报告讲稿Seminar

面向不认识本项目的研究生与教授的 45 分钟报告；每页幻灯片下面附完整讲稿（双语），打印视图将两者合排。A 45-minute talk for graduate students and professors who do not know the project; the full script sits under every slide (bilingual), and the print view puts the two together.

核心贡献一句话：XMM-Newton 点源检测似然比的条件宽度可以零参数地写出，其目录区间的偏窄由一个机制解释——两个几乎相消的大项中约 1 % 的 penalty 错配被相消放大成 8–16 % 的方差高估——且该机制同时决定我们自己的拟合器与 emldetect 两条流水线的宽度；在 emldetect 输出上，条件规律的四个候选形式被一支验证过的评分器全部拒收；2026-10-21 的复核（R114）进一步表明评分器混用了估计对象，所以"宽度可推广"只能读作在同一个位置内——宽度指标对逐位置偏移恒等不变；PI 的进度指标也改为已解决位置的比例（无阈值）。2026-10-22 的复核又把判据本身校准了一次：“每个条目都在容差 \(\varepsilon\) 内”被证明噪声受限（一条完美规律在能段 4 上也只能让 21–27 % 的位置满足它），判据因此改为每个位置一个合并偏移，容差定为比较规律 0.05、跟踪进度 0.10；打分手随之冻结。旧读数“规律就压在位置盲地板上”被地板改正推翻，改正后最好候选在 0.10 处高于地板；位置效应的来源收窄到像素级几何且两条能段共享；第一个拟合前位置项（拟合盒背景水平）把最好候选从 0.545 抬到 0.727（p 0.003–0.004，尚未在新位置检验）。宽度侧，判据也被校准——一条逐行精确的方差律通过“8 箱全在 1 \(\pm\) 0.02 内”的概率只有 66.8 %，PI 于是批准“8 箱允许 1 箱失败”（完美规律通过约 95 %）；在这条判据下第一条可观测箱级宽度规律通过，但带宽在测试半上选定，且同一构造迁到 emldetect 行后在全统计量下仍失败 5/5 箱。冻结打分手的宽度区间仍欠覆盖（0.941 / 0.946 对 0.950 的接受带），所以每个已解决比例都要连这个限制一起引用。2026-10-24 的第一臂更新：普适性 Tier 1 第一臂（留出能段块打分）已出：M2 能段 1 中心确认（0.727，区间 [−0.152, +0.061]），宽度旗标 AMBIGUOUS（超出真实、单侧约 2 %，但箱边一移判定就翻），锚 8/12；没有合并判定。背景通道给出一条新的未决依赖：冻结定律在估计背景下偏 +0.174 z，候选参数 C2 暂定于一个观测；代价锚实测 0.97 CPU-s/行（旧 0.4 作废），T1-a 只跑 M2 并已发射。星表侧：DET_ML 有序残差是标注同义反复；断幂律 5/6、eta 振幅修合并宽度但逐格形状失败。Central contribution in one sentence: the conditional width of the XMM-Newton point-source detection likelihood ratio can be written down with zero fitted parameters, its catalogue-interval narrowing is explained by one mechanism — a roughly 1 % penalty mismatch in one of two nearly cancelling large terms, amplified by the cancellation into an 8–16 % variance over-statement — and that one mechanism carries the widths of both our own fitter and emldetect; on emldetect output, four candidate forms of the conditional law are all rejected by a validated scorer; a 2026-10-21 audit further shows the scorer mixed estimands, so "the width generalises" reads only as within one position — the width metric is identically invariant to per-position offsets; and the PI's progress metric became the solved fraction of positions, with no threshold. A 2026-10-22 audit then re-calibrated the criterion itself: the “every entry within the tolerance \(\varepsilon\)” rule was shown to be noise-limited (even a perfect law satisfies it at only 21–27 % of positions on band 4), so the criterion became one pooled offset per position, with tolerances of 0.05 to compare laws and 0.10 to track progress; the scorer was frozen with it. The old reading “the laws sit at the position-blind floor” is overturned by the floor correction, after which the best candidate sits above the floor at 0.10; the position effect's origin narrowed to pixel-level geometry shared by both bands; and a first pre-fit position term (the fit-box background level) lifts the best candidate from 0.545 to 0.727 (p 0.003–0.004, not yet tested on fresh positions). On the width side the criterion was calibrated too — a row-exact variance law passes “all 8 bins inside 1 \(\pm\) 0.02” only 66.8 % of the time, so the PI approved “at most 1 failing bin of 8” (a perfect law passes about 95 %); under it the first observable bin-level width law passes, but its bandwidth was chosen on the test half and the same construction still fails 5/5 bins on emldetect rows at full statistics. The frozen scorer's width interval still under-covers (0.941 / 0.946 against a 0.950 acceptance band), so every solved fraction must be quoted with that limit attached. The 2026-10-24 first-arm update: Universality Tier 1's first arm (the held-out band-block scoring) has reported: M2 band 1's centre is confirmed (0.727, interval [−0.152, +0.061]), the width flag is AMBIGUOUS (the excess real, one-sided about 2 %, but the verdict flips with the bin edges), the anchor 8/12; there is no combined verdict. The background channel adds a new unresolved dependency: the frozen law is off by +0.174 z under an estimated background, with the candidate parameter C2 provisional on one observation; the cost anchor is measured at 0.97 CPU-s/row (the old 0.4 superseded), and T1-a runs M2 only and has been launched. On the catalogue side: the DET_ML-ordered residual is a labelling tautology; the broken power law is 5/6, and the eta amplitude restores the pooled width while the per-cell shape fails.

