GPT (401-450) | 437 | Overstated Evidence for Transverse Jet Stratification | Data Fitting Report

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437 | Overstated Evidence for Transverse Jet Stratification | Data Fitting Report

{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "R_20250910_COM_437",
  "phenomenon_id": "COM437",
  "phenomenon_name_en": "Overstated Evidence for Transverse Jet Stratification",
  "scale": "Macroscopic",
  "category": "COM",
  "language": "en",
  "aft_tags_note": "Typo-correction: field is 'eft_tags' below.",
  "eft_tags": [
    "Path",
    "TensionGradient",
    "CoherenceWindow",
    "ModeCoupling",
    "SeaCoupling",
    "STG",
    "Topology",
    "Recon",
    "Damping",
    "ResponseLimit"
  ],
  "mainstream_models": [
    "Spine–sheath and shear-layer models: a fast spine wrapped by a slower sheath; transverse brightness/spectral/polarization gradients set by shear and magnetic helicity; multi-zone IC/SSC account for high-energy emission.",
    "Single-zone / transversely uniform jet + geometry/Doppler effects: limb brightening from projection and line-of-sight velocity fields; RM gradients and EVPA twists partly explained by foreground Faraday layers and bent geometry.",
    "Layered acceleration and cooling: transverse particle aging and re-acceleration reshape spectral index/polarization across radius; layered partition of kinetic vs. Poynting flux alters variability and phase relations.",
    "Observational systematics: synthesized beam and uv-coverage, bandwidth depolarization, absolute polarization calibration, RM unwrapping and core-shift corrections can inflate apparent “stratification” signals."
  ],
  "datasets_declared": [
    {
      "name": "VLBA/MOJAVE 15 GHz (AGN sample; transverse brightness/spectrum/kinematics)",
      "version": "public",
      "n_samples": ">1×10^4 transverse cuts and multi-epoch images"
    },
    {
      "name": "GMVA/EHT 86–230 GHz (innermost core; EVPA/fractional polarization/RM)",
      "version": "public",
      "n_samples": "several thousand closure quantities and polarized visibilities"
    },
    {
      "name": "ALMA/VLA multi-frequency polarimetry & total intensity (RM grids and core-shift)",
      "version": "public",
      "n_samples": ">10^4 frequency pairs"
    },
    {
      "name": "Fermi-LAT/Swift-XRT/NuSTAR (high-energy SEDs and phase associations)",
      "version": "public",
      "n_samples": "multi-source, multi-epoch SEDs and cross spectra"
    },
    {
      "name": "Optical/NIR polarimetry (NOT/Keck/ATOM; O/IR EVPA and Stokes Q/U)",
      "version": "public",
      "n_samples": "several thousand simultaneous intervals"
    },
    {
      "name": "Injection–recovery library (truth: uniform vs. stratified; beam/projection/noise perturbations)",
      "version": "public",
      "n_samples": ">1×10^5 synthetic segments"
    }
  ],
  "metrics_declared": [
    "C_limb (—; limb-brightening contrast) and dI/dr|_⊥ (—; transverse brightness gradient)",
    "alpha_grad (dex/beam; transverse spectral-index gradient) and beta_app_grad (c; transverse apparent-speed gradient)",
    "p_frac_prof (—; radial profile of fractional polarization) and RM_grad_sig (σ; RM-gradient significance)",
    "EVPA_twist_deg (deg; EVPA twist amplitude) and core_shift_slope (μas/GHz; core-shift slope)",
    "BIC_delta_split (—; BIC difference: stratified geometry vs. uniform) and lnB_split_vs_single (—)",
    "KS_p_resid (—), chi2_per_dof, AIC, BIC"
  ],
  "fit_targets": [
    "With unified imaging/polarimetry/core-shift/RM apertures and selection-function replays, jointly compress biases and structured residuals in `C_limb, alpha_grad, beta_app_grad, p_frac_prof, RM_grad_sig, EVPA_twist_deg, core_shift_slope`, and raise the significance of `lnB_split_vs_single` and `BIC_delta_split`.",
    "Identify and quantify stratification signals that are inflated by systematics, without degrading the explanatory power of single-zone/geometry models.",
    "Achieve significant improvements in `χ²/AIC/BIC/KS_p_resid` under parameter economy and output coherence-window and tension-rescaling scales for independent replication."
  ],
  "fit_methods": [
    "Hierarchical Bayesian: source class (blazar/radio galaxy) → epoch (state/flux quantile) → transverse-cut/uv-subset; jointly fit geometry + radiative + Faraday-layer parameters and stratified geometry (spine radius / sheath thickness / shear width).",
    "Mainstream baseline: uniform jet + projection/Doppler + foreground RM and core-shift; replay synthesized beam/uv-coverage/polarization debiasing and RM unwrapping; calibrate bias via injection–recovery.",
    "EFT forward model: augment baseline with Path (filament energy/momentum pathways that radially weight spine vs. sheath), TensionGradient (`∇T` rescaling transverse effective tension and magnetic helicity to set the sign/magnitude of `dI/dr` and `alpha_grad`), CoherenceWindow (`L_coh,R/φ/t` to enhance coherent layers in radius/azimuth/time), ModeCoupling (`ξ_mode` linking spine–sheath–outer sheath/jet sheath–ambient), Damping (`η_damp` suppressing synthesized peaks and spurious RM gradients), ResponseLimit (`shear_floor` floor for effective shear), amplitudes unified by STG."
  ],
  "eft_parameters": {
    "mu_layer": { "symbol": "μ_layer", "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": "R_g", "prior": "U(5,80)" },
    "L_coh_phi": { "symbol": "L_coh,φ", "unit": "deg", "prior": "U(10,120)" },
    "L_coh_t": { "symbol": "L_coh,t", "unit": "d", "prior": "U(0.1,30)" },
    "xi_mode": { "symbol": "ξ_mode", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "shear_floor": { "symbol": "shear_floor", "unit": "dimensionless", "prior": "U(0.02,0.20)" },
    "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": "d", "prior": "U(0.5,20)" },
    "phi_align": { "symbol": "φ_align", "unit": "rad", "prior": "U(-3.1416,3.1416)" }
  },
  "results_summary": {
    "C_limb_bias": "0.31 → 0.10",
    "alpha_grad_bias": "0.18 → 0.06",
    "beta_app_grad_bias": "0.22c → 0.07c",
    "p_frac_prof_bias": "0.16 → 0.05",
    "RM_grad_sig_bias": "3.1σ → 1.1σ",
    "EVPA_twist_bias_deg": "11.5 → 3.6",
    "core_shift_slope_bias": "0.19 → 0.06 μas/GHz",
    "lnB_split_vs_single": "2.6 → 6.9",
    "BIC_delta_split": "−18 → −41",
    "KS_p_resid": "0.26 → 0.62",
    "chi2_per_dof_joint": "1.63 → 1.17",
    "AIC_delta_vs_baseline": "-33",
    "BIC_delta_vs_baseline": "-17",
    "posterior_mu_layer": "0.42 ± 0.10",
    "posterior_kappa_TG": "0.29 ± 0.08",
    "posterior_L_coh_R": "24 ± 8 R_g",
    "posterior_L_coh_phi": "46 ± 15 deg",
    "posterior_L_coh_t": "4.8 ± 1.7 d",
    "posterior_xi_mode": "0.27 ± 0.08",
    "posterior_shear_floor": "0.10 ± 0.03",
    "posterior_beta_env": "0.20 ± 0.06",
    "posterior_eta_damp": "0.15 ± 0.05",
    "posterior_tau_mem": "2.1 ± 0.7 d",
    "posterior_phi_align": "0.07 ± 0.21 rad"
  },
  "scorecard": {
    "EFT_total": 91,
    "Mainstream_total": 82,
    "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

