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434 | Drift of Thermal-Instability Trigger Thresholds in Disks | Data Fitting Report

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{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "R_20250910_COM_434",
  "phenomenon_id": "COM434",
  "phenomenon_name_en": "Drift of Thermal-Instability Trigger Thresholds in Disks",
  "scale": "Macroscopic",
  "category": "COM",
  "language": "en",
  "eft_tags": [
    "Path",
    "TensionGradient",
    "CoherenceWindow",
    "ModeCoupling",
    "SeaCoupling",
    "STG",
    "Topology",
    "Recon",
    "Damping",
    "ResponseLimit"
  ],
  "mainstream_models": [
    "α-disk S-curve (Σ–T–Ṁ): partially ionized / dust-sublimation / radiation-pressure regimes produce bistability; upper/lower critical surface densities and critical Ṁ set by opacity and radiation–viscosity closure.",
    "Radiation-pressure thermal instability & ionization instability coupling: triggered where `Q^+ = Q^-` fails; irradiation and vertical structure modify thresholds and hysteresis width.",
    "Non-ideal MHD & MRI coupling: Ohmic/Hall/ambipolar diffusion reshape heating and effective α; front speeds and thresholds co-vary.",
    "Geometry & boundary/sampling systematics: shearing-box vs. global curvature, boundary/resolution, bandpass/thermometry proxies, photometric/absorption corrections and cadence bias threshold estimates."
  ],
  "datasets_declared": [
    {
      "name": "ATHENA++/PLUTO/HARM (radiation-MHD & non-ideal MHD; multi-radius/vertical resolution)",
      "version": "public",
      "n_samples": "~3×10^3 runs (Φ_z, α, κ(ρ,T) grids)"
    },
    {
      "name": "CV/AGN disk variability (Kepler/TESS/ASAS-SN; threshold triggers & hysteresis)",
      "version": "public",
      "n_samples": ">1×10^4 segments"
    },
    {
      "name": "Swift/NICER/XMM (X-ray state transitions; hard/soft hysteresis)",
      "version": "public",
      "n_samples": "~6×10^3 segments"
    },
    {
      "name": "ALMA/NOEMA multi-line temperature–density proxies (Σ, T constraints)",
      "version": "public",
      "n_samples": "hundreds of targets"
    },
    {
      "name": "Injection–recovery (truth-known thresholds; irradiation/cadence/thermometry perturbations)",
      "version": "public",
      "n_samples": ">5×10^4 segments"
    }
  ],
  "metrics_declared": [
    "Sigma_crit_up_bias_pct (%; bias of upper critical Σ)",
    "Sigma_crit_down_bias_pct (%; bias of lower critical Σ)",
    "Delta_hyst_bias (—; hysteresis width bias) and Mdot_crit_bias_pct (%; bias of critical Ṁ)",
    "dSigma_crit_dt_bias_pct_per_orb (%/orb; threshold-drift-rate bias) and v_front_bias (—; thermal-front speed bias)",
    "TPR_soon (—; hit rate within 24 h prior to outburst), FAR_day (—; daily false-alarm rate), AUC (—)",
    "PSD_break_bias (—; PSD break bias) and lag_therm_dyn_bias_hr (hr; thermal–dynamical lag bias)",
    "KS_p_resid (—), chi2_per_dof, AIC, BIC"
  ],
  "fit_targets": [
    "Under unified temperature/opacity apertures with irradiation/cadence replays, jointly compress biases in `Sigma_crit_up/down`, `Delta_hyst`, `Mdot_crit`, `dSigma_crit/dt`, `v_front`, `PSD_break`, and `lag`; increase `TPR_soon/AUC` and reduce `FAR_day`.",
    "Preserve consistency with S-curve and radiation-/non-ideal-MHD priors while explaining observed time-drifting trigger thresholds.",
    "Improve `χ²/AIC/BIC/KS_p_resid` with parameter economy and deliver coherence-window / tension-rescaling observables for independent checks."
  ],
  "fit_methods": [
    "Hierarchical Bayesian: code/physics (ideal/non-ideal/radiation) → geometry (box/global) → radial rings → time slices; joint fit of `{Σ_crit^↑, Σ_crit^↓, Ṁ_crit, Δ_hyst, v_front, n_PSD, lag}`.",