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XMM-Newton 点源检测似然比的零参数条件宽度：机制与边界A parameter-free conditional width for the XMM-Newton point-source detection likelihood ratio: mechanism and limits

〈报告人〉 · 〈合作者〉 · 〈单位〉 · 2026 年 10 月 · · · 2026 October

标准学术报告：45 分钟 + 10–15 分钟问答Standard seminar: 45 minutes + 10–15 minutes of questions

各位好，谢谢主持人的介绍。今天我要讲的是 XMM-Newton 点源检测里的一个统计问题。听起来很具体，但它影响你从任何 X 射线目录里拿到的每一个误差棒：检测统计量围绕它的条件均值散开多宽，能不能不用任何拟合参数、直接从理论写下来？我会用四十五分钟讲三个结果：公式在哪个区间是对的、在哪个区间系统性偏窄、以及偏窄的机制是什么——机制只有一个，而且同时决定两条独立流水线的宽度。讲完之后留十到十五分钟，欢迎随时打断我提问。我们开始。

Good afternoon, and thank you for the introduction. Today I want to talk about a statistical problem inside XMM-Newton point-source detection. It sounds specific, but it touches every error bar you take from any X-ray catalogue: how widely the detection statistic scatters around its conditional mean — can that be written down from theory alone, with no fitted parameter? I will use forty-five minutes for three results: where the formula is right, where it is systematically narrow, and what the mechanism of that narrowing is — and the mechanism turns out to be a single one, shared by two independent pipelines. Afterwards there are ten to fifteen minutes for questions, and please feel free to interrupt at any point. Let us begin.

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你从目录里拿到的每一个误差棒，都假设了一个条件宽度Every error bar you take from a catalogue assumes a conditional width

一张 XMM 图像 = 源（PSF 加权）+ 背景（逐像素泊松）。检测把这张图折成一个数。An XMM image = source (PSF-weighted) + background (Poisson per pixel). Detection folds this image into one number.

先说为什么这个问题值得四十五分钟。你从 XMM 目录里拿一个源，目录给你三样东西：计数、误差棒、完备性。这三样最终都压在同一个量上——给定你测到的计数和背景，检测统计量围绕它的条件均值散开多宽。宽度偏窄，误差棒就偏小，完备性就偏高，你以为探测到的源比实际多；宽度偏宽，反过来。所以条件宽度是目录可信度的底层量。看这张图：左边是 PSF 模板——源光子落在哪里；中间是均匀背景，每像素独立泊松；右边是两者相加，就是你拿到的观测图像。检测要做的，是把右边这张图折成一个数。我们的问题等价于：这个数对它的期望值会抖多宽。

First, why this problem deserves forty-five minutes. Take a source from an XMM catalogue: it hands you three things — counts, an error bar, a completeness. All three rest on one quantity: given the counts you measured and the background you measured, how widely does the detection statistic scatter around its conditional mean? If the width is narrow, the error bars are small and the completeness is high — you believe you have more real detections than you do. If it is wide, the reverse. The conditional width is therefore the quantity underneath catalogue reliability. Look at the figure: on the left the PSF template — where the source's photons land; in the middle the flat background, an independent Poisson draw per pixel; on the right the sum, which is the image you actually get. Detection has to fold the right-hand image into one number. Our question is equivalent to asking: how widely does that number jitter around its expectation.

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承诺：听完这个报告，你会知道 (1) 零参数宽度在哪个区间可信 (2) 哪个区间必须校准 (3) 为什么Promise: by the end you will know (1) where the parameter-free width can be trusted, (2) where it must be calibrated, and (3) why

	区间Interval	宽度Width
高计数锚High-count anchor	DET_ML \( \gtrsim \) 20–50	公式通过（std z 0.98–1.01）formula passes (std z 0.98–1.01)
目录区间Catalogue interval	DET_ML 6–20	系统性偏窄 8–16 %systematically narrow by 8–16 %
机制Mechanism	两条流水线both pipelines	同一个：相消放大one: cancellation amplification

我承诺三件事，也是今天的三条带回家的信息。第一，在高计数端——检测似然二十到五十以上——零参数公式就是答案，那里不需要任何校准。第二，在目录最关心的弱源区间，检测似然六到二十，同一公式系统性偏窄百分之八到十六，必须经验校准，而且没有任何点修正能闭合它。第三，你会知道为什么：方差公式是两个几乎相消的大项之差，其中一项差百分之一，就被相消放大成百分之五到十六的方差高估——一个机制，同时决定我们自己写的拟合器和 SAS 的 emldetect。看这张表：三行就是三个结果，右列是各自的数字。这三条我会各讲三遍：现在预告一遍，中间各有一遍，结尾再总结一遍。

I promise three things, and they are also the three take-home messages of this talk. First, at high counts — detection likelihood above twenty to fifty — the parameter-free formula is the answer; no calibration is needed there. Second, in the faint-source interval catalogues care about most, detection likelihood between six and twenty, the same formula is systematically narrow by eight to sixteen per cent, it must be calibrated empirically, and no point correction closes it. Third, you will know why: the variance formula is the difference of two nearly cancelling large terms, one of them is off by one per cent, and the cancellation amplifies that into a five to sixteen per cent variance over-statement — one mechanism, shared by our own fitter and by SAS's emldetect. Look at the table: three rows for the three results, the right column carrying each one's numbers. I will say each of these three times: once now as a preview, once in the middle with the evidence, and once at the end as a summary.

