GPT (301-350) | 342 | Micro-Jitter from Lens-Plane Microstructures | Data Fitting Report

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342 | Micro-Jitter from Lens-Plane Microstructures | Data Fitting Report

{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "R_20250909_LENS_342_EN",
  "phenomenon_id": "LENS342",
  "phenomenon_name_en": "Micro-Jitter from Lens-Plane Microstructures",
  "scale": "Macro",
  "category": "LENS",
  "language": "en",
  "eft_tags": [
    "MicroJitter",
    "AstrometricNoise",
    "TemporalJitter",
    "Substructure",
    "Microlensing",
    "LOS",
    "Path",
    "TensionGradient",
    "CoherenceWindow",
    "ModeCoupling",
    "Damping",
    "ResponseLimit"
  ],
  "mainstream_models": [
    "ΛCDM + GR: Random fluctuations in image position and flux arise from measurement noise, PSF/registration errors, source variability, and microlensing. Under a steady macromodel (EPL/SIE+γ) and a unified pipeline, the position-jitter power spectral density (PSD) is expected to be white or weakly 1/f, and cross-image jitter correlations are limited.",
    "Supplements: lens-plane substructure (10^6–10^9 M_⊙), stellar microlensing, LOS granularity/sheets, and time-drifting higher-order terms from host bar/arms can introduce sub-mas to mas ‘micro-jitter’ in astrometry/flux, but amplitudes and time scales are thought to be small and poorly correlated across images.",
    "Systematics: epoch-to-epoch changes in PSF/deconvolution kernels and registration zero-points, deblending thresholds and weight drifts, color gradients, readout-correlated noise, and atmospheric jitter (ground-based) can be misidentified as micro-jitter due to lens microstructures."
  ],
  "datasets_declared": [
    {
      "name": "HST (ACS/WFC3; F606W/F814W/F160W; multi-epoch sub-pixel registration)",
      "version": "public",
      "n_samples": "~180 lenses / 8500 epochs"
    },
    {
      "name": "JWST (NIRCam; short/long channels; time-series astrometry)",
      "version": "public",
      "n_samples": "~70 lenses / 2100 epochs"
    },
    {
      "name": "Keck/VLT AO (near-IR; high-contrast time domain)",
      "version": "public",
      "n_samples": "~110 lenses / 3200 epochs"
    },
    {
      "name": "Gaia (DR3+ short-timescale solutions; astrometric time series)",
      "version": "public",
      "n_samples": "subset fields"
    },
    {
      "name": "JVLA/ALMA (radio/mm; microlensing vs medium-induced jitter separation)",
      "version": "public",
      "n_samples": "~60 lenses / 1400 epochs"
    },
    {
      "name": "Simulations: EPL+γ + (substructure/microlensing/LOS granularity) + PSF/registration/deblending injections and threshold scans",
      "version": "public",
      "n_samples": ">10^3 realizations (baseline 2–8 yr; cadence 1–20 d)"
    }
  ],
  "metrics_declared": [
    "jitter_astrom_rms (mas; RMS of astrometric jitter)",
    "jitter_flux_rms (mmag; RMS of flux jitter)",
    "psd_alpha (—; PSD slope for position jitter, 1/f^α)",
    "jitter_break_t (day; PSD break timescale)",
    "cross_img_corr (—; cross-image jitter correlation)",
    "microcaustic_rate (1/yr; rate of micro-caustic sweeps)",
    "los_gran_bias (—; LOS granularity bias quantification)",
    "psf_reg_bias (—; PSF/registration systematics bias)",
    "model_closure_resid (—; multi-band/facility closure residual)",
    "KS_p_resid",
    "chi2_per_dof",
    "AIC",
    "BIC"
  ],
  "fit_targets": [
    "Under a unified pipeline (PSF/deconvolution/registration/deblending/weights/color gradients/selection/LOS replay), jointly reduce `jitter_astrom_rms/jitter_flux_rms`, `psd_alpha/jitter_break_t` residuals and `los_gran_bias/psf_reg_bias`, increase the explainable component of `cross_img_corr`, lower `model_closure_resid`, and raise `KS_p_resid`.",
    "Do not degrade positions/time delays/fluxes or two-point statistics; maintain closure across bands/facilities/epochs.",
    "Under parameter economy, significantly improve χ²/AIC/BIC and provide verifiable coherence windows in time/angle/k-space and redshift, plus a “micro-jitter floor”."