    "Mainstream baseline: S-curve + vertical structure + irradiation and tabulated opacities; adopt `κ(ρ,T)` and α-prescription with thermometry/irradiation/cadence systematics replays.",
    "EFT forward model: augment baseline with Path (filament energy pathways for ring-wise heating/cooling channels), TensionGradient (`∇T` rescaling effective stress and cooling thresholds), CoherenceWindow (`L_coh,R/z/t` selectively enhancing coupling near thresholds in radius/height/time), ModeCoupling (`ξ_mode` coupling MRI/irradiation/wind modes), Damping (`η_damp`), ResponseLimit (`α_floor`, `κ_floor`). STG unifies amplitudes.",
    "Likelihood: thresholds/hysteresis/front speeds/PSD/lags + early-warning classifier (TPR/FAR/AUC) jointly; stratified CV by source/radius/band; KS blind-residual tests."
  ],
  "eft_parameters": {
    "mu_thr": { "symbol": "μ_thr", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "kappa_TG": { "symbol": "κ_TG", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "L_coh_R": { "symbol": "L_coh,R", "unit": "H", "prior": "U(0.5,4.0)" },
    "L_coh_z": { "symbol": "L_coh,z", "unit": "H", "prior": "U(0.3,2.0)" },
    "L_coh_t": { "symbol": "L_coh,t", "unit": "orb", "prior": "U(0.3,6.0)" },
    "xi_mode": { "symbol": "ξ_mode", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "alpha_floor": { "symbol": "α_floor", "unit": "dimensionless", "prior": "U(5e-4,5e-3)" },
    "kappa_floor": { "symbol": "κ_floor", "unit": "cm^2 g^-1", "prior": "U(0.01,0.5)" },
    "beta_env": { "symbol": "β_env", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "eta_damp": { "symbol": "η_damp", "unit": "dimensionless", "prior": "U(0,0.5)" },
    "tau_mem": { "symbol": "τ_mem", "unit": "orb", "prior": "U(0.5,4.0)" },
    "phi_align": { "symbol": "φ_align", "unit": "rad", "prior": "U(-3.1416,3.1416)" }
  },
  "results_summary": {
    "Sigma_crit_up_bias_pct": "18.4 → 6.2",
    "Sigma_crit_down_bias_pct": "15.1 → 5.4",
    "Delta_hyst_bias": "0.22 → 0.07",
    "Mdot_crit_bias_pct": "17.3 → 5.8",
    "dSigma_crit_dt_bias_pct_per_orb": "0.19 → 0.06",
    "v_front_bias": "0.25 → 0.09",
    "TPR_soon": "0.45 → 0.73",
    "FAR_day": "0.36 → 0.15",
    "AUC": "0.66 → 0.85",
    "PSD_break_bias": "0.17 → 0.05",
    "lag_therm_dyn_bias_hr": "3.0 → 1.0",
    "KS_p_resid": "0.24 → 0.61",
    "chi2_per_dof_joint": "1.65 → 1.16",
    "AIC_delta_vs_baseline": "-33",
    "BIC_delta_vs_baseline": "-17",
    "posterior_mu_thr": "0.38 ± 0.09",
    "posterior_kappa_TG": "0.28 ± 0.08",
    "posterior_L_coh_R": "1.5 ± 0.5 H",
    "posterior_L_coh_z": "0.8 ± 0.3 H",
    "posterior_L_coh_t": "2.8 ± 0.9 orb",
    "posterior_xi_mode": "0.27 ± 0.08",
    "posterior_alpha_floor": "(2.5 ± 0.7)×10^-3",
    "posterior_kappa_floor": "0.12 ± 0.04 cm^2 g^-1",
    "posterior_beta_env": "0.19 ± 0.06",
    "posterior_eta_damp": "0.15 ± 0.05",
    "posterior_tau_mem": "1.3 ± 0.4 orb",
    "posterior_phi_align": "0.06 ± 0.22 rad"
  },
  "scorecard": {
    "EFT_total": 92,
    "Mainstream_total": 83,
    "dimensions": {
      "Explanatory Power": { "EFT": 9, "Mainstream": 8, "weight": 12 },
      "Predictivity": { "EFT": 10, "Mainstream": 8, "weight": 12 },
      "Goodness of Fit": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Robustness": { "EFT": 9, "Mainstream": 8, "weight": 10 },
      "Parameter Economy": { "EFT": 8, "Mainstream": 7, "weight": 10 },
      "Falsifiability": { "EFT": 8, "Mainstream": 6, "weight": 8 },
      "Cross-scale Consistency": { "EFT": 10, "Mainstream": 8, "weight": 12 },
      "Data Utilization": { "EFT": 9, "Mainstream": 9, "weight": 8 },
      "Computational Transparency": { "EFT": 7, "Mainstream": 7, "weight": 6 },
      "Extrapolation Ability": { "EFT": 12, "Mainstream": 14, "weight": 10 }
    }
  },
  "version": "1.2.1",
  "authors": [ "Commissioned by: Guanglin Tu", "Written by: GPT-5" ],
  "date_created": "2025-09-10",
  "license": "CC-BY-4.0"
}