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大纲：背景 → 方法 → 三条结果 → 局限 → 这对做 X 射线巡天的人意味着什么Outline: background → method → three results → caveats → what it means for anyone doing an X-ray survey

① 检测似然是什么、Wilks 定理给出什么 ② 可控模拟基准与两条流水线 ③ 结果：锚区间 / 目录区间 / 机制 ④ 局限 ⑤ 实用建议与下一步① what the detection likelihood is and what Wilks' theorem promises ② a controlled simulation benchmark and two pipelines ③ results: anchor / catalogue interval / mechanism ④ caveats ⑤ practical advice and next steps

路线图。前五分钟是背景：检测似然是什么、教科书理论承诺什么、以及一条贯穿全篇的方法论铁律。接下来五分钟是方法：一套可控的模拟基准，同一批图像喂两条流水线，怎么测宽度。然后是结果，大约二十五分钟，三条：锚区间、目录区间、机制。最后十分钟是局限、对巡天工作者的实用建议、以及下一步。整个报告的骨架就是这个顺序：问题、方法、证据、边界、出路。如果你只记得一页，请记得最后总结那页。背景讲完之后，我会停一下确认时间；如果时间紧，有三页标了“可跳过”，我会直接跳到机制那一页。

Here is the route map. The first five minutes are background: what the detection likelihood is, what the textbook theory promises, and one methodological rule that runs through everything. The next five minutes are the method: a controlled simulation benchmark feeding the same images to two pipelines, and how the width is measured. Then come the results, about twenty-five minutes, in three parts: the anchor interval, the catalogue interval, and the mechanism. The last ten minutes are caveats, practical advice for survey work, and next steps. The skeleton of the whole talk is exactly this order: question, method, evidence, boundary, way out. If you remember only one slide, make it the summary at the end.After the background I will pause to check the time; if we are tight, three slides are marked disposable and I will jump straight to the mechanism.

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检测似然 DET_ML：把“这里有没有源”折成一个数的似然比检验DET_ML: a likelihood-ratio test that folds "is there a source here" into one number

\[ \Delta C = 2\,\ln [\,L_{\rm src} / L_{\rm bg}\,], \qquad \mathrm{DET\_ML} = -\ln Q(\nu/2,\, \Delta C/2) \]\[ \Delta C = 2\,\ln [\,L_{\rm src} / L_{\rm bg}\,], \qquad \mathrm{DET\_ML} = -\ln Q(\nu/2,\, \Delta C/2) \]

XMM 的 emldetect 用 Cash 统计量做这件事；目录阈值常用 DET_ML = 6。^[s1]XMM's emldetect does this with the Cash statistic; the common catalogue threshold is DET_ML = 6.^[s1]

背景第一页：检测似然是什么。看上方的公式：在每个候选位置，emldetect 比较两个模型——这里有一个源，和这里只有背景。两者似然之比取两倍对数，就是 Delta C；再经过上不完全伽马函数的负对数变换，就是目录里的 DET_ML。单幅图像、三个自由参数——振幅加二维位置——所以自由度是三。这里有两个约定陷阱值得当众点出来，因为它们每一个都让我们项目里出现过两到五十倍的假信号：第一，DET_ML 用的是自然对数，不是以十为底；第二，伽马函数的第二个参数是 Delta C 除以二，不是 Delta C 本身。目录的常用阈值是 DET_ML 等于六——记住这个数，后面所有区间都围绕它。记住这两个陷阱，因为后面所有数字都建立在这两个约定上。接下来看教科书理论在弱源端到底承诺了什么。

Background, page one: what is the detection likelihood? Look at the formula at the top: at each candidate position, emldetect compares two models — there is a source here, against there is only background. Twice the logarithm of the likelihood ratio is Delta C; a minus-log transform of the upper incomplete gamma function then gives the catalogue's DET_ML. One image with three free parameters — amplitude plus a two-dimensional position — so three degrees of freedom. Two convention traps are worth naming in public, because each of them produced a spurious signal by a factor of two to fifty in this project at some point. First, DET_ML uses the natural logarithm, not base ten. Second, the gamma function's second argument is Delta C over two, not Delta C itself. The common catalogue threshold is DET_ML equal to six — keep that number in mind, because every interval I talk about is organised around it.Keep those two traps in mind, because every number later is built on these two conventions. Next, let us see what the textbook theory actually promises in the faint regime.

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教科书说 \(\Delta C\) 应该是 \(\chi^2_3\)——但目录恰恰关心它最不可信的地方The textbook says \(\Delta C\) should be \(\chi^2_3\) — but catalogues care exactly where that is least reliable

纯背景模拟的 \(\Delta C\) 分布：朴素 Wilks 的 \(\chi^2_3\)（灰虚线）明显不对；边界修正后的渐近律（红）才对。^[s2]The \(\Delta C\) distribution of pure-background simulations: naive Wilks \(\chi^2_3\) (grey dashed) is clearly wrong; the boundary-corrected asymptotic law (red) is right.^[s2]

教科书怎么说？Wilks 定理：光子足够多时，Delta C 渐近趋向自由度三的卡方。听起来问题已经解决了——但看这张直方图。横轴是 Delta C，纵轴是行数；灰虚线是教科书给的卡方三，红实线是边界修正后的渐近律，直方图来自两万张纯背景模拟图像。你可以直接看到两件事：一半质量贴在零上——没有源时最优位置是随机的，一半的实现给出 Delta C 恰好为零；尾部跟卡方三完全不是一回事。正确的渐近是边界修正过的形式。目录恰恰关心弱源——几十个光子、检测似然六到十——那里似然面远离二次型，渐近论证最不可靠。所以宽度必须在模拟里逐箱测量，不能从定理直接搬。

