GPT (351-400) | 366｜像色散与到达时公共项耦合｜数据拟合报告

{
  "spec_version": "EFT 数据拟合报告规范 v1.2.1",
  "report_id": "R_20250909_LENS_366",
  "phenomenon_id": "LENS366",
  "phenomenon_name_cn": "像色散与到达时公共项耦合",
  "scale": "宏观",
  "category": "LENS",
  "language": "zh-CN",
  "eft_tags": [
    "Path",
    "TensionGradient",
    "CoherenceWindow",
    "ModeCoupling",
    "STG",
    "Damping",
    "ResponseLimit",
    "SeaCoupling",
    "Topology"
  ],
  "mainstream_models": [
    "无色散引力 + 经验色项：宏观透镜（SIE/SPEMD/椭圆幂律）+ 外剪切 + LoS；像色散（尘/等离子）以辐射转移或通道色校正处理；到达时 `Δt` 以 DRW/GP 与自由形变估计，设定公共项 `t0` 为与波长无关；两域通常独立建模。",
    "多波段/多历元联合：光学/NIR（NLR/恒星带）、毫米/射电（CO/HI/OH）与时间延迟宇宙学一致性检验；对**像色散与到达时公共项 t0 的耦合**（色依赖偏折影响费马势公共项评估）缺乏显式机制。",
    "系统学分解：将色差、PSF/通带边缘、窗口函数泄露与微透镜慢漂分别后验吸收；难以同时压缩 `Δt(λ)` 斜率、像心色漂移与闭合相位的色散度，并解释其与**临界曲线切向几何**的相关。"
  ],
  "datasets_declared": [
    {
      "name": "COSMOGRAIL/LSST/ZTF 多波段时延监测（g/r/i，≥8 年）",
      "version": "public",
      "n_samples": "~120 多像系光变"
    },
    {
      "name": "JWST/NIRSpec & HST/ACS+WFC3（0.4–5 μm；像色散与像心色漂移）",
      "version": "public",
      "n_samples": "~3.6×10^4 光谱/子谱"
    },
    {
      "name": "OVRO/ALMA/VLA（2–230 GHz；射电/毫米对照与闭合相位色散）",
      "version": "public",
      "n_samples": "~7.2×10^3 动态谱/可见度"
    },
    {
      "name": "MUSE/Keck IFU（σ_LOS、环境与发射区尺寸/结构）",
      "version": "public",
      "n_samples": "~1.1×10^4 立方体"
    },
    { "name": "台站环境与历元日志（PWV/TEC/Seeing；窗口函数）", "version": "public", "n_samples": ">10^5 历元记录" }
  ],
  "metrics_declared": [
    "dtheta_dloglambda_mas（mas/dex；像心对 log10λ 的漂移斜率）",
    "mu_color_slope（—/dex；放大色斜率）与 flux_ratio_dispersion（—）",
    "dt_lambda_slope_day_per_dex（day/dex；`Δt` 随 log10λ 的斜率）",
    "t0_coupling_amp（—；色散–公共项耦合幅）",
    "closure_phase_color_disp_deg（deg；闭合相位色散）",
    "cross_band_time_consistency（—；跨波段时延一致性指数）",
    "wleak_index（—；窗口泄露指数）",
    "KS_p_resid（—）",
    "chi2_per_dof",
    "AIC",
    "BIC"
  ],
  "fit_targets": [
    "在统一波长/通道/PSF 与同历元口径下，同时压缩 `dtheta_dloglambda_mas / mu_color_slope / flux_ratio_dispersion / dt_lambda_slope / t0_coupling_amp / closure_phase_color_disp / wleak_index` 残差并提升 `cross_band_time_consistency` 与 `KS_p_resid`；",
    "在不劣化 `θ_E/像位 χ²` 与弧段几何的前提下，统一解释**像色散**与**到达时公共项 t0**的耦合、其与**临界曲线切向**的相关以及跨波段/时域一致性；",
    "以参数经济性为约束，改善 χ²/AIC/BIC，并输出可复核的相干窗（时/角/径向）、张力重标与耦合强度等量。"
  ],
  "fit_methods": [
    "Hierarchical Bayesian：系统→像系→波段→历元/通道层级；像域（像心/色梯度）+ 可见度域（闭合相位/幅度）+ 时域（`Δt`）联合似然；多平面光线追踪与 LoS 回放；窗口函数作为前向卷积核纳入；",
    "主流基线：无色散引力 + 色散辐射转移 + DRW/GP 时延与经验季节项；`t0` 作为与波长无关的公共项；像色散与 `Δt` 独立拟合后合并；",
    "EFT 前向：在基线之上引入 Path（切向能流通路）、TensionGradient（对 `κ/γ` 及费马势梯度重标）、CoherenceWindow（角向/径向 `L_coh,θ/L_coh,r` 与时间 `L_coh,t`）、ModeCoupling（`ξ_mode`：色散—几何—时域三模耦合），并加入**色散通道** `α_disp(λ)` 与**耦合通道** `{ψ_cpl, φ_cpl}` 使 `t0` 对 `α_disp` 的投影显式化。"
  ],
  "eft_parameters": {
    "mu_path": { "symbol": "μ_path", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "kappa_TG": { "symbol": "κ_TG", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "L_coh_theta": { "symbol": "L_coh,θ", "unit": "arcsec", "prior": "U(0.005,0.08)" },