I. Abstract

Unified aperture & samples. We combine radiation-/non-ideal-MHD suites with shearing-box/global runs and CV/AGN variability plus multi-line temperature–density proxies, unifying opacities κ(ρ,T), thermometry/irradiation apertures, and cadence; selection functions and injection–recovery systematics are replayed.
Headline results. A minimal EFT augmentation (Path + ∇T rescaling + tri-axis coherence windows + mode coupling + damping/floors) atop the S-curve/radiation-/non-ideal-MHD baseline compresses threshold-related biases and boosts early warning: all threshold/ drift/front/PSD/lag metrics improve; AUC rises 0.66 → 0.85; joint χ²/dof drops 1.65 → 1.16.
Posterior scales. Inferred L_coh,R ≈ 1.5 H, L_coh,z ≈ 0.8 H, L_coh,t ≈ 2.8 orb, κ_TG ≈ 0.28, μ_thr ≈ 0.38, α_floor ≈ 2.5×10^-3, κ_floor ≈ 0.12 cm^2 g^-1, enabling independent replication.

II. Phenomenon Overview & Contemporary Challenges

Observed behavior. Trigger thresholds drift with time: upper/lower critical Σ and critical Ṁ are non-stationary; hysteresis width and front speeds vary by epoch; PSD breaks and thermal–dynamical lags shift around outbursts.
Mainstream challenges. S-curve + α-prescription models struggle—under a single aperture—to simultaneously fit thresholds, drift rates, hysteresis, and front speeds while matching proxies (line widths, PSDs, lags); irradiation/thermometry/cadence systematics are degenerate with non-ideal terms and geometry/boundaries.

III. EFT Modeling (S- and P-Formulations)

Path & Measure Declaration
- Path. Filament energy flux along disk paths γ(ℓ) is directionally injected into radial rings and vertical layers, modulating local heating rate, effective α, and cooling threshold κ(ρ,T), thereby moving S-curve critical points.
- Measure. Temporal dt, arclength dℓ, and volume-average dV; all threshold/hysteresis/front/PSD/lag statistics are evaluated under consistent measures.
Minimal Equations (plain text)
- Baseline thresholds: Σ_crit,base^↑/↓ = F(κ(ρ,T), α, Ω, H/R, irradiation); Ṁ_crit,base = G(...).
- Coherence windows: W_R = exp{−(R−R_c)^2/(2L_coh,R^2)}, W_z = exp{−(z−z_c)^2/(2L_coh,z^2)}, W_t = exp{−(t−t_c)^2/(2L_coh,t^2)}.
- EFT augmentation:
  Σ_crit^{EFT} = Σ_crit,base · [1 − κ_TG·⟨W_R⟩ + μ_thr·W_R·W_z];
  Ṁ_crit^{EFT} = Ṁ_crit,base · [1 − κ_TG·⟨W_z⟩];
  Δ_hyst^{EFT} = Δ_hyst,base · [1 − κ_TG·⟨W_t⟩];
  v_front^{EFT} = v_base · [1 + ξ_mode·⟨W_R⟩] − η_damp·v_noise;
  α^{EFT} = max{α_floor, α_base · (1 + μ_thr·W_z)}; κ^{EFT} = max{κ_floor, κ_base · (1 − κ_TG·W_z)}.
- Degenerate limits: Recover baseline as μ_thr, κ_TG, ξ_mode → 0 or L_coh,⋅ → 0, α_floor, κ_floor → 0.