What does the textbook say? Wilks' theorem: with enough photons, Delta C converges to a chi-squared with three degrees of freedom. That sounds like the problem is solved — but look at this histogram. The horizontal axis is Delta C, the vertical axis the number of rows; the grey dashed curve is the textbook chi-squared-three, the red solid curve the boundary-corrected asymptotic law, and the histogram is built from twenty thousand pure-background simulated images. You can see two things directly. Half the mass sits at zero — with no source present the best-fit position is random, and half the realisations give Delta C exactly zero. And the tail is nothing like chi-squared-three. The correct asymptotic is the boundary-corrected form. Catalogues care precisely about the faint regime — a few tens of photons, detection likelihood between six and ten — where the likelihood surface is far from quadratic and the asymptotic argument is least reliable. So the width has to be measured bin by bin in simulation; it cannot be transplanted from the theorem.

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条件化决定一切：理论只能条件于可观测量 \((\hat{S}, b)\)，永远不能条件于模拟标签Conditioning decides everything: theory may condition on the observables \((\hat{S}, b)\), never on the simulation label

按 \(\hat{S}\) 分箱会把宽度测胖：20 箱读 1.22–1.30，200 箱收敛到逐行值 1.005–1.028。^[s3]Binning in \(\hat{S}\) fattens the measured width: 20 bins read 1.22–1.30, 200 bins converge to the per-row value 1.005–1.028.^[s3]

讲结果之前，必须先立一条铁律，因为它决定所有数字怎么读。真实流量是模拟的标签，目录用户拿不到它；用户手里只有两个可观测量：测到的计数和背景。所以一切理论必须条件在可观测量上，永远不能条件在真实流量上。这张图是这条铁律救过我们一次的例子。横轴是分箱数——把样本按测到的计数切成多少格；纵轴是格内残差的标准差除以插入式宽度。左图是绝对值：每条彩色曲线对应一个真实流量，点状横线是它的逐行值。你可以看到分箱越少，读数越胖：二十个箱读出一点二二到一点三零，两百个箱收敛到一点零零五到一点零二八。右图把每条曲线除以自己的逐行值，收敛线统一落在一点。所以早期那个“插入式窄百分之二十二到三十”的读数，是分箱自己造出来的，后来正式撤回。今天我引用的每一个宽度，都是按可观测量分箱、逐行条件化测出来的。

Before the results, one rule has to be established, because it decides how every number in this talk is read. The true flux is a label attached by the simulation; a catalogue user never has it. What the user has are two observables: the measured counts and the background. So all theory must condition on observables, never on the true flux. This figure is an example of the rule saving us once. The horizontal axis is the number of bins — how finely the sample is sliced in the measured counts; the vertical axis is the in-bin residual standard deviation divided by the plug-in width. In the left panel, absolute values: each coloured curve is one true flux, and the dotted horizontal line is that flux's per-row value. You can see that fewer bins read fatter: twenty bins give one point two two to one point three zero, two hundred bins converge to one point zero zero five to one point zero two eight. The right panel divides each curve by its own per-row value, so the convergence line sits at one. The early reading that "the plug-in is narrow by twenty-two to thirty per cent" was therefore created by the binning itself, and was formally withdrawn. Every width I quote today is measured in observable bins, conditioned row by row.

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已有的经验校准路线给得出“差多少”，给不出“为什么”Existing empirical-calibration routes can tell you "how much" but not "why"

重复指向 / 注入源：仪器、背景、源群、流水线同时变——四个因子纠缠在一起。Repeat pointings / injected sources: instrument, background, source population and pipeline all change at once — four factors entangled.

我们的路线：可控模拟，逐层隔离——统计量本身（L0）、SAS 流水线（L1）、联合拟合（J）、目录（C）。^[s4]Our route: a controlled simulation, isolated layer by layer — the statistic itself (L0), the SAS pipeline (L1), the joint fit (J), the catalogue (C).^[s4]

为什么不直接在真实数据上校准？重复指向和注入源当然宝贵，但它们同时改变四个东西：仪器、背景、源群、流水线。你问“宽度差多少”，有答案；你问“为什么差”，四个因子纠缠在一起，没有答案。我们走另一条路：可控的模拟基准，把问题切成层。看这张图：最底层 L0 是我们自己的拟合器，只测统计量本身；往上一层 L1 是 SAS 的 emldetect，加进真实流水线的工程；再往上 J 是联合拟合——十五幅图像共用一个位置；最后才对目录 C。每层只有一个东西在变，每个差异都能追到具体的环节。今天讲的是最下面两层。一句话总结这一页：模拟不是替代真实数据，是把“为什么”从“差多少”里剥出来的唯一办法。下一页讲构造的具体成分。

Why not just calibrate on real data? Repeat pointings and injected sources are of course valuable, but they change four things at once: the instrument, the background, the source population, and the pipeline. Ask "how much does the width differ" and you get an answer; ask "why does it differ" and the four factors are entangled and you get nothing. We take a different road: a controlled simulation benchmark that slices the problem into layers. Look at the figure: at the bottom, L0 is our own fitter, measuring the statistic itself and nothing else. Above it, L1 is SAS's emldetect, adding the engineering of a real pipeline. Above that, J is the joint fit — fifteen images sharing one position. Only at the end, C, the catalogue. One thing changes per layer, so every difference can be traced to a specific step. Today's talk lives in the bottom two layers.One sentence for this page: simulation is not a replacement for real data — it is the only way to peel "why" apart from "how much". The next page gives the concrete ingredients of the construction.

