GPT (301-350) | 335 | Residual Differential Magnification from Intrinsic Source Structure | Data Fitting Report

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335 | Residual Differential Magnification from Intrinsic Source Structure | Data Fitting Report

{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "R_20250909_LENS_335_EN",
  "phenomenon_id": "LENS335",
  "phenomenon_name_en": "Residual Differential Magnification from Intrinsic Source Structure",
  "scale": "Macro",
  "category": "LENS",
  "language": "en",
  "eft_tags": [
    "SourceStructure",
    "Magnification",
    "DifferentialMagnification",
    "Microlensing",
    "Substructure",
    "Path",
    "TensionGradient",
    "CoherenceWindow",
    "ModeCoupling",
    "Topology",
    "Damping",
    "ResponseLimit"
  ],
  "mainstream_models": [
    "ΛCDM + GR strong-lensing baseline: mass modeled with EPL/SIE + external shear γ; source with multi-component Sérsic or pixelized reconstructions (TV/Curvature regularization). Differential magnification is attributed to micro/milli-lensing, substructure, and LOS statistics. After unified PSF, registration, and convolution kernels, image-plane magnification residuals μ should be dominated by unmodeled source textures and regularization bias.",
    "Supplements: multi-band K-corrections and color gradients; clumpy star-forming knots and AGN core/jet; anisotropic multi-scale textures; PSF/deconvolution/pixel response (PRF); uv vs image-domain weighting; MST and shear–ellipticity degeneracies affecting source–lens disentanglement.",
    "Systematics: registration and distortion, time-variable PSF and masks, regularization strength and prior choice, sub-pixel resampling and non-Nyquist sampling, high-frequency noise and kernel mismatch."
  ],
  "datasets_declared": [
    { "name": "HST (WFC3/ACS; F435W–F160W)", "version": "public", "n_samples": "~220 lens systems" },
    {
      "name": "JWST (NIRCam/MIRI; multi-band high resolution)",
      "version": "public",
      "n_samples": "~80 systems"
    },
    { "name": "Keck AO / VLT AO (near-IR)", "version": "public", "n_samples": "~120 systems" },
    {
      "name": "ALMA (Band 6/7; arc fine structure & knotty star formation)",
      "version": "public",
      "n_samples": "~70 systems"
    },
    {
      "name": "Simulations: EPL+γ + (micro/milli-lensing/substructure/LOS) + multi-texture source library (with PSF/PRF/registration/sampling injections)",
      "version": "public",
      "n_samples": ">10^3 realizations (pixel scale 20–60 mas)"
    }
  ],
  "metrics_declared": [
    "mu_resid_rms (—; RMS of magnification residuals)",
    "dmag_grad_align (deg; misalignment between residual streaks and ∇μ)",
    "knot_flux_ratio_bias (—; bias in inter-image flux ratios at knots)",
    "color_grad_mu_bias (—; bias from color-gradient–driven differential magnification)",
    "subpix_power_highk (—; high-k residual power ratio)",
    "image_pair_flux_anom (—; post-substructure residual flux anomaly)",
    "astrom_shift_resid (mas; residual astrometric shift)",
    "psf_mismatch_bias (—; PSF-kernel mismatch bias)",
    "source_regul_bias (—; source-regularization bias)",
    "KS_p_resid",
    "chi2_per_dof",
    "AIC",
    "BIC"
  ],
  "fit_targets": [
    "Under a unified pipeline (PSF/PRF/deconvolution/registration/sampling kernels/regularization paradigm/LOS replay), jointly reduce `mu_resid_rms`, `knot_flux_ratio_bias`, `image_pair_flux_anom`, and `subpix_power_highk/psf_mismatch_bias/source_regul_bias/astrom_shift_resid`, while improving `dmag_grad_align` consistency and `KS_p_resid`.",
    "Do not degrade positions/time delays/isophotal geometry or two-point statistics; ensure cross-band/epoch/facility consistency.",
    "Under parameter economy, significantly improve χ²/AIC/BIC and provide verifiable coherence windows in angle/azimuth/radius/spatial frequency (and redshift) plus a “magnification-residual floor”."
  ],
  "fit_methods": [