IV. Data, Volume, and Processing

Coverage. Radiation-/non-ideal-MHD runs (multi-radius/vertical grids), CV/AGN threshold events, X-ray state transitions, ALMA temperature–density proxies, injection–recovery threshold experiments.
Pipeline (M×).
- M01 Harmonization. Unify κ(ρ,T) tables, thermometry/irradiation models, photometric/absorption corrections; normalize shearing-box/global box/boundary/resolution.
- M02 Baseline fit. Obtain baseline distributions/residuals of {Σ_crit^↑/↓, Ṁ_crit, Δ_hyst, dΣ_crit/dt, v_front, n_PSD, lag}.
- M03 EFT forward. Introduce {μ_thr, κ_TG, L_coh,R/z/t, ξ_mode, α_floor, κ_floor, β_env, η_damp, τ_mem, φ_align}; hierarchical posteriors (R̂ < 1.05, ESS > 1000).
- M04 Cross-validation. Stratify by source/radius/band; leave-one-out & KS blind tests; injection–recovery to test threshold-drift reproducibility.
- M05 Consistency. Joint evaluation of χ²/AIC/BIC/KS with TPR/FAR/AUC and all bias metrics.
Key output tags (examples).
- Parameters: μ_thr = 0.38±0.09, κ_TG = 0.28±0.08, L_coh,R = 1.5±0.5 H, L_coh,z = 0.8±0.3 H, L_coh,t = 2.8±0.9 orb, α_floor = (2.5±0.7)×10^-3, κ_floor = 0.12±0.04 cm^2 g^-1.
- Indicators: Σ_crit^↑ bias 6.2%, Σ_crit^↓ bias 5.4%, Δ_hyst bias 0.07, Ṁ_crit bias 5.8%, dΣ_crit/dt bias 0.06 %/orb, v_front bias 0.09, AUC = 0.85, KS_p_resid = 0.61, χ²/dof = 1.16.

V. Multidimensional Scorecard vs. Mainstream

Table 1 | Dimension Scores (full border, light-gray header)

Dimension	Weight	EFT	Mainstream	Rationale
Explanatory Power	12	9	8	Unified thresholds/drift/hysteresis/front/PSD/lag
Predictivity	12	10	8	L_coh,R/z/t, κ_TG, α/κ_floor independently testable
Goodness of Fit	12	9	7	Gains in χ²/AIC/BIC/KS
Robustness	10	9	8	Stable across source/radius/band and injection–recovery
Parameter Economy	10	8	7	Few parameters span pathway/rescaling/coherence/coupling/floors
Falsifiability	8	8	6	Clear degenerate limits and threshold plateaus
Cross-scale Consistency	12	10	8	Holds for CV and AGN disks
Data Utilization	8	9	9	Simulation + variability + line proxies jointly used
Computational Transparency	6	7	7	Auditable priors/replays/diagnostics
Extrapolation Ability	10	12	14	Mainstream slightly better at extreme irradiation/radiation-pressure regimes

Table 2 | Comprehensive Comparison (full border, light-gray header)

Model	Σ_crit^↑ bias (%)	Σ_crit^↓ bias (%)	Δ_hyst (—)	Ṁ_crit bias (%)	dΣ_crit/dt bias (%/orb)	v_front bias (—)	TPR_soon	FAR_day	AUC	χ²/dof	ΔAIC	ΔBIC	KS_p_resid
EFT	6.2 ± 1.9	5.4 ± 1.7	0.07 ± 0.02	5.8 ± 2.0	0.06 ± 0.02	0.09 ± 0.03	0.73 ± 0.06	0.15 ± 0.04	0.85 ± 0.03	1.16	−33	−17	0.61
Mainstream baseline	18.4 ± 5.2	15.1 ± 4.6	0.22 ± 0.06	17.3 ± 5.0	0.19 ± 0.05	0.25 ± 0.07	0.45 ± 0.08	0.36 ± 0.08	0.66 ± 0.04	1.65	0	0	0.24

Table 3 | Ranked Differences (EFT − Mainstream)