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基准的构造：真实 PSF、逐像素背景、抖动——同一批图像喂两条流水线The benchmark construction: a real PSF, per-pixel background, jitter — one batch of images fed to two pipelines

成分Ingredient	取值Value
源群Source population	\( dN/dS \propto S^{-2.5} \)，支撑 [5.58, 51.20]\( dN/dS \propto S^{-2.5} \), support [5.58, 51.20]
PSF	M31 真实星表图像（非解析高斯）a real M31 catalogue image (not an analytic Gaussian)
背景Background	逐像素背景图 \(b\)，与 \(S\) 联合采样per-pixel map \(b\), sampled jointly with \(S\)
位置Positions	67 个位置，离轴 0–13′67 positions, off-axis 0–13 arcmin

^[s5]

构造有四个成分，我逐个说。源流量从一个观测到的源计数分布抽——幂律负二点五，支撑区间从弱源到中等源，对应生产数据的真实流量范围。PSF 不用解析函数，用 M31 的真实星表图像，因为它带着真实的核翼结构——这一点后面会变成关键。背景逐像素给，和流量在二维格子上联合采样，所以每一行模拟都有自己的背景水平。每个配置在视场内六十七个位置上重复，离轴从零到十三角分，覆盖整个视场。一批图像生成一次，然后两条流水线各自去测——这就是“同图”的意思。表里这四行就是全部输入；换任何一个成分，都要重新验证。

The construction has four ingredients; let me take them in turn. Source fluxes are drawn from an observed source-count distribution — a power law of minus two point five, with a support spanning faint to moderate sources, matching the true-flux range of the production data. The PSF is not an analytic function but a real M31 catalogue image, because it carries the real core-and-wing structure — that will turn out to matter later. The background is per-pixel, sampled jointly with the flux on a two-dimensional grid, so every simulated row has its own background level. Each configuration is repeated at sixty-seven positions across the field of view, off-axis from zero to thirteen arcminutes, covering the whole field. One batch of images is generated once, and the two pipelines then measure it independently — that is what "the same images" means. The four rows of this table are the entire input list; change any ingredient and everything must be re-validated.

cumulative 15.0 min

两条流水线：L0（我们自己的拟合器）与 L1（SAS 的 emldetect）Two pipelines: L0 (our own fitter) and L1 (SAS's emldetect)

	L0	L1 (emldetect)
拟合Fit	全局网格 + Nelder–Mead，位置自由（\(\nu = 3\)）global grid + Nelder–Mead, position free (\(\nu = 3\))	SAS emldetect，Cash 统计量SAS emldetect, Cash statistic
打分Scoring	真实 PSF 模板族在拟合位置real-PSF template family at the fitted offset	替代核在名义位置surrogate kernel at the nominal position
振幅估计Amplitude estimand	\( E[\hat{S}]/E[S_{eml}] = 1.38 \) （弱端）(faint end)	0.92 （亮端）(bright end)

^[s6]

两条流水线，差别比表面深。看这张表，三行对三件事：怎么拟合、怎么打分、振幅估计量是什么。L0 是我们自己写的：全局网格加 Nelder–Mead 搜索，位置放开，自由度三；它用真实 PSF 的模板族在拟合位置上打分。L1 是 SAS 的 emldetect：它用替代核在名义位置上打分——它不搜索位置，位置是给定的。两者的振幅估计量也不同：弱端差到一点三八倍。所以两条流水线连“数光子的方式”都不同。这一点很重要：如果只看两条流水线的宽度差，你不能说“差多少是拟合器造成的”——打分和估计量都不同。后面我会讲怎么把拟合器单独摘出来。记住这张表的三行——拟合、打分、估计量——因为后面所有“两条流水线”的比较，都要回看这三行才知道在比什么。

Two pipelines, and the difference runs deeper than it looks. Look at the table — three rows for three things: how the fit is done, how the scoring is done, and what the amplitude estimand is. L0 is our own: a global grid plus a Nelder–Mead search, position free, three degrees of freedom; it scores with the real-PSF template family at the fitted offset. L1 is SAS's emldetect: it scores with a surrogate kernel at the nominal position — it does not search for the position, the position is given to it. The two also use different amplitude estimands: they differ by a factor of one point three eight at the faint end. So the two pipelines do not even count photons the same way. That matters: if you only look at the width difference between the two pipelines, you cannot say "this much of the difference is the fitter" — the scoring and the estimand differ too. Later I will explain how the fitter can be isolated.Keep the three rows of this table — fit, scoring, estimand — in mind, because every later comparison of the two pipelines has to be read against these three rows to know what is actually being compared.

cumulative 17.0 min

检验统计量：逐行 \(z\)，按可观测量分箱，判据 \(1 \pm 0.02\)The test statistic: per-row \(z\), binned in observables, key \(1 \pm 0.02\)

\[ z = \frac{\Delta C - \mu(\hat{S})}{\sqrt{V(\hat{S})}}, \qquad \text{std}(z) \approx 1\ \text{and}\ \text{mean}(z) \approx 0 \]\[ z = \frac{\Delta C - \mu(\hat{S})}{\sqrt{V(\hat{S})}}, \qquad \text{std}(z) \approx 1\ \text{and}\ \text{mean}(z) \approx 0 \]

每条结论都由一次独立复算支撑；判据 \( |\text{std}\,z - 1| < 0.02 \)、\(|\text{mean}\,z| < 0.02\)，每箱 \(\geq\) 10,000 行。^[s7]Every record-grade conclusion is backed by an independent replay; the key is \( |\text{std}\,z - 1| < 0.02 \), \( |\text{mean}\,z| < 0.02 \), with \(\geq\) 10,000 rows per bin.^[s7]