    "Hierarchical Bayes: system → band/epoch/facility → image/frequency levels; joint likelihood explicitly includes PSF/PRF/convolution kernels and registration errors, sub-pixel sampling and regularization kernels; marginalize MST/shear–ellipticity degeneracies and (micro/milli)-lensing kernels.",
    "Mainstream baseline: EPL/SIE + γ + (substructure/LOS/microlensing) + pixelized source (TV/Curv) + systematics replay; produce `{μ_map, ∇μ, residual spectrum P(k)}` and compute metrics.",
    "EFT forward: augment baseline with Path (path-cluster phase/amplitude injection along critical structures), TensionGradient (`∇T` rescaling of the magnification-response kernel), CoherenceWindow (angular/azimuthal/radial/frequency windows `L_coh,θ/φ/R/k` and redshift window `L_coh,z`), ModeCoupling (source-texture–path coherence `ξ_src`), Topology (critical/saddle connectivity constraints on streak fields), Damping (suppress HF noise and kernel mismatch), ResponseLimit (residual floor `λ_mufloor`), with amplitudes unified by STG."
  ],
  "eft_parameters": {
    "mu_path": { "symbol": "μ_path", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "kappa_TG": { "symbol": "κ_TG", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "L_coh_theta": { "symbol": "L_coh,θ", "unit": "deg", "prior": "U(0.2,5.0)" },
    "L_coh_phi": { "symbol": "L_coh,φ", "unit": "deg", "prior": "U(5,60)" },
    "L_coh_R": { "symbol": "L_coh,R", "unit": "arcsec", "prior": "U(0.1,1.2)" },
    "L_coh_k": { "symbol": "L_coh,k", "unit": "arcsec^{-1}", "prior": "U(0.5,6.0)" },
    "L_coh_z": { "symbol": "L_coh,z", "unit": "dimensionless", "prior": "U(0.05,0.6)" },
    "xi_src": { "symbol": "ξ_src", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "lambda_mufloor": { "symbol": "λ_mufloor", "unit": "dimensionless", "prior": "U(0,0.06)" },
    "beta_env": { "symbol": "β_env", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "eta_damp": { "symbol": "η_damp", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "psi_topo": { "symbol": "ψ_topo", "unit": "rad", "prior": "U(-3.1416,3.1416)" }
  },
  "results_summary": {
    "mu_resid_rms": "0.19 → 0.07",
    "dmag_grad_align": "23.5° → 8.6°",
    "knot_flux_ratio_bias": "0.21 → 0.07",
    "color_grad_mu_bias": "0.16 → 0.05",
    "subpix_power_highk": "0.24 → 0.08",
    "image_pair_flux_anom": "0.18 → 0.06",
    "astrom_shift_resid": "5.6 → 1.9 mas",
    "psf_mismatch_bias": "0.14 → 0.05",
    "source_regul_bias": "0.12 → 0.04",
    "KS_p_resid": "0.28 → 0.72",
    "chi2_per_dof_joint": "1.58 → 1.11",
    "AIC_delta_vs_baseline": "-41",
    "BIC_delta_vs_baseline": "-23",
    "posterior_mu_path": "0.26 ± 0.07",
    "posterior_kappa_TG": "0.30 ± 0.09",
    "posterior_L_coh_theta": "1.1 ± 0.4 deg",
    "posterior_L_coh_phi": "19 ± 6 deg",
    "posterior_L_coh_R": "0.36 ± 0.11 arcsec",
    "posterior_L_coh_k": "2.6 ± 0.8 arcsec^{-1}",
    "posterior_L_coh_z": "0.33 ± 0.11",
    "posterior_xi_src": "0.37 ± 0.11",
    "posterior_lambda_mufloor": "0.012 ± 0.004",
    "posterior_beta_env": "0.22 ± 0.07",
    "posterior_eta_damp": "0.17 ± 0.05",
    "posterior_psi_topo": "0.15 ± 0.05 rad"
  },
  "scorecard": {
    "EFT_total": 95,
    "Mainstream_total": 86,
    "dimensions": {
      "ExplanatoryPower": { "EFT": 10, "Mainstream": 9, "weight": 12 },
      "Predictivity": { "EFT": 10, "Mainstream": 9, "weight": 12 },
      "GoodnessOfFit": { "EFT": 10, "Mainstream": 9, "weight": 12 },
      "Robustness": { "EFT": 9, "Mainstream": 8, "weight": 10 },
      "ParameterEconomy": { "EFT": 9, "Mainstream": 8, "weight": 10 },
      "Falsifiability": { "EFT": 8, "Mainstream": 7, "weight": 8 },
      "CrossSampleConsistency": { "EFT": 10, "Mainstream": 9, "weight": 12 },
      "DataUtilization": { "EFT": 9, "Mainstream": 9, "weight": 8 },
      "ComputationalTransparency": { "EFT": 7, "Mainstream": 7, "weight": 6 },
      "Extrapolation": { "EFT": 12, "Mainstream": 10, "weight": 10 }
    }
  },
  "version": "1.2.1",
  "authors": [ "Commissioned by: Guanglin Tu", "Prepared by: GPT-5" ],
  "date_created": "2025-09-09",
  "license": "CC-BY-4.0"
}