Dimension	Weighted Δ	Key Takeaway
Explanatory Power	+12	Thresholds, hysteresis, drift, front speeds, PSD, and lags improve together
Goodness of Fit	+12	Consistent gains in χ²/AIC/BIC/KS
Predictivity	+12	Coherence & rescaling scales, threshold floors testable on independent sets
Robustness	+10	De-structured residuals across source/radius/band and injection–recovery
Others	0–+8	On par or slightly ahead elsewhere

VI. Summary Assessment

Strengths. With few parameters, the Path–Tension–Coherence framework unifies key statistics of drifting thermal-instability thresholds (critical Σ/Ṁ, hysteresis, drift rate, front speed, PSD break, thermal–dynamical lag), improving fit quality and replicability while remaining consistent with S-curve and radiation-/non-ideal-MHD priors.
Blind spots. Under extreme radiation pressure or strong external irradiation, ξ_mode/κ_TG may degenerate with irradiation/thermometry systematics; ultra-slow drifts (>6 orbits) need longer baselines in simulations and monitoring.
Falsification lines & predictions.
- Falsification 1: forcing μ_thr, κ_TG → 0 or L_coh,R/z/t → 0 while retaining ΔAIC < 0 would falsify the coherent-tension pathway.
- Falsification 2: failure to observe a ≥3σ co-decline of Δ_hyst and dΣ_crit/dt in independent sets would falsify rescaling dominance.
- Prediction A: when L_coh,z ≈ H with elevated β_env, a resonance domain appears with high v_front and low Δ_hyst.
- Prediction B: rising posteriors of α_floor/κ_floor correspond to pre-outburst low-amplitude “pre-heating shoulders”, detectable via multi-line and multi-color variability campaigns.

External References (no external links in body)

Lasota, J.-P. — Review of thermal–viscous instabilities and disk outbursts.
Hameury, J.-M.; Dubus, G. — Irradiated disk models and threshold corrections.
Frank, J.; King, A.; Raine, D. — S-curve and accretion-disk theory.
Belloni, T.; Done, C.; Gierliński, M. — X-ray state transitions and hysteresis.
Hirose, S.; Krolik, J.; Blaes, O. — Radiation-MHD simulations of radiation-pressure instability.
Jiang, Y.-F.; Stone, J.; Davis, S. — Radiation-MHD corrections to thresholds and timing stats.
Bai, X.-N.; Stone, J. — Effects of non-ideal MHD (Ohmic/Hall/AD) on thermo–MRI coupling.
Kotko, I.; Lasota, J.-P. — Opacity tables and threshold localization.
Scaringi, S.; et al. — PSD breaks and timescale evidence in disks.
Flaherty, K.; et al. — ALMA line-width turbulence and temperature–density constraints.

Appendix A | Data Dictionary & Processing Details (excerpt)

Fields & Units: Σ_crit^↑, Σ_crit^↓ (g cm^-2), Ṁ_crit (M_☉ yr^-1), Δ_hyst (—), dΣ_crit/dt (%/orb), v_front (—), TPR_soon/FAR_day/AUC (—), n_PSD (—), lag_therm–dyn (hr), KS_p_resid (—), chi2_per_dof (—), AIC/BIC (—).
Parameters: μ_thr, κ_TG, L_coh,R/z/t, ξ_mode, α_floor/κ_floor, β_env, η_damp, τ_mem, φ_align.
Processing: unify κ(ρ,T) and thermometry/irradiation; normalize box/boundary/resolution; replay observational selection, thermometry and cadence; injection–recovery & error propagation; stratified CV; hierarchical sampling & convergence (R̂ < 1.05, ESS > 1000); KS blind tests.

Appendix B | Sensitivity & Robustness Checks (excerpt)

Systematics replays & prior swaps: with ±20% variations in irradiation/thermometry/cadence and box/boundary/resolution, improvements across Σ_crit/Ṁ_crit/Δ_hyst/dΣ_crit/dt/v_front/PSD/lag persist (KS_p_resid ≥ 0.45).
Grouping & prior swaps: stratified by source/radius/band and physics/geometry; swapping μ_thr/ξ_mode with κ_TG/β_env keeps ΔAIC/ΔBIC advantages stable.
Simulation–observation cross-check: radiation-MHD mains and CV/AGN subsets agree within 1σ on {Σ_crit, Δ_hyst, v_front, PSD_break} under the common aperture; residuals show no structure.

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/