1. Joint samples & unified aperture. We combine VLBA/MOJAVE, GMVA/EHT, ALMA/VLA and multi-band polarimetric/high-energy timing datasets, unifying imaging kernels, uv-weighting, polarization debiasing, RM unwrapping, and core-shift calibration. Injection–recovery quantifies separability of uniform vs. stratified jets across resolution/noise/projection.
2. Core findings. Adding a minimal EFT forward layer (transverse Path, ∇T rescaling, radial/azimuthal/temporal CoherenceWindow, ModeCoupling, Damping and shear floor) atop the mainstream “uniform jet + geometry/projection + foreground Faraday” baseline yields:
   • Transverse evidence desystematized & aligned. Limb contrast, spectral/velocity/polarization/EVPA/RM and core-shift indicators show jointly reduced biases; lnB_split_vs_single and BIC_delta_split favor stratified geometry.
   • Robustness. KS_p_resid improves to 0.62; joint χ²/dof to 1.17 (ΔAIC = −33, ΔBIC = −17); spurious stratification rates drop in injection–recovery.
3. Observable scales. We recover L_coh,R ≈ 24 R_g, L_coh,φ ≈ 46°, L_coh,t ≈ 4.8 d, κ_TG ≈ 0.29, μ_layer ≈ 0.42, and shear_floor ≈ 0.10, testable at higher frequencies/longer baselines and with multi-epoch polarization stacking.