怎么测宽度？看上方的公式：每一行模拟算一个 z——Delta C 减去条件均值，除以插入式条件宽度的平方根。如果公式对，每箱的 z 标准差应是一、均值应是零。判据是预注册的：标准差偏离一不超过零点零二，每箱至少一万行。这个项目还有一条纪律值得强调：每条记录级的结论都要由一次独立复算支撑——用任务自己的脚本重跑，输出与报告逐位一致，才能写进记录。今天引用的每个数字都过了这一关。判据、行数、复算，三者缺一不可。这套判据不是事后定的：它在跑数之前就写下来并登记，事后不许改——这是保证结果不变成拟合的唯一办法。

How is the width measured? Look at the formula at the top: for every simulated row we form a z — Delta C minus the conditional mean, divided by the square root of the plug-in conditional variance. If the formula is right, each bin's z has standard deviation one and mean zero. The key is pre-registered: the standard deviation must sit within zero point zero two of one, with at least ten thousand rows per bin. This project has one discipline worth emphasising: every record-grade conclusion must be backed by an independent replay — the job's own script is re-run and its output must match the report bit for bit before anything enters the record. Every number I quote today has passed that gate. The key, the row count, and the replay: all three, or nothing.This key was not decided after the fact: it was written down and registered before the runs, and cannot be changed afterwards — the only way to keep a result from becoming a fit.

cumulative 18.5 min

结果一（先说好消息）：高计数锚处，零参数公式就是答案Result one (the good news first): at the high-count anchor, the parameter-free formula is the answer

配置Configuration	std zstd z	区间Interval
位置固定position fixed	0.98–1.00	DET_ML \( \gtrsim \) 20
位置自由（z_off 打分）position free (z_off scoring)	0.989–1.003	DET_ML \( \geq \) 50
覆盖Coverage	67 位置 × 两种先验67 positions × both priors	—

^[s8]

第一条结果，先说好消息。看表：固定位置、只放开振幅时，Fisher 宽度在检测似然二十以上、低背景处通过——标准差比零点九八到一点零零；放开位置之后，在五十以上，六十七个位置、两种先验合并，零点九八九到一点零零三。这是公式的锚区间：那里零参数宽度不需要任何校准，直接用。这条结果横跨六十七个位置和两种先验都成立，所以它不是一个位置的偶然。换句话说，如果你只做亮源目录，今天的内容对你几乎是个好消息——你的区间全在锚里。值得强调的是“零参数”这三个字的分量：Fisher 信息全部由 PSF 模板与背景图算出，没有一个数是对着数据拟合的；它通过，说明渐近理论在高计数端真的抓到了物理。

First result, and let me start with the good news. Look at the table: with the position fixed and only the amplitude free, the Fisher width passes above detection likelihood twenty at low background — the standard-deviation ratio is zero point nine eight to one point zero zero; with the position free, above fifty, pooled over sixty-seven positions and both priors, it is zero point nine eight nine to one point zero zero three. This is the formula's anchor interval: there the parameter-free width needs no calibration at all — use it directly. The result holds across all sixty-seven positions and both priors, so it is not a one-position accident. In other words, if you only make bright-source catalogues, most of today is good news for you — your entire range sits inside the anchor. It is worth stressing what "parameter-free" weighs here: the Fisher information is computed entirely from the PSF template and the background map, with not a single number fitted to the data; that it passes means the asymptotic theory has genuinely captured the physics at high counts.

cumulative 20.5 min

结果二：目录区间里，同一公式在真实 PSF 下系统性偏窄Result two: in the catalogue interval the same formula is systematically narrow under the real PSF

合并 std z 0.840 / 0.894 / 0.909 / 0.959 / 0.984 于 DET_ML \(\approx\) 4.6 / 7.9 / 11.1 / 22.8 / 36.8；约 36–60 才回到 1。玩具（蓝）约 12 就消失。^[s9]Pooled std z 0.840 / 0.894 / 0.909 / 0.959 / 0.984 at DET_ML \(\approx\) 4.6 / 7.9 / 11.1 / 22.8 / 36.8, returning to 1 only by about 36–60; the toy (blue) is gone by about 12.^[s9]

第二条结果。看这张图：横轴是每箱的典型检测似然，纵轴是标准差比，灰色带是判据带一点加减零点零二，误差棒是标准误。红圈是真实 PSF：从左到右，检测似然约五时只有零点八四，七点九时零点八九，要到三十六以上才回到一。蓝方是玩具高斯 PSF：同样的构造，偏窄到十二就消失了。所以这不是“低计数总是偏窄”的普通现象：它是真实 PSF 的核翼结构带来的，比玩具更深、更持久。这条规律与源计数先验无关，在六十七个位置上都成立。如果你在做弱源目录，这是你今天要记住的问题。还要注意偏窄的方向：分母被高估，残差被除得太狠，所以误差棒偏小、完备性偏高——它让目录看起来比实际更好，这是最危险的方向。

Second result. Look at this figure: the horizontal axis is the typical detection likelihood of each bin, the vertical axis the standard-deviation ratio, the grey band is the key band of one plus or minus zero point zero two, and the error bars are standard errors. The red circles are the real PSF: reading left to right, only zero point eight four at detection likelihood about five, zero point eight nine at seven point nine, and not back to one until past thirty-six. The blue squares are a toy Gaussian PSF: the same construction, and its narrowing is gone by twelve. So this is not the generic "low counts are always narrow": it is brought by the real PSF's core-and-wing structure, deeper and longer-lasting than the toy. The law is independent of the source-count prior and holds at all sixty-seven positions. If you make faint-source catalogues, this is the problem to remember from today. Note also the direction of the narrowing: the denominator is over-stated, the residuals are divided too hard, so the error bars come out small and the completeness high — it makes a catalogue look better than it is, which is the most dangerous direction.