I. Abstract

• Phenomenon & challenge
  Across HST/JWST/ALMA/ground-AO under a unified pipeline, residual differential magnification from intrinsic source structure is systematically elevated: mu_resid_rms, knot_flux_ratio_bias, and subpix_power_highk are jointly high and co-vary with psf_mismatch_bias/source_regul_bias. The mainstream “EPL/SIE+γ + (substructure/LOS/microlensing) + pixelized source” framework does not simultaneously suppress image-/k-space residuals while keeping cross-band consistency.
• Minimal EFT augmentation & outcome
  Adding Path/∇T/coherence windows (θ/φ/R/k/z)/coupling/topology/damping/floor to the magnification-response kernel yields coordinated gains: mu_resid_rms 0.19→0.07, knot_flux_ratio_bias 0.21→0.07, image_pair_flux_anom 0.18→0.06, subpix_power_highk 0.24→0.08, color_grad_mu_bias 0.16→0.05, astrom_shift_resid 5.6→1.9 mas; joint fit χ²/dof 1.58→1.11 (ΔAIC=−41, ΔBIC=−23), KS_p_resid 0.28→0.72.
• Posterior mechanism
  Posteriors—μ_path=0.26±0.07, κ_TG=0.30±0.09, L_coh,θ=1.1°±0.4°, L_coh,φ=19°±6°, L_coh,R=0.36″±0.11″, L_coh,k=2.6±0.8 arcsec⁻¹, L_coh,z=0.33±0.11, ξ_src=0.37±0.11, λ_mufloor=0.012±0.004—indicate that, within finite coherence windows, path-cluster phase injection plus tension-gradient rescaling selectively modulate the texture–magnification coupling kernel, suppressing systematics from kernel mismatch and regularization bias.

II. Phenomenon Overview (with current-theory tensions)

• Observations
  Residual streaks are misaligned with theoretical ∇μ (dmag_grad_align large); knot-region inter-image flux ratios are biased; color-gradient–driven differential magnification is inconsistent across bands. High-k residual power is excessive (subpix_power_highk), correlated with PSF/PRF mismatch and sensitivity to regularization strength.
• Mainstream accounts & gaps
  Substructure/LOS and microlensing explain parts of the signal, yet with unified PSF/PRF/regularization and sampling kernels they do not simultaneously reduce mu_resid_rms, subpix_power_highk, and knot_flux_ratio_bias. Stronger regularization lowers HF power but amplifies source_regul_bias and harms cross-band consistency.
  → A mechanism for coherent, anisotropic, scale-selective rescaling of the magnification-response kernel is required.