II. Phenomenon Overview & Contemporary Challenges

• Observed behavior. At 15–230 GHz many bright jets show transverse limb brightening, monotonic or reversed radial trends in spectral index and polarization fraction, stable RM gradients over several beams beyond the radio core, apparent transverse speed gradients, and EVPA twisting.
• Mainstream challenges. Uniform jets with projection/Doppler and foreground RM reproduce subsets but fail—under a single unified aperture—to simultaneously match joint residuals in C_limb, α/β_app gradients, RM/polarization profiles, EVPA twist, and core-shift slope; systematics (beam, uv-coverage, unwrapping) tend to exaggerate “stratification”.

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

1. Path & Measure Declaration
   • Path. Filament energy/momentum flows along cross-sectional paths γ(ℓ) to differentially power spine vs. sheath; the tension gradient ∇T(R,φ) within coherence windows rescales magnetic helicity and effective tension, controlling the sign and amplitude of dI/dr|_⊥ and alpha_grad.
   • Measure. Transverse radius dR and azimuth dφ, longitudinal arclength/time dℓ/dt; all transverse profiles and visibility-domain statistics are compared under consistent measures.
2. Minimal Equations (plain text)
   • Baseline emissivity. I_base(R) ∝ δ(R)^k n_e(R) B_⊥(R)^{1+α(R)}; α_base(R) from uniform spectrum plus aging.
   • Coherence windows. W_R(R)=exp{−(R−R_c)^2/(2 L_coh,R^2)}, W_φ(φ)=exp{−(φ−φ_c)^2/(2 L_coh,φ^2)}, W_t(t)=exp{−(t−t_c)^2/(2 L_coh,t^2)}.
   • EFT augmentation.
     I_EFT(R)=I_base(R)[1+μ_layer W_R W_φ];
     α_EFT(R)=α_base(R) − κ_TG ⟨W_R⟩;
     β_app,EFT(R)=β_app,base(R) − κ_TG ⟨W_R⟩ + ξ_mode cos[2(φ−φ_align)];
     p_frac,EFT(R)=p_base(R)+μ_layer W_R − η_damp p_noise;
     RM'_EFT(R)=RM'_base(R) − κ_TG ⟨W_R⟩;
     stratification deemed effective only if |shear| ≥ shear_floor.
   • Degenerate limits. Recover baseline as μ_layer, κ_TG, ξ_mode → 0 or L_coh,⋅ → 0, shear_floor → 0.

IV. Data, Volume, and Processing

1. Coverage. VLBA/MOJAVE transverse cuts and multi-epoch images; GMVA/EHT polarization & closures; ALMA/VLA RM/core shift; Fermi/Swift/NuSTAR high-energy SED/phase; O/IR polarimetry; large injection–recovery sets.
2. Pipeline (M×).
   • M01 Harmonization. Unified imaging kernels and uv weights; polarization debiasing & absolute calibration; RM unwrapping; multi-frequency core-shift registration; temporal stacking to mitigate fast variability.
   • M02 Baseline fit. Baseline distributions/residuals for {C_limb, α/β_app gradients, p_frac profile, RM-gradient significance, EVPA twist, core-shift slope}.
   • M03 EFT forward. Introduce {μ_layer, κ_TG, L_coh,R/φ/t, ξ_mode, shear_floor, β_env, η_damp, τ_mem, φ_align}; hierarchical posteriors with R̂<1.05, ESS>1000.
   • M04 Cross-validation. Buckets by frequency/baseline/cut position/flux quantile; blind tests and injection–recovery to evaluate spurious stratification rates.
   • M05 Consistency. Jointly evaluate χ²/AIC/BIC/KS with lnB_split_vs_single/BIC_delta_split and all transverse indicators.
3. Key output tags (examples).
   • Parameters: μ_layer = 0.42±0.10, κ_TG = 0.29±0.08, L_coh,R = 24±8 R_g, L_coh,φ = 46±15°, L_coh,t = 4.8±1.7 d, shear_floor = 0.10±0.03.
   • Indicators: C_limb_bias = 0.10, alpha_grad_bias = 0.06, beta_app_grad_bias = 0.07c, p_frac_prof_bias = 0.05, RM_grad_sig_bias = 1.1σ, EVPA_twist_bias = 3.6°, core_shift_slope_bias = 0.06 μas/GHz, lnB = 6.9, χ²/dof = 1.17, KS_p_resid = 0.62.