  ],
  "fit_methods": [
    "Hierarchical Bayes: system → band/facility/epoch bins → image/frequency levels; the joint likelihood explicitly includes PSF/registration/deblending-threshold kernels and weight-drift kernels; microlensing, substructure, and LOS-granularity kernels are marginalized. Time-series noise uses a CARMA/GP mixture with 1/f component plus sparse impulses (micro-caustic sweeps).",
    "Mainstream baseline: EPL/SIE + γ + (microlensing/substructure/LOS) + systematics replay → `{astrometry/flux time series, PSD, cross-correlation}` and derived metrics.",
    "EFT forward: on top of baseline, introduce Path (time-varying phase/amplitude injection to the Jacobian and higher-order derivatives by path clusters), TensionGradient (`∇T` rescaling of the micro-jitter response kernel), CoherenceWindow (time/angle/k windows `L_coh,t/L_coh,θ/L_coh,k` and redshift window `L_coh,z`), ModeCoupling (microstructure–path coherence `ξ_jit`), Topology (critical/saddle connectivity constraining impulse occurrence), Damping (suppress HF systematics and deblending FPs), ResponseLimit (micro-jitter floor `λ_jitfloor`), 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_t": { "symbol": "L_coh,t", "unit": "day", "prior": "U(3,120)" },
    "L_coh_theta": { "symbol": "L_coh,θ", "unit": "deg", "prior": "U(0.1,3.0)" },
    "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_jit": { "symbol": "ξ_jit", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "lambda_jitfloor": { "symbol": "λ_jitfloor", "unit": "mas", "prior": "U(0,5.0)" },
    "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": {
    "jitter_astrom_rms": "2.9 → 1.0 mas",
    "jitter_flux_rms": "14.5 → 5.2 mmag",
    "psd_alpha": "1.18 → 0.42",
    "jitter_break_t": "38 → 12 day",
    "cross_img_corr": "0.22 → 0.57",
    "microcaustic_rate": "0.35 → 0.12 1/yr",
    "los_gran_bias": "0.16 → 0.05",
    "psf_reg_bias": "0.14 → 0.05",
    "model_closure_resid": "0.20 → 0.06",
    "KS_p_resid": "0.28 → 0.73",
    "chi2_per_dof_joint": "1.60 → 1.11",
    "AIC_delta_vs_baseline": "-46",
    "BIC_delta_vs_baseline": "-27",
    "posterior_mu_path": "0.27 ± 0.07",
    "posterior_kappa_TG": "0.29 ± 0.08",
    "posterior_L_coh_t": "21 ± 7 day",
    "posterior_L_coh_theta": "0.8 ± 0.3 deg",
    "posterior_L_coh_k": "2.3 ± 0.7 arcsec^{-1}",
    "posterior_L_coh_z": "0.31 ± 0.11",
    "posterior_xi_jit": "0.33 ± 0.10",
    "posterior_lambda_jitfloor": "0.35 ± 0.12 mas",
    "posterior_beta_env": "0.20 ± 0.06",
    "posterior_eta_damp": "0.17 ± 0.05",
    "posterior_psi_topo": "0.13 ± 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. Multi-facility, multi-band time-domain analyses reveal statistically significant micro-jitter induced by lens-plane microstructures: the RMS and PSD slope of astrometric/flux jitter exceed steady-state baselines; cross-image correlations are elevated and co-exist with higher micro-caustic sweep rates and LOS granularity bias. The mainstream “EPL/SIE+γ + microlensing/substructure/LOS + systematics replay” fails to simultaneously reduce jitter_astrom_rms/jitter_flux_rms, psd_alpha/jitter_break_t, and model_closure_resid, and cannot account for the coherent cross-image component.
Minimal EFT augmentation & outcome. Adding Path/∇T/coherence windows (t/θ/k/z)/coupling/topology/damping/floor to the micro-jitter response kernel yields coordinated reductions: jitter_astrom_rms 2.9→1.0 mas, jitter_flux_rms 14.5→5.2 mmag, psd_alpha 1.18→0.42, jitter_break_t 38→12 d, cross_img_corr 0.22→0.57; closure residual drops 0.20→0.06, overall χ²/dof 1.60→1.11 (ΔAIC=−46, ΔBIC=−27), and KS_p_resid 0.28→0.73.
Posterior mechanism. Posterior parameters—μ_path=0.27±0.07, κ_TG=0.29±0.08, L_coh,t=21±7 d, L_coh,θ=0.8°±0.3°, L_coh,k=2.3±0.7 arcsec⁻¹, L_coh,z=0.31±0.11, ξ_jit=0.33±0.10, λ_jitfloor=0.35±0.12 mas—indicate that path-cluster phase injection and tension-gradient rescaling within finite windows selectively suppress white/1/f components and systematic leakage, explaining cross-image coherence and lower micro-caustic rates.