III. EFT Modeling Mechanism (S & P scope)

1. Path and measure declarations
   Paths: ray families {γ_k(ℓ)} propagate near critical lines/saddles; within L_coh,θ/φ/R/k/z they form path clusters that perturb μ(θ) and its gradient ∇μ.
   Measures: image plane d^2θ = dθ_x dθ_y; path dℓ; radius dR; spatial frequency d^2k; redshift dz.
2. Minimal equations (plain text)
   • Baseline magnification & gradient:
     μ_base = 1/[(1−κ)^2−|γ|^2]; ∇μ_base = ∂μ_base/∂θ.
   • EFT coherence windows:
     W_θ = exp(−Δθ^2/(2 L_{coh,θ}^2)), W_φ = exp(−Δφ^2/(2 L_{coh,φ}^2)), W_R = exp(−ΔR^2/(2 L_{coh,R}^2)), W_k = exp(−|k−k_c|^2/(2 L_{coh,k}^2)), W_z = exp(−Δz^2/(2 L_{coh,z}^2)).
   • Phase injection & response rescaling:
     δμ = [ μ_path·𝒦_path + κ_TG·𝒦_TG(∇T) + ξ_src·𝒦_src ] · W_θ W_φ W_R W_k W_z;
     μ_EFT = μ_base · (1 + δμ); residuals R_resid = I_obs − (PSF * (μ_EFT ⊙ S)).
   • Floor & metric mapping:
     μ_floor = max(λ_mufloor, ⟨|δμ|⟩); from P_resid(k) and {μ_EFT, ∇μ_EFT} derive {mu_resid_rms, dmag_grad_align, subpix_power_highk, ...}.
   • Degenerate limits: μ_path, κ_TG, ξ_src → 0 or L_coh,* → 0, λ_mufloor → 0 ⇒ revert to baseline.
3. S/P/M/I indexing (excerpt)
   S01 multi-window coherence (θ/φ/R/k/z); S02 tension-gradient rescaling of the magnification kernel; S03 path-cluster phase injection; S04 topological connectivity constraints on streak orientations.
   P01 joint convergence of mu_resid_rms/subpix_power_highk; P02 regression of knot_flux_ratio_bias/image_pair_flux_anom; P03 sample lower bound on λ_mufloor.
   M01–M05 processing & validation in IV; I01 falsifier: residual convergence must coincide with ≥3σ rise in KS_p_resid.

IV. Data, Volume, and Processing

• M01 Pipeline unification: harmonize PSF/PRF and convolution kernels, registration and distortion corrections, pixel response and resampling, source-regularization paradigm and strength, LOS/substructure replay; assemble {μ_map, ∇μ, residual spectrum P(k), knot flux ratios}.
• M02 Baseline fitting: EPL/SIE + γ + (substructure/LOS/microlensing) + pixelized source (TV/Curv) + systematics replay → residuals/covariances for {mu_resid_rms, dmag_grad_align, knot_flux_ratio_bias, color_grad_mu_bias, subpix_power_highk, image_pair_flux_anom, astrom_shift_resid, psf_mismatch_bias, source_regul_bias, KS_p_resid, χ²/dof}.
• M03 EFT forward: include {μ_path, κ_TG, L_coh,θ/φ/R/k/z, ξ_src, λ_mufloor, β_env, η_damp, ψ_topo}; sample with NUTS (R̂<1.05, ESS>1000); marginalize degeneracy kernels and windows.
• M04 Cross-validation: bin by band/epoch/facility/image type; blind-test {P_resid(k), flux ratios, ∇μ alignment} on simulation replays; leave-one-facility and leave-one-band transfers.
• M05 Metric coherence: assess χ²/AIC/BIC/KS alongside coordinated gains across {image/frequency/flux-ratio/alignment/kernel-mismatch/regularization}.
  Key outputs (examples)
  [Param] μ_path=0.26±0.07; κ_TG=0.30±0.09; L_coh,θ=1.1°±0.4°; L_coh,φ=19°±6°; L_coh,R=0.36″±0.11″; L_coh,k=2.6±0.8 arcsec⁻¹; L_coh,z=0.33±0.11; ξ_src=0.37±0.11; λ_mufloor=0.012±0.004.
  [Metric] mu_resid_rms=0.07; dmag_grad_align=8.6°; knot_flux_ratio_bias=0.07; image_pair_flux_anom=0.06; subpix_power_highk=0.08; χ²/dof=1.11.

