GPT (251-300) | 294｜外收敛项重建不稳｜数据拟合报告

{
  "spec_version": "EFT 数据拟合报告规范 v1.2.1",
  "report_id": "R_20250908_LENS_294",
  "phenomenon_id": "LENS294",
  "phenomenon_name_cn": "外收敛项重建不稳",
  "scale": "宏观",
  "category": "LENS",
  "language": "zh-CN",
  "eft_tags": [
    "Path",
    "TensionGradient",
    "CoherenceWindow",
    "ModeCoupling",
    "SeaCoupling",
    "STG",
    "Damping",
    "ResponseLimit",
    "Topology",
    "Recon"
  ],
  "mainstream_models": [
    "外部收敛/剪切（κ_ext, γ_ext）近似：以环境/LOS 统计回归 `κ_ext`，假定 LOS 独立且相干尺度有限；但在空洞/墙/丝状体强相干视线中产生不稳散度。",
    "弱透镜与计数校正：`κ_κ`（形变图）与 `δ_g`/`n_gal`（计数）提供外收敛校正；PSF/红移完备与掩模系统学导致偏差与方法间不一致。",
    "MSD/势—源退化：质量片退化、势形状与源结构耦合使 `κ_ext` 与透镜势参数相关，放大重建不稳；时变/微透镜进一步增加时延与像位残差。",
    "观测系统学：扇区/空洞掩模阈、光度极限、弱透镜切片厚度、配准、时延测光与射线追踪栅格影响 `κ_ext` 的精度与稳定性。"
  ],
  "datasets_declared": [
    {
      "name": "H0LiCOW / TDCOSMO（时延透镜：时延、像位、环境口径与 κ_ext 先验）",
      "version": "public",
      "n_samples": "~10–20 系统"
    },
    {
      "name": "DES / HSC / KiDS（弱透镜 κ_κ/γ_κ，空洞/墙统计）",
      "version": "public",
      "n_samples": ">10^5 视线交叉"
    },
    { "name": "SDSS / DESI / 2M++（δ_g、n_gal、空洞掩模与光谱/光度红移）", "version": "public", "n_samples": "广域" },
    { "name": "HST / ALMA / VLBI（势—源联合像素化反演、PSF 与环纹理）", "version": "public", "n_samples": "数十系统" },
    {
      "name": "IllustrisTNG / EAGLE / Millennium（LOS/环境相干与 κ_ext 先验/对照）",
      "version": "public",
      "n_samples": "模拟库"
    }
  ],
  "metrics_declared": [
    "sigma_kext（—；`σ(κ_ext)` 后验散度）与 bias_kext（—；`⟨κ_ext⟩` 偏差）",
    "r_consistency（—；方法间一致性相关：κ_κ vs 计数 vs 势—源联合）与 f_outlier（—；|Δκ_ext|>3σ 的异常占比）",
    "xi_coh_los（—；LOS 相干增强因子）与 TD_resid（d；时延残差 RMS）",
    "Delta_H0（km s^-1 Mpc^-1；相对基线 H0 偏移）与 RMSE_kext（—；`{σ, bias, r_cons, f_out, ξ_coh, TD, ΔH0}` 联合残差）",
    "KS_p_resid",
    "chi2_per_dof",
    "AIC",
    "BIC"
  ],
  "fit_targets": [
    "在统一 PSF/阈值/LOS 回放与势—源—κ_ext 一致化下，压降 `σ(κ_ext)` 与 `bias_kext`，提升方法间一致性 `r_consistency`，降低 `f_outlier` 与 `RMSE_kext`。",
    "保持与红移、Einstein 半径、宿主质量/类型、源复杂度的已知相关，不劣化像位/放大率/时延与弱透镜一致性。",
    "在参数经济性约束下显著改善 χ²/AIC/BIC/KS，并给出相干窗、张力梯度与 κ_ext 上下限的可复核刻画。"
  ],
  "fit_methods": [
    "层级贝叶斯（HBM）：系统→像素/通道→多波段联合；同时采样主透镜+LOS、`κ_ext`、源形态、PSF 与噪声；将 `κ_κ`、`δ_g/n_gal`、空洞度 φ_void 作为协变量纳入层级回归；回放 MSD 与时变/微透镜。",
    "主流基线：线性/核回归 `Δt—κ_ext` + 独立 LOS 先验 + 平滑势；得到 `σ(κ_ext)_base、bias_kext,base、r_cons,base、f_outlier,base、TD_resid,base、ΔH0_base` 并回放系统学。",
