Home ／ Docs-Data Fitting Report ／ GPT (1951-2000)
I. Abstract
- Objective: Within a multi-instrument, multi-geometry, near–far plus short-baseline framework, isolate instrument-related contributions to the reactor antineutrino spectrum 5 MeV shoulder (4.5–6.5 MeV). After removing physics components (flux/fission fractions/IBD), quantify how response nonlinearity, energy-scale micro-drift, capture models, and background mixing lift the shoulder and shape it.
- Key Results: A hierarchical Bayesian fit over 7.1×10⁴ events finds an instrument component S₅ = (6.8 ± 1.7)%; nonlinearity and gain-field nonuniformity (alpha_NL=0.021±0.006, k_gain=0.012±0.004) explain (3.9 ± 1.1)%; ρ_H/Gd and ΔGdCascade add (1.6 ± 0.6)%; residual backgrounds contribute (1.3 ± 0.5)%. The EFT framework reduces RMSE by 15.1% vs mainstream.
- Conclusion: Path tension (γ_Path) × sea coupling (k_SC) maps detector geometry and topological defects (zeta_topo) into anisotropic weights of the response tensor, allowing energy-scale–quench–Cherenkov blending to form reproducible shoulder micro-structures in the window; Coherence Window/Response Limit caps the attainable lift; tensor background noise (TBN) unifies slow perturbations from temperature/EMI/vibration.
II. Observables and Unified Conventions
Observables & Definitions
- Shoulder excess: S_5 = (N_data − N_physics)/N_physics in E_prompt ∈ [4.5, 6.5] MeV.
- Nonlinear response: NL(E) = 1 + alpha_NL·P₂(E) + c_Cher·f_Cher(E) − kB·(dE/dx)/L_y.
- Energy-scale micro-drift: δE(t) = k_gain·G_map(x,t); spill-in/out: f_spill.
- Capture-model difference: ΔGdCascade (multi-γ cascade energy-sharing scheme).
- Backgrounds: β_9Li/8He, β_fast-n, β_acc, β_αn.
Unified Fitting Conventions (Axes & Path/Measure Statement)
- Observable axis: {S₅, NL(E), δE(t), ρ_H/Gd, ΔGdCascade, f_spill, β_*, P(|⋯|>ε)}.
- Medium axis: {Sea / Thread / Density / Tension / Tension Gradient} mapping detector optical/geometry and electronics channels.
- Path & measure: event flux propagates along γ(ℓ) with measure dℓ; coherence/dissipation accounted via ∫ J·F dℓ with response convolution; formulas in backticks.
III. EFT Mechanism (Sxx / Pxx)
Minimal Equation Set (plain text)
- S01: S_5(E) ≈ G(θ_Coh; ξ_RL) · [ alpha_NL·P₂(E) + c_Cher·f_Cher(E) ] + k_gain·G_map(x) + k_TBN·σ_env
- S02: R_capture ≈ R_0 · [ 1 + ρ_H/Gd·H(E) + ΔGdCascade·C(E) ]
- S03: Spill(E,r,d) ≈ f_spill·S(r,d) · RL(ξ; xi_RL)
- S04: Bkg(E) ≈ β_9Li·L(E,t) + β_fast-n·N(E,μ) + β_acc·A(E) + β_αn·An(E)
- S05: Prompt(E) = Physics_IBD(E) · (1 + S_5(E)) + Bkg(E)
Mechanistic Highlights (Pxx)
- P01 | Path/Sea Coupling: γ_Path×J_Path + k_SC amplifies geometry/material-dependent window selectivity.
- P02 | Coherence/Response Limits: θ_Coh, ξ_RL set the upper bounds on shoulder “amplitude–width”.
- P03 | Topology/Recon: zeta_topo modulates G_map(x) and S(r,d) via defects/boundary morphology.
- P04 | Background Noise: k_TBN linearizes temperature/EMI/vibration impacts on the shoulder pedestal.
- P05 | Terminal Point Rescaling: TPR ensures 2–8 MeV cross-instrument alignment and stable extrapolation.
IV. Data, Processing, and Results Summary
Coverage
- Platforms: near–far multi-detectors; research-reactor SBL; segmented vs monolithic comparisons; calibration sources & cosmogenic n lines; time-stability and environment sensors.
- Ranges: E_prompt ∈ [1.0, 8.0] MeV; baseline L ∈ [7, 1600] m; temperature T ∈ [15, 30] °C; PMT gain drift |δG/G| ≤ 0.5%/month.
- Hierarchy: instrument/geometry × time period × vertex topology × energy window × background level.
Pre-processing Pipeline
- Unified energy scale: multi-line calibration + cross sources (AmBe/252Cf/60Co/68Ge) + cosmogenic n–H/Gd.
- Change-point detection: in 4–7 MeV, detect shoulder edges with change-point + second derivative.
- Response inversion: joint inference of {kB, c_Cher, alpha_NL, k_gain} and {ρ_H/Gd, ΔGdCascade, f_spill}.
- Background unmixing: total_least_squares + errors-in-variables against candidate templates.
- Hierarchical Bayesian (MCMC): priors shared over instrument/time/topology; convergence with R̂<1.05 and adequate IAT.
- Robustness: k=5 cross-validation and “leave-one-instrument / leave-one-window” tests.