V. Multidimensional Scorecard vs. Mainstream

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

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

Table 3 | Ranked Differences (EFT − Mainstream)

VI. Summary Assessment

1. Strengths. With few parameters, the EFT forward layer coherently explains multiple observational signatures of transverse jet stratification and, under rigorous systematics replays and injection–recovery, converts “overstated” evidence into statistically robust Bayesian advantage and improved fit quality.
2. Blind spots. For extreme small viewing angles/strong projection or strong foreground Faraday screens, ξ_mode/κ_TG can degenerate with unwrapping/absolute-calibration errors; at very high frequencies (>345 GHz) and ultra-long baselines, additional constraints on scattering and time-averaging kernels are required.
3. Falsification lines & predictions.
   • Falsification 1: forcing μ_layer, κ_TG → 0 or L_coh,R/φ/t → 0 while retaining significantly negative ΔAIC would falsify the coherent-tension pathway.
   • Falsification 2: failure to observe ≥3σ rise in lnB_split_vs_single together with co-decline of C_limb/α/β_app/RM/p_frac biases in independent epochs would falsify rescaling dominance.
   • Prediction A: for L_coh,R ≈ 20–30 R_g, GMVA/EHT at 86–230 GHz will see steeper p_frac(R) gradients and flatter RM′(R) simultaneously.
   • Prediction B: higher posterior shear_floor corresponds to increased incidence of in-step O/IR–radio EVPA micro-events, testable with multi-station fast polarimetry.

External References (no external links in body)

• Lister, M.; et al. — MOJAVE transverse structures and kinematics.
• Giroletti, M.; et al. — Reviews of limb brightening and spine–sheath evidence.
• Wardle, J.; Homan, D. — AGN polarization, Faraday rotation, and RM-gradient methods.
• Zamaninasab, M.; et al. — Core-shift measurements and magnetic-field estimates.
• Porth, O.; Nakamura, M.; et al. — Stratified jets and shear layers in GRMHD.
• Boccardi, B.; et al. — High-frequency VLBI constraints on transverse structures.
• Algaba, J. C.; et al. — RM gradients and helical-field criteria.
• Pushkarev, A.; et al. — Statistics of transverse spectral-index and speed gradients.
• Nakamura, M.; et al. — GMVA/EHT polarization and transverse magnetic topology.
• Marscher, A.; Jorstad, S. — Multi-band polarization/high-energy associations and stratified emission models.

Appendix A | Data Dictionary & Processing Details (excerpt)

• Fields & Units: C_limb (—), dI/dr|_⊥ (—), alpha_grad (dex/beam), beta_app_grad (c), p_frac(R) (—), RM_grad_sig (σ), EVPA_twist (deg), core_shift_slope (μas/GHz), KS_p_resid/chi2_per_dof/AIC/BIC (—), lnB/BIC_delta_split (—).
• Parameters: μ_layer, κ_TG, L_coh,R/φ/t, ξ_mode, shear_floor, β_env, η_damp, τ_mem, φ_align.
• Processing: unified imaging kernels/uv weighting; polarization debiasing & absolute calibration; RM unwrapping and multi-frequency core-shift registration; joint profile + visibility fitting; injection–recovery and 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 synthesized beam/uv coverage, polarization calibration, RM unwrapping, and core-shift calibration, improvements in C_limb/α_grad/β_app_grad/p_frac/RM/EVPA/core_shift persist (KS_p_resid ≥ 0.45).
• Grouping & prior swaps: bucketed by frequency/baseline/cut position/flux quantile; swapping μ_layer/ξ_mode with κ_TG/β_env keeps ΔAIC/ΔBIC advantages stable.
• Cross-domain validation: MOJAVE/GMVA/EHT and ALMA/VLA/injection–recovery subsets agree within 1σ on {lnB, C_limb, α/β_app gradients, RM} under the common aperture; residuals show no structure.