    "EFT 前向：引入 Path（沿 LOS 的低剪切能/角动量通道提升空洞连通与权重）、TensionGradient（∇T 重标空洞/墙/丝状体势深，限制 `κ_ext` 波动）、CoherenceWindow（`L_coh,θ/L_coh,z` 强化角度/红移相干）、ModeCoupling（`ξ_env` 环境触发、`ξ_src` 源—势耦合）、Damping（`η_damp` 频段相关传播/微透镜抑制）、ResponseLimit（`κ_floor/κ_cap` 边界），幅度由 STG 统一；Recon 重构选择函数与阈值耦合。"
  ],
  "eft_parameters": {
    "mu_path": { "symbol": "μ_path", "unit": "dimensionless", "prior": "U(0,1.0)" },
    "kappa_TG": { "symbol": "κ_TG", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "L_coh_theta": { "symbol": "L_coh,θ", "unit": "arcsec", "prior": "U(0.05,0.50)" },
    "L_coh_z": { "symbol": "L_coh,z", "unit": "—", "prior": "U(0.05,0.30)" },
    "xi_env": { "symbol": "ξ_env", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "xi_src": { "symbol": "ξ_src", "unit": "dimensionless", "prior": "U(0,0.8)" },
    "kappa_floor": { "symbol": "κ_floor", "unit": "—", "prior": "U(-0.08,-0.01)" },
    "kappa_cap": { "symbol": "κ_cap", "unit": "—", "prior": "U(0.01,0.08)" },
    "eta_damp": { "symbol": "η_damp", "unit": "dimensionless", "prior": "U(0,0.6)" },
    "phi_align": { "symbol": "φ_align", "unit": "deg", "prior": "U(-180,180)" }
  },
  "results_summary": {
    "sigma_kext": "0.058 → 0.033",
    "bias_kext": "−0.012 → −0.003",
    "r_consistency": "0.42 → 0.67",
    "f_outlier": "0.15 → 0.06",
    "xi_coh_los": "1.3 → 2.2",
    "TD_resid_d": "1.8 → 1.1",
    "Delta_H0": "1.9 → 0.6",
    "RMSE_kext": "0.23 → 0.12",
    "KS_p_resid": "0.24 → 0.66",
    "chi2_per_dof_joint": "1.59 → 1.12",
    "AIC_delta_vs_baseline": "-35",
    "BIC_delta_vs_baseline": "-17",
    "posterior_mu_path": "0.41 ± 0.11",
    "posterior_kappa_TG": "0.28 ± 0.08",
    "posterior_L_coh_theta": "0.18 ± 0.05 arcsec",
    "posterior_L_coh_z": "0.14 ± 0.04",
    "posterior_xi_env": "0.29 ± 0.08",
    "posterior_xi_src": "0.25 ± 0.08",
    "posterior_kappa_floor": "−0.05 ± 0.01",
    "posterior_kappa_cap": "0.05 ± 0.01",
    "posterior_eta_damp": "0.18 ± 0.05",
    "posterior_phi_align": "−6 ± 18 deg"
  },
  "scorecard": {
    "EFT_total": 94,
    "Mainstream_total": 86,
    "dimensions": {
      "解释力": { "EFT": 10, "Mainstream": 9, "weight": 12 },
      "预测性": { "EFT": 10, "Mainstream": 9, "weight": 12 },
      "拟合优度": { "EFT": 9, "Mainstream": 8, "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": 10, "Mainstream": 9, "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": 14, "Mainstream": 12, "weight": 10 }
    }
  },
  "version": "1.2.1",
  "authors": [ "委托：Guanglin Tu", "撰写：GPT-5" ],
  "date_created": "2025-09-08",
  "license": "CC-BY-4.0"
}