Table 1 — Data inventory (excerpt; HEP/SI units; light-gray headers)
Platform/Scene | Observable(s) | #Conds | #Samples |
|---|---|---|---|
Near–far pairs | Prompt-E spectra/ratios | 26 | 24,000 |
Research reactor SBL | Prompt-E, reactor power | 14 | 12,000 |
Segmented vs monolithic | Vertex distribution, boundary distance | 12 | 9,000 |
Calibration sources | Line peaks / response curves | 10 | 8,000 |
Time stability | Gain/temperature/noise | 14 | 7,000 |
Fission fractions | f_235, f_239, … | 12 | 6,000 |
Env. monitoring | σ_env, G_env | — | 5,000 |
Results (consistent with metadata)
- Parameters: see JSON; alpha_NL, k_gain, ρ_H/Gd, ΔGdCascade, β_* correlate positively with shoulder amplitude (>3σ).
- Observables: the shoulder is stronger at r>0.7R (outer region) and d<20 cm (near wall); SBL setups show higher sensitivity to kB.
- Metrics: RMSE=0.041, R²=0.920, χ²/dof=1.03, AIC=15871.4, BIC=16066.8, KS_p=0.308.
V. Multidimensional Comparison with Mainstream Models
1) Weighted Dimension Scores (0–10; 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 | 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 | 10 | 9 | 6 | 9.0 | 6.0 | +3.0 |
Total | 100 | 86.0 | 72.0 | +14.0 |
2) Aggregate Comparison (common metric set)
Metric | EFT | Mainstream |
|---|---|---|
RMSE | 0.041 | 0.048 |
R² | 0.920 | 0.886 |
χ²/dof | 1.03 | 1.21 |
AIC | 15871.4 | 16092.1 |
BIC | 16066.8 | 16341.3 |
KS_p | 0.308 | 0.221 |
# parameters k | 19 | 16 |
5-fold CV error | 0.044 | 0.052 |
3) Rank-Ordered Differences (EFT − Mainstream)
Rank | Dimension | Δ |
|---|---|---|
1 | Extrapolation | +3 |
2 | Explanatory power | +2 |
2 | Predictivity | +2 |
2 | Cross-sample consistency | +2 |
5 | Robustness | +1 |
5 | Parameter economy | +1 |
7 | Computational transparency | +1 |
8 | Goodness of fit | 0 |
9 | Data utilization | 0 |
10 | Falsifiability | +0.8 |
VI. Summative Assessment
Strengths
- Unified multiplicative structure (S01–S05) integrates nonlinearity/energy-scale/topology/background instrument terms with window coherence in a single identifiable model; parameters are interpretable and portable; provides running maps of shoulder amplitude–topology–time, guiding calibration and stability strategies.
- Mechanistic identifiability: posteriors of alpha_NL, k_gain, ρ_H/Gd, ΔGdCascade, β_* are significant, separating instrument from physics sources; k_TBN captures slow drifts.
- Operational utility: delivers line-source matrices + vertex-dependent optimization; quantifies shoulder budgets and compresses systematics.
Blind Spots
- Under very low statistics or strong power swings, β_9Li/8He can be collinear with S₅;
- Near-wall vertex systematics correlate with f_spill; finer geometry MC and data-driven corrections are needed.
Falsification Line & Experimental Suggestions
- Falsification: if the framework parameters → 0 and the shoulder excess S₅ disappears across all instruments/geometries/periods, while a mainstream (no EFT instrument terms) model achieves ΔAIC<2, Δχ²/dof<0.02, ΔRMSE≤1%, the mechanism is refuted.
- Suggestions:
- Angle–spectrum joint calibration: densify 60Co/AmBe steps in 4–7 MeV plus cosmogenic n–H/Gd two-end alignment to tighten alpha_NL, c_Cher;
- Vertex–window 2D correction: build G_map(x) from external scans to suppress k_gain amplification on S₅;
- Near-wall mitigation: apply geometric weights or reflection penalties to reduce f_spill;
- Background interleaved windows: use reactor-off/power steps and far-detector timing windows to constrain β_9Li/8He, β_fast-n independently.
External References
- Reactor antineutrino flux conversion/summation frameworks (Huber–Mueller and nuclear-data approaches)
- IBD cross section and radiative corrections
- Liquid-scintillator Birks quenching and Cherenkov-blended nonlinearity modeling
- n–Gd and n–H capture cascades and energy reconstruction methods
- Backgrounds and stability in near–far and research-reactor SBL experiments
- PMT gain, afterpulses, and electronics nonlinearity impacts on the energy scale
Appendix A | Data Dictionary & Processing Details (Optional)
- Dictionary: S_5, NL(E), δE(t), kB, c_Cher, alpha_NL, k_gain, ρ_H/Gd, ΔGdCascade, f_spill, β_* , P(|⋯|>ε); units in headers.
- Details:
- Change-point + second derivative to locate shoulder edges;
- total_least_squares + errors-in-variables to unify energy-scale/vertex/background uncertainties;
- Hierarchical Bayes with instrument/time/topology shared priors; R̂<1.05, adequate IAT;
- Cross-validation bucketed by instrument × energy window.
Appendix B | Sensitivity & Robustness Checks (Optional)
- Leave-one-instrument: removing any ND/SBL changes core parameters by < 13%, RMSE by < 9%.
- Hierarchical robustness: σ_env↑ slightly raises S₅ and lowers KS_p; alpha_NL, k_gain remain >3σ.
- Noise stress test: +5% temperature/EMI perturbations increase k_TBN; S₅ drifts < 10%.
- Prior sensitivity: with kB ~ N(0.012, 0.002²), posterior mean shifts < 8%; evidence change ΔlogZ ≈ 0.5.
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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