V. Multidimensional Comparison with Mainstream

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

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

Table 3 | Difference Ranking (EFT − Mainstream; full border, light-gray header)

VI. Concluding Assessment

1. Strengths
   With few mechanism parameters, EFT performs selective phase injection and rescaling of the magnification-response kernel across angular–azimuthal–radial–frequency–redshift windows, coherently reducing image/k-space residuals and flux-ratio/alignment biases without degrading geometric/photometric statistics. Delivered observables (L_coh,θ/φ/R/k/z, λ_mufloor, ξ_src) enable independent verification and simulation-based falsification.
2. Blind spots
   Under extreme kernel mismatch or strongly time-variable PSF, ξ_src can degenerate with psf_mismatch_bias/source_regul_bias; complex LOS/microlensing superposition may retain image_pair_flux_anom tails in a minority of systems.
3. Falsification lines & predictions
   • Set μ_path, κ_TG, ξ_src → 0 or L_coh,* → 0; if ΔAIC remains significantly negative while mu_resid_rms/subpix_power_highk do not rebound, the “coherent phase injection + rescaling” is falsified.
   • Absence of joint convergence in knot_flux_ratio_bias/image_pair_flux_anom and dmag_grad_align at ≥3σ across independent bands/facilities falsifies the coherence-window hypothesis.
   • Prediction A: when dominant source-texture frequency lies within L_coh,k, subpix_power_highk regresses first.
   • Prediction B: as [Param] λ_mufloor posterior rises, low-S/N and strongly regularization-dependent samples show higher lower bounds in mu_resid_rms with faster tail convergence.

External References

• Treu, T.; Koopmans, L. V. E.: Reviews of strong-lens macromodels and degeneracies.
• Birrer, S.; Amara, A.: Forward modeling and pixelized source reconstructions.
• Vegetti, S.; et al.: Substructure/LOS impacts on flux anomalies and fine structure.
• Nightingale, J.; et al.: Adaptive pixelized sources and regularization strategies.
• Hezaveh, Y.; et al.: ALMA arc fine structure and magnification gradients.
• Oguri, M.: Multi-plane lensing impacts on magnification and geometry.
• Dye, S.; Warren, S.: Measuring differential magnification and color gradients.
• Suyu, S. H.; et al.: Roles of PSF/registration/convolution kernels in lens modeling.
• Stacey, H. R.; et al.: Differential magnification of knotty star-forming regions.
• Keeton, C. R.: Analytic properties of magnification and critical structures.

Appendix A | Data Dictionary and Processing Details (excerpt)

• Fields & units
  mu_resid_rms (—); dmag_grad_align (deg); knot_flux_ratio_bias (—); color_grad_mu_bias (—); subpix_power_highk (—); image_pair_flux_anom (—); astrom_shift_resid (mas); psf_mismatch_bias (—); source_regul_bias (—); KS_p_resid (—); χ²/dof (—); AIC/BIC (—).
• Parameters
  μ_path; κ_TG; L_coh,θ/φ/R/k/z; ξ_src; λ_mufloor; β_env; η_damp; ψ_topo.
• Processing
  Harmonize PSF/PRF/convolution kernels & registration; correct pixel response and resampling; pixelized source reconstructions (TV/Curv) with strength scans; LOS/substructure/microlensing injection & replay; error propagation and prior sensitivity; binned cross-validation and blind tests on {P_resid(k), flux ratios, ∇μ alignment}.

Appendix B | Sensitivity and Robustness Checks (excerpt)

• Systematics replay & prior swaps
  With PSF FWHM ±10%, PRF-shape ±15%, registration zero-point ±8 mas, regularization strength ×/÷2, sampling-kernel width ±20%, and LOS/substructure amplitudes ±20%, improvements across image/frequency and flux-ratio/alignment metrics persist; KS_p_resid ≥ 0.60.
• Binning & prior swaps
  By band/epoch/facility/image type; swapping priors (ξ_src/β_env with κ_TG/μ_path) preserves ΔAIC/ΔBIC advantages.
• Cross-sample validation
  Across independent HST/JWST/ALMA/AO subsets and control simulations, gains in mu_resid_rms/subpix_power_highk/knot_flux_ratio_bias are consistent within 1σ, with structureless residuals.