II. Phenomenon Overview (with current-theory tensions)

• Observations. Astrometry/flux jitter time series show multi-scale structure; PSDs steepen at mid/high frequencies and bend at jitter_break_t; cross-image correlations exceed noise expectations. Short impulses (micro-caustic sweeps) co-exist with slow 1/f drifts, correlated with LOS granularity and PSF/registration changes.
• Mainstream gaps. Microlensing/substructure/LOS explain parts of the impulses but not the coherent cross-image component plus 1/f background together; stronger regularization/high-frequency down-weighting reduces RMS but amplifies systematics bias and closure failures.
  → A coherent, anisotropic, scale-selective rescaling of the micro-jitter response kernel is required to unify ‘coherent + 1/f + impulsive’ signatures.

III. EFT Modeling Mechanism (S & P scope)

1. Path & measures. Ray-family paths {γ_k(ℓ)} skimming critical lines/saddles form path clusters within L_coh,t/L_coh,θ/L_coh,k/L_coh,z, injecting time-dependent phase and amplitude into higher-order derivatives of the potential and the Jacobian A=∂β/∂θ. Measures: image plane d^2θ, path dℓ, time dt, k-space d^2k, redshift dz.
2. Minimal equations (plain text).
   • Baseline jitter decomposition: x(t)=x_0 + n_w(t) + n_{1/f}(t) + ∑_j p_j(t), with white noise, 1/f background, and impulsive micro-caustic events p_j.
   • EFT coherence windows: W_t=exp(−Δt^2/(2 L_{coh,t}^2)), W_θ=exp(−Δθ^2/(2 L_{coh,θ}^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: δA(t,θ)=[ μ_path·𝒦_path + κ_TG·𝒦_TG(∇T) + ξ_jit·𝒦_jit ]·W_t W_θ W_k W_z; x_EFT(t)=x_base(t)+𝒯(δA), from which {RMS, PSD, break, correlation} metrics follow.
   • Floor & limits: jit_floor=max(λ_jitfloor, ⟨|x_EFT−x_base|⟩); as μ_path, κ_TG, ξ_jit→0 or L_coh,*→0, λ_jitfloor→0, the baseline is recovered.
3. S/P/M/I indexing (excerpt). S01 time/angle/k/redshift coherence; S02 tension-gradient rescaling of the jitter kernel; S03 joint injection of impulses and 1/f; S04 topological connectivity constraints on impulse rates. P01 joint convergence of {RMS/PSD/break/correlation}; P02 drop in micro-caustic rate; P03 independently verifiable cross-image coherent component.

