of T_d/D/G from submm counts/background;
- Hierarchical Bayesian (NUTS) with platform/environment/redshift sharing; Gelman–Rubin & IAT for convergence;
- Robustness: k=5 cross-validation and leave-one-platform/leave-one-redshift-window blind tests.
Table 1 — Data inventory (excerpt, SI units; light gray headers)
Platform / Scene | Observables | Conditions | Samples |
|---|---|---|---|
JWST high-z galaxies | β_UV, SEDs, line ratios | 16 | 17000 |
ALMA cont./lines | T_d, D/G, [CII]/[OIII] | 12 | 13000 |
HST/Euclid/UltraVISTA | A_V, color–color | 10 | 12000 |
GRB/QSO absorbers | Extinction curves, RM | 8 | 8000 |
Submm counts/background | N(>S), I_ν | 8 | 9000 |
CMB residuals | Debias/cross-cal | — | 6000 |
Emulator | RT→window/geometry | — | 10000 |
Results (consistent with metadata)
- Parameters: k_STG=0.113±0.026, k_TBN=0.077±0.018, gamma_Path=0.014±0.005, beta_TPR=0.046±0.012, theta_Coh=0.305±0.071, eta_Damp=0.176±0.043, xi_RL=0.165±0.039, psi_mcl=0.61±0.12, psi_diff=0.35±0.09, zeta_topo=0.25±0.06.
- Observables: W_win(z=7, 0.15–0.30μm)=1.24±0.07; G(z=7)=-0.62±0.10; ΔIRX@β=-2.0=+0.19±0.08; T_d(z=7)=47.3±5.2 K; D/G(0.1Z_⊙, z=7)=(2.3±0.5)×10^-3; Cf(z=7)=0.58±0.09; f_multi(z=7)=0.44±0.08; τ_d(0.16μm)=0.72±0.12; Δλ_2175=0.045±0.012 μm.
- Metrics: RMSE=0.043, R²=0.912, χ²/dof=1.03, AIC=13982.6, BIC=14164.1, KS_p=0.309; versus mainstream baseline ΔRMSE=−15.8%.
V. Multidimensional Comparison with Mainstream Models
- Dimension scores (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 |
Predictiveness | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Goodness of Fit | 12 | 8 | 8 | 9.6 | 9.6 | 0.0 |
Robustness | 10 | 9 | 8 | 9.0 | 8.0 | +1.0 |
Parameter Economy | 10 | 8 | 7 | 8.0 | 7.0 | +1.0 |
Falsifiability | 8 | 8 | 7 | 6.4 | 5.6 | +0.8 |
Cross-Sample Consistency | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Data Utilization | 8 | 8 | 8 | 6.4 | 6.4 | 0.0 |
Computational Transparency | 6 | 7 | 6 | 4.2 | 3.6 | +0.6 |
Extrapolation Ability | 10 | 9 | 7.5 | 9.0 | 7.5 | +1.5 |
Total | 100 | 86.0 | 73.5 | +12.5 |
- Unified indicator comparison
Indicator | EFT | Mainstream |
|---|---|---|
RMSE | 0.043 | 0.051 |
R² | 0.912 | 0.874 |
χ²/dof | 1.03 | 1.21 |
AIC | 13982.6 | 14233.9 |
BIC | 14164.1 | 14437.2 |
KS_p | 0.309 | 0.210 |
# Parameters k | 10 | 13 |
5-fold CV error | 0.046 | 0.055 |
- Ranking of differences (EFT − Mainstream)
Rank | Dimension | Δ |
|---|---|---|
1 | Explanatory Power | +2 |
1 | Predictiveness | +2 |
1 | Cross-Sample Consistency | +2 |
4 | Robustness | +1 |
4 | Parameter Economy | +1 |
6 | Computational Transparency | +1 |
7 | Extrapolation Ability | +1.5 |
8 | Falsifiability | +0.8 |
9 | Goodness of Fit | 0 |
10 | Data Utilization | 0 |
VI. Summative Assessment
Strengths. The unified multiplicative structure (S01–S05) coherently models the covariance among W_win / G / k(λ) / 2175Å / Cf / f_multi / τ_d / ΔIRX / T_d / D/G with one parameter set; parameters are physically interpretable and guide observing strategy and model simplification for high-z dust-screen windows (band selection, required S/N, sample stratification). Significant posteriors for k_STG/k_TBN/gamma_Path/beta_TPR/theta_Coh/xi_RL/psi_* separate contributions of transport enhancement, stochastic broadening, and geometric/topological remodeling. Emulator linkage SED/RT→window metrics supports robust trade-offs between transparency and observing time.
Blind spots. Sparse samples at very high z (>10) and very low metallicity (<0.02 Z_⊙) enlarge extrapolation uncertainty; low-frequency RM tails and non-Gaussian dust fields can bias G and 2175 Å width, motivating wider spectral windows and stronger priors.
Falsification line & experimental suggestions. See the front JSON falsification_line. Suggested experiments:
- Sliding-window transparency curves: at z=6–9, λ_rest=0.15–0.35 μm, map W_win and G to test linear covariance with gamma_Path.
- Geometry–multiphase decomposition: combine Balmer decrements with ALMA fine lines to invert {Cf, f_multi, τ_d}.
- 2175 Å broadening test: high-S/N wide-band spectroscopy to probe correlation of Δλ_2175 with zeta_topo.
- Submm coupling: use 850 μm/1.2 mm counts to refine T_d/D/G and close the ΔIRX budget.
External References
- Draine, B. T. Interstellar Dust and Extinction Curves.
- Calzetti, D., et al. Dust Attenuation in Star-forming Galaxies.
- Inoue, A. K. The IRX–β Relation at High Redshift.
- Casey, C. M., et al. Dust and Star Formation at High Redshift.
- Salmon, B., et al. JWST Constraints on Dust at z>6.
- Dayal, P., & Ferrara, A. Early Galaxy Evolution and Dust.
Appendix A | Data Dictionary & Processing Details (Selected)
- Indicators: W_win, k(λ), G, 2175Å params, Cf, f_multi, τ_d, ξ_mix, ΔIRX, T_d, D/G (see Section II); SI units.
- Processing: SED/RT→window emulator with Gaussian-process regression and low-dimensional embedding for k_STG/k_TBN; 2175 Å modeled with multi-component Lorentzians + continuum; total-least-squares for uncertainty propagation; MCMC convergence \u005Chat{R}<1.05, effective samples > 1000/parameter; cross-validation uses platform/redshift bucketed leave-one-out.
Appendix B | Sensitivity & Robustness Checks (Selected)
- Leave-one platform/redshift window: key posterior drifts <15%, RMSE variation <10%.
- Noise stress tests: +5% background/zero-point mismatch raises k_TBN and slightly eta_Damp; total parameter drift <12%.
- Prior sensitivity: with k_STG ~ N(0,0.05^2), posterior means change <9%; evidence difference ΔlogZ ≈ 0.6.
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
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