可观测量条件化 ΔC 理论闭合 / Observable-conditioned ΔC theory closure

3b. draft 风格视图：理论匹配 fitter 在稿件 17 个 PN band-4 位置上（E096） / Draft-style view: the theory-matched fitter at the manuscript's 17 PN band-4 positions (E096)

与稿件图 "deltac-scatter-variance" 和上面 4b 的 emldetect 图同一格式，但点来自我们自己的理论匹配 fitter：FFT 相位连续模板族，psfgen PN band-4 模板，稿件的 17 个位置，S_true ∈ {3, 5, 7, 10, 15, 20, 30, 50}，b ∈ {0.01, 0.04, 0.16}，每格 300 行（共 122,400 行）。左列：ΔC 对 Ŝ 散点，实线为解析 μ_3p(Ŝ) + δ₁（δ₁ = 3 + ε − ½tr(H I⁻¹) − ∇μ·b，无拟合系数；只在解析域 DET_ML ≳ 5 内画）。每组位置两幅图。第一幅是数据与模型的对比（稿件格式）：中列为分档均值 ⟨ΔC⟩ 对 Ŝ，实线 μ_3p，虚线 μ_3p + δ₁；右列为分档 σ_ΔC（绕 μ_3p）对 √V_3p；灰色空心方块为同一批图像用稿件的整数格 fitter 得到的同一统计量。第二幅是残差图（同一批行）：中列为位移 ⟨ΔC − μ_3p⟩ ± SE 对 Ŝ，实线为 δ₁（只在解析域内画），注意理论对位移的预言是 δ₁ 而不是 0；右列为宽度比 σ_{ΔC − μ3p} / √V_3p ± SE，理论目前没有宽度项，参考线为 1。在对数坐标的 ΔC 图上 δ₁ ≈ 1 与 μ_3p 重合看不出来，残差图把它拉开。可见 Ŝ ≲ 10 处宽度比 0.7–0.9（已知的小计数宽度亏损，三档背景和各位置一致），Ŝ ≳ 15 处回到 1.0；位移在解析域内与 δ₁ 一致，高背景档在阈值带附近低约 0.1–0.3。曲线在该档 b、模板零偏移处解析计算。这里显示 6 个位置；全部 17 个位置的归一化位移 F 对 μ_3p 见下面的网格图：pooled 带内 χ²/bin 2.37，δ₁/经验 1.031，μ_3p ≥ 25 处 χ²/bin 0.62；整数格分支复现稿件 fitter（F 0.326 vs 0.330），连续族 F 0.447 vs δ₁ 0.461。

Same format as the manuscript figure "deltac-scatter-variance" and as the emldetect figures in 4b, but the points come from our own theory-matched fitter: the FFT-phase continuous template family on psfgen PN band-4 templates at the manuscript's 17 positions, S_true ∈ {3, 5, 7, 10, 15, 20, 30, 50}, b ∈ {0.01, 0.04, 0.16}, 300 rows per cell (122,400 rows). Left: ΔC against Ŝ, solid line the analytic μ_3p(Ŝ) + δ₁ (δ₁ = 3 + ε − ½tr(H I⁻¹) − ∇μ·b, no fitted coefficient; drawn only inside the analytic domain DET_ML ≳ 5). Two figures per position set. The first is the data-vs-model comparison in the manuscript's format: middle, binned mean ⟨ΔC⟩ against Ŝ with μ_3p (solid) and μ_3p + δ₁ (dashed); right, binned σ_ΔC (about μ_3p) against √V_3p; grey open squares are the same statistics for the manuscript's integer-grid fitter on the same images. The second is the residual view of the same rows: middle, the shift ⟨ΔC − μ_3p⟩ ± SE against Ŝ with δ₁ as the solid line (analytic domain only) — the theory predicts the shift to be δ₁, not zero; right, the width ratio σ_{ΔC − μ3p} / √V_3p ± SE, with the reference line at 1 because the theory has no width term yet. On the log axis of ΔC the offset δ₁ ≈ 1 coincides with μ_3p; the residual view separates it. The width ratio is 0.7–0.9 for Ŝ ≲ 10 (the known small-count width deficit, the same at all three background levels and positions) and returns to 1.0 for Ŝ ≳ 15; the shift agrees with δ₁ inside the domain, with the high-background level 0.1–0.3 below it near the threshold band. Curves are analytic at the level's b with the template at zero offset. Six positions are shown here; the normalised shift F against μ_3p for all 17 positions is in the grid below: pooled band χ²/bin 2.37, δ₁/empirical 1.031, χ²/bin 0.62 at μ_3p ≥ 25; the integer-grid branch reproduces the manuscript fitter (F 0.326 vs 0.330) while the continuous family sits at 0.447 against δ₁ 0.461. Source: scripts/plot_e096_draft_style.py on results/e096_pos*_rows.csv; results/e096_summary.md.

4b. clean subset draft 风格视图：散点、binned 均值、binned σ / 4b. Clean-subset draft-style view: scatter, binned mean, binned sigma

与 3b 同一格式，每个 config 两幅图。第一幅为数据与模型对比：左列 ΔC 对 S_eml 散点与解析均值 μ_pix + δ（实线，只在解析域内加 δ）；中列分档均值 ⟨ΔC⟩，实线 μ_pix，虚线 μ_pix + δ；右列分档 σ_ΔC 对 √V_pix。第二幅为同一批行的残差图：中列位移 ⟨ΔC − μ_pix⟩ ± SE 对 S_eml，实线为 δ（δ₀^pix + ε，无系数，只在解析域内画；理论预言的位移是 δ 而非 0）；右列宽度比 σ/√V_pix ± SE，理论无宽度项，参考线为 1。灰色空心方块为同一行对 single-b eff 参考的同一统计量。分档统计使用该位置的全部行（E073 行无 DET_ML 截断，mlmin = 0.001）。全部只显示 clean positions：M1 band 4 为 8 / 20 / 0，M2 band 4 为 29 / 47 / 63。可见：解析域内位移落在 δ 上，最低背景档在 S_eml 5–15 处高出 δ 约 0.5；宽度比在 S_eml ≲ 15 处 0.85–0.95，其上为 1.0，与 3b 的理论匹配 fitter 行为一致。 / Same layout as 3b, two figures per configuration. The first is the data-vs-model comparison: left, ΔC against S_eml with the analytic mean μ_pix + δ (solid; δ added inside the analytic domain only); middle, binned mean ⟨ΔC⟩ with μ_pix (solid) and μ_pix + δ (dashed); right, binned σ_ΔC against √V_pix. The second is the residual view of the same rows: middle, the shift ⟨ΔC − μ_pix⟩ ± SE against S_eml with δ (δ₀^pix + ε, no coefficient, analytic domain only) as the solid line — the theory predicts the shift to be δ, not zero; right, the width ratio σ/√V_pix ± SE, reference line at 1 because the theory has no width term. Grey open squares are the same statistics of the same rows against the single-b eff reference. Binned statistics use every row of the position (the E073 rows carry no DET_ML truncation, mlmin = 0.001). Clean positions only: M1 band 4 positions 8 / 20 / 0, M2 band 4 positions 29 / 47 / 63. The shift sits on δ inside the domain, with the lowest background level about 0.5 above δ at S_eml 5–15; the width ratio is 0.85–0.95 for S_eml ≲ 15 and 1.0 above, the same behaviour as the theory-matched fitter in 3b.