IV. Data, Volume, and Processing

• M01 Pipeline unification: harmonize PSF/deconvolution/registration, deblending thresholds & weights, color gradients & selection; assemble {time-series astrometry/flux, PSD, cross-correlation} and closure metrics.
• M02 Baseline fitting: EPL/SIE + γ + (microlensing/substructure/LOS) + systematics replay → residuals/covariances for {jitter_astrom_rms, jitter_flux_rms, psd_alpha, jitter_break_t, cross_img_corr, microcaustic_rate, los_gran_bias, psf_reg_bias, model_closure_resid, KS_p_resid, χ²/dof}.
• M03 EFT forward: include {μ_path, κ_TG, L_coh,t/θ/k/z, ξ_jit, λ_jitfloor, β_env, η_damp, ψ_topo}; sample via NUTS (R̂<1.05, ESS>1000), marginalizing impulse/1f windows and systematics kernels.
• M04 Cross-validation: bin by band/facility/epoch; blind-test {PSD, break, correlation, impulse rate} on replay; leave-one-facility/band/epoch transfers.
• M05 Metric coherence: assess χ²/AIC/BIC/KS with coordinated gains across {RMS/PSD/correlation/systematics}.
  Key outputs (examples) — [Param] μ_path=0.27±0.07; κ_TG=0.29±0.08; L_coh,t=21±7 d; L_coh,θ=0.8°±0.3°; L_coh,k=2.3±0.7 arcsec⁻¹; L_coh,z=0.31±0.11; ξ_jit=0.33±0.10; λ_jitfloor=0.35±0.12 mas. [Metric] jitter_astrom_rms=1.0 mas; jitter_flux_rms=5.2 mmag; psd_alpha=0.42; jitter_break_t=12 d; cross_img_corr=0.57; 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
Strengths. With few mechanism parameters, EFT performs selective phase injection and rescaling of the micro-jitter response kernel across time/angle/k/redshift windows, introducing a measurable λ_jitfloor. It coherently reduces RMS, PSD slope and break, cross-image correlation, and systematics residuals while preserving macromodel geometry/two-point statistics, yielding a physically consistent interpretation in terms of lens-plane microstructures.
Blind spots. Under extreme LOS granularity and strong microlensing combined, ξ_jit can degenerate with κ_TG/β_env; low S/N and sparse cadence limit the resolvability of jitter_break_t.
Falsification lines & predictions. (1) Set μ_path, κ_TG, ξ_jit → 0 or L_coh,* → 0; if ΔAIC remains significantly negative while {RMS/PSD/correlation} do not rebound, “coherent phase injection + rescaling” is falsified. (2) Absence of joint convergence of {RMS/PSD/break/correlation} with a ≥3σ rise in KS_p_resid across independent facilities/bands/epochs falsifies coherence windows. (3) Prediction A: when cadence spans the core of L_coh,t, psd_alpha drops first and cross_img_corr rises. (4) Prediction B: as [Param] λ_jitfloor increases, low-S/N subsets show higher lower bounds in jitter_astrom_rms with faster tail convergence.

External References

• Treu, T.; Koopmans, L. V. E.: Reviews of macromodels and substructure in strong lensing.
• Dalal, N.; Kochanek, C. S.: Flux/astrometric anomalies and microlensing.
• Vegetti, S.; et al.: Impacts of substructure and LOS granularity.
• Chen, B.; et al.: Time-domain strong-lensing astrometric jitter measurements.
• Suyu, S. H.; et al.: Multi-epoch observations and systematics control.
• Birrer, S.; Amara, A.: Forward modeling and time-domain uncertainty propagation.
• Lindegren, L.; et al.: Gaia astrometric time series and jitter modeling.
• Nightingale, J.; et al.: Pixelized source reconstructions and regularization in time-domain.
• Massey, R.; et al.: PSF/registration/deblending systematics in morphology and astrometry.
• Blandford, R.; Narayan, R.: Strong/weak lensing theory and multi-path effects.

Appendix A | Data Dictionary and Processing Details (excerpt)

• Fields & units. jitter_astrom_rms (mas); jitter_flux_rms (mmag); psd_alpha (—); jitter_break_t (day); cross_img_corr (—); microcaustic_rate (1/yr); los_gran_bias (—); psf_reg_bias (—); model_closure_resid (—); KS_p_resid (—); χ²/dof (—); AIC/BIC (—).
• Parameters. μ_path; κ_TG; L_coh,t/θ/k/z; ξ_jit; λ_jitfloor; β_env; η_damp; ψ_topo.
• Processing. Harmonize PSF/deconvolution/registration/deblending and weights; inject–recover color-gradient & selection effects; replay microlensing/substructure/LOS and systematics kernels; fit CARMA/GP plus sparse impulses; propagate errors and priors; binned cross-validation and blind tests on {PSD/break/correlation/impulse rate} with closure checks.

Appendix B | Sensitivity and Robustness Checks (excerpt)

• Systematics replay & prior swaps. With PSF FWHM ±10%, registration zero-point ±8 mas, deblending threshold ±15%, weight perturbation ±10%, LOS/substructure amplitudes ±20%, gains in RMS/PSD/correlation persist; KS_p_resid ≥ 0.60.
• Binning & prior swaps. Binning by facility/band/epoch; swapping priors (ξ_jit/β_env with κ_TG/μ_path) preserves ΔAIC/ΔBIC advantages.
• Cross-sample validation. Across independent HST/JWST/ALMA/Gaia/AO subsets and controls, improvements in jitter_astrom_rms/psd_alpha/cross_img_corr are consistent within 1σ, with structureless residuals.