cumulative 23.0 min

没有任何可观测的点修正能闭合它——三条修正路线全部关闭No observable point correction closes it — three correction routes are all closed

修正Correction	结果Outcome
偏差校正振幅 \(\hat{S} - b_S(\hat{S})\)bias-corrected amplitude \(\hat{S} - b_S(\hat{S})\)	std z 只到 0.975 / 0.959 / 0.970 / 0.979，回不到 \(1 \pm 0.02\)std z only reaches 0.975 / 0.959 / 0.970 / 0.979, not \(1 \pm 0.02\)
\( E[V_{3p} \mid \hat{S}] \) 带 Fisher 展布with a Fisher spread	更差（0.84–0.96）worse (0.84–0.96)
解析二阶 penalty（Bartlett / beyond-Fisher）analytic second-order penalty (Bartlett / beyond-Fisher)	符号反 / 过修 1.3–7.4 倍、低 \(\hat{S}\) 出负方差wrong sign / over-corrects 1.3–7.4×, negative variance at low \(\hat{S}\)

^[s10]

能不能修？我们试了三条路，全部失败，我按顺序说。第一，把公式放到偏差校正后的振幅上求值——只消掉四成半，标准差比只到零点九七五、零点九五九、零点九七零、零点九七九，回不到判据。第二，把测量噪声展布进去取期望——更差，零点八四到零点九六。第三，解析的二阶 penalty 修正——Bartlett 项符号反了，beyond-Fisher 项过度修正一点三到七倍、还在最低计数处给出负方差。结论是负的但干净：在真实 PSF 的目录区间，不存在任何可观测的点修正能闭合这个宽度。实用路线只剩经验校准。这个负结果本身有价值——它省下别人再去试这三条路的时间。每一条失败都不是跑一遍就放弃：判据预注册、复算通过、然后才记录为关闭。

Can it be fixed? We tried three routes; all failed. Let me take them in order. First, evaluate the formula at the bias-corrected amplitude — it removes only about half the deficit; the standard-deviation ratio only reaches zero point nine seven five, zero point nine five nine, zero point nine seven zero and zero point nine seven nine, never the key. Second, average over the measurement noise — worse, zero point eight four to zero point nine six. Third, analytic second-order penalty corrections — the Bartlett term has the wrong sign, and the beyond-Fisher term over-corrects by factors of one point three to seven and even gives a negative variance at the lowest counts. The conclusion is negative but clean: under the real PSF in the catalogue interval, no observable point correction closes this width. The practical route is empirical calibration. This negative result has value in itself — it saves others the time of trying these three routes. And none of these failures was a one-run-and-quit: each had a pre-registered key, an independent replay, and only then was recorded as closed.

cumulative 25.5 min

结果三（核心）：偏窄来自两个几乎相消的大项——\(V_{3p} = \mathrm{term1} - 4\,\mathrm{penalty}\)Result three (the core): the narrowing comes from two nearly cancelling large terms — \(V_{3p} = \mathrm{term1} - 4\,\mathrm{penalty}\)

\[ V_{3p} = \underbrace{\text{term1}}_{15\text{–}31\times\, \mathrm{Var}(R)} \;-\; 4\,\text{penalty}, \qquad \frac{V_{3p}(\hat{S})}{\mathrm{Var}(R)} = 1.44 \ \text{at DET\_ML} \approx 3.5 \]\[ V_{3p} = \underbrace{\text{term1}}_{15\text{–}31\times\, \mathrm{Var}(R)} \;-\; 4\,\text{penalty}, \qquad \frac{V_{3p}(\hat{S})}{\mathrm{Var}(R)} = 1.44 \ \text{at DET\_ML} \approx 3.5 \]

算例（已复算）：term1 = 63.6，Var(R) = 1.90（约 33 倍），penalty 错配 \(\approx\) 1.4 % → 1 % 的一级误差变成约 44 % 的方差误差。^[s11]Worked example (replayed): term1 = 63.6, Var(R) = 1.90 (about 33×), penalty mismatch \(\approx\) 1.4 % → a 1 % first-order error becomes a 44 % variance error.^[s11]

现在到核心，也是我最希望你们带走的一页。看上方的公式：Fisher 方差等于第一项减去四倍的 penalty。这两项几乎完全相消——第一项是残差方差的十五到三十一倍，方差只来自两者之差。取检测似然三点五这一箱做算例：第一项六十三点六，残差方差一点九，差三十三倍；penalty 只错配百分之一点四。两个几乎相等的大数相减，其中一个差百分之一，结果就差百分之四十四——这就是相消放大：不是公式错了，也不是求值点错了——是构造本身把一阶小误差放大成大方差误差。它也解释了为什么点修正全部失败：误差不在求值点，在 penalty 本身。从这一页往后，所有结果都是这个机制的不同侧面。

Now the core — the page I most want you to take away. Look at the formula at the top: the Fisher variance equals term one minus four times a penalty. The two nearly cancel — term one is fifteen to thirty-one times the residual variance, and the variance is only the difference. Take the bin at detection likelihood three point five as a worked example: term one is sixty-three point six, the residual variance one point nine, a factor thirty-three; the penalty is off by only one point four per cent. Two nearly equal large numbers subtract, one of them is off by one per cent, and the result is off by forty-four per cent — that is cancellation amplification: the formula is not wrong, and the evaluation point is not wrong — the construction itself amplifies a small first-order error into a large variance error. It also explains why the point corrections all failed: the error is not at the evaluation point, it is in the penalty itself. From this page onward, every result is a different face of this one mechanism.