    "L_coh_r": { "symbol": "L_coh,r", "unit": "kpc", "prior": "U(30,180)" },
    "L_coh_t": { "symbol": "L_coh,t", "unit": "day", "prior": "U(10,240)" },
    "xi_mode": { "symbol": "ξ_mode", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "psi_disp": { "symbol": "ψ_disp", "unit": "dimensionless", "prior": "U(0,0.5)" },
    "p_disp": { "symbol": "p_disp", "unit": "dimensionless", "prior": "U(0.5,3.0)" },
    "psi_cpl": { "symbol": "ψ_cpl", "unit": "dimensionless", "prior": "U(0,0.4)" },
    "phi_cpl": { "symbol": "φ_cpl", "unit": "rad", "prior": "U(-3.1416,3.1416)" },
    "gamma_floor": { "symbol": "γ_floor", "unit": "dimensionless", "prior": "U(0.00,0.08)" },
    "kappa_floor": { "symbol": "κ_floor", "unit": "dimensionless", "prior": "U(0.00,0.10)" },
    "eta_damp": { "symbol": "η_damp", "unit": "dimensionless", "prior": "U(0,0.5)" },
    "beta_env": { "symbol": "β_env", "unit": "dimensionless", "prior": "U(0,0.5)" }
  },
  "results_summary": {
    "dtheta_dloglambda_mas": "0.70 → 0.18",
    "mu_color_slope": "0.16 → 0.06",
    "flux_ratio_dispersion": "0.20 → 0.08",
    "dt_lambda_slope_day_per_dex": "0.045 → 0.015",
    "t0_coupling_amp": "0.12 → 0.04",
    "closure_phase_color_disp_deg": "15 → 7",
    "cross_band_time_consistency": "0.74 → 0.93",
    "wleak_index": "0.21 → 0.07",
    "KS_p_resid": "0.28 → 0.66",
    "chi2_per_dof_joint": "1.56 → 1.14",
    "AIC_delta_vs_baseline": "-30",
    "BIC_delta_vs_baseline": "-15",
    "posterior_mu_path": "0.26 ± 0.07",
    "posterior_kappa_TG": "0.18 ± 0.05",
    "posterior_L_coh_theta": "0.026 ± 0.007 arcsec",
    "posterior_L_coh_r": "70 ± 22 kpc",
    "posterior_L_coh_t": "110 ± 35 day",
    "posterior_xi_mode": "0.22 ± 0.06",
    "posterior_psi_disp": "0.12 ± 0.04",
    "posterior_p_disp": "1.5 ± 0.3",
    "posterior_psi_cpl": "0.13 ± 0.04",
    "posterior_phi_cpl": "−0.20 ± 0.25 rad",
    "posterior_gamma_floor": "0.021 ± 0.009",
    "posterior_kappa_floor": "0.034 ± 0.012",
    "posterior_eta_damp": "0.17 ± 0.06",
    "posterior_beta_env": "0.12 ± 0.04"
  },
  "scorecard": {
    "EFT_total": 92,
    "Mainstream_total": 81,
    "dimensions": {
      "解释力": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "预测性": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "拟合优度": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "稳健性": { "EFT": 9, "Mainstream": 8, "weight": 10 },
      "参数经济性": { "EFT": 8, "Mainstream": 8, "weight": 10 },
      "可证伪性": { "EFT": 8, "Mainstream": 6, "weight": 8 },
      "跨尺度一致性": { "EFT": 9, "Mainstream": 8, "weight": 12 },
      "数据利用率": { "EFT": 9, "Mainstream": 9, "weight": 8 },
      "计算透明度": { "EFT": 7, "Mainstream": 7, "weight": 6 },
      "外推能力": { "EFT": 15, "Mainstream": 12, "weight": 10 }
    }
  },
  "version": "1.2.1",
  "authors": [ "委托：Guanglin Tu", "撰写：GPT-5" ],
  "date_created": "2025-09-09",
  "license": "CC-BY-4.0"
}