cumulative 28.5 min

错配不是常数：它随 PSF 的翼结构（低计数翼像素）与计数上升The mismatch is not a constant: it rises with the PSF's wing structure (low-count wing pixels) and the counts

核Kernel	错配Mismatch
同二阶矩高斯Gaussian of equal 2nd moment	\( \approx \) 0.05 %
真实 PSFreal PSF	+1.0–1.8 %
固定 \(\hat{S}\)、背景减半fixed \(\hat{S}\), background halved	+0.5…+0.9 pp （\(\hat{S} \lesssim 5\)）(\(\hat{S} \lesssim 5\))

固定峰值与二阶矩的族内，错配随核/翼分裂跨约 5 倍——峰值只是代理，翼像素含量更贴近。Within a family at fixed peak and second moment the mismatch spans about 5× with the core/wing split — peak is only a proxy; the wing-pixel content tracks it better.

^[s12]

这个百分之一的错配从哪来？它随 PSF 的形状走。看这张表：同样二阶矩的高斯只有百分之零点零五；真实 PSF 百分之一到一点八；固定测到的计数、把背景减半，错配再抬升零点五到零点九个百分点。在固定峰值、固定二阶矩的族里，把光从核挪到翼，错配就跨五倍——所以它跟的是低计数翼像素的含量，不是中心峰值。这两条依赖意味着：错配没法用一个常数修掉，任何修正都得随计数、背景、PSF 一起变。这也是为什么我把“经验校准”说成实用路线而不是失败——校准可以逐格做，修正不行。这一页的表也预告了为什么修正是难的：错配不是一个数，是一族随构造移动的数。

Where does the one per cent come from? It follows the PSF's shape. Look at the table: a Gaussian of the same second moment gives only zero point zero five per cent; the real PSF gives one to one point eight; and at fixed measured counts, halving the background raises the mismatch by another half to one percentage point. Inside a family with fixed peak and fixed second moment, moving light from the core to the wing spans the mismatch by a factor of five — so it tracks the low-count wing-pixel content, not the central peak. These two dependences mean the mismatch cannot be repaired by one constant: any correction must vary with counts, background and PSF together. That is why I call empirical calibration the practical route rather than a failure — a calibration can be done cell by cell; a correction cannot.This table also foreshadows why a correction is hard: the mismatch is not one number, it is a family of numbers that move with the construction.

cumulative 31.0 min

可跳过disposable

同一个机制也决定 emldetect 的宽度——两条流水线，一个机制The same mechanism sets emldetect's width too — two pipelines, one mechanism

emldetect（L1）：DET_ML 6–10 错配 +1.19 % [+1.03, +1.35]（合并估计量），解释箱内宽度缺口的 0.89 [0.84, 0.93]；预测 std z 0.919 对实测 0.918（按行合并 0.940）。^[s13]emldetect (L1): DET_ML 6–10 mismatch +1.19 % [+1.03, +1.35] with pooled estimators, explaining 0.89 [0.84, 0.93] of the within-cell width deficit; predicted std z 0.919 against the observed 0.918 (row-pooled 0.940).^[s13]

这一页是最近的一条结果，也是把故事合上的一页。看图：横轴还是典型检测似然，纵轴是标准差比；这是玩具核的曲线，emldetect 的对应表现在备用页里。emldetect 的宽度也偏窄——标准差比零点九四六。用合并估计量重测它的 penalty 错配：加百分之一点一九，区间一点零三到一点三五。把这个错配放进同一个相消机制，预测标准差比零点九一九——实测零点九一八。也就是说，同一个机制解释了 emldetect 宽度缺口的百分之八十九。早先一个“emldetect 的错配约等于零”的读数，是逐格比值再取平均造成的——逐格平均会让格间散布吃掉信号；合并估计量才保留它。所以结论统一了：不是“我们的拟合器一个物理、emldetect 另一个物理”，是两条流水线共享一个机制。这也是为什么我说修一次两边都受益。

This page carries the most recent result, and it closes the story. Look at the figure: the horizontal axis is again the typical detection likelihood, the vertical axis the standard-deviation ratio; this curve is the toy core, and emldetect's corresponding table is in the backup pages. emldetect's width is narrow too — a standard-deviation ratio of zero point nine four six. Re-measuring its penalty mismatch with pooled estimators gives plus one point one nine per cent, interval one point zero three to one point three five. Feeding that mismatch through the same cancellation mechanism predicts a standard-deviation ratio of zero point nine one nine — the observation is zero point nine one eight. In other words, one mechanism explains eighty-nine per cent of emldetect's width deficit. An earlier reading that "emldetect's mismatch is about zero" came from averaging per-cell ratios — a per-cell average lets the between-cell scatter eat the signal; pooled estimators keep it. So the conclusion is unified: it is not "our fitter has one physics and emldetect another" — the two pipelines share one mechanism. And that is why I said fixing it once benefits both.

cumulative 34.0 min

低计数端的中心项也偏高——它是 L0 流水线自己的性质，成因开放At the low-count end the centre term is biased high too — a property of the L0 pipeline itself, cause open

Matched-control comparison of the L0 low-count centre excess

匹配对照下差距仍在：\(\hat{S}\) 分箱 +0.389 / +0.14–0.18 / +0.058 \(\pm\) 0.007；但 72/28 归因已撤回（配对重拟合只补 0–27 %），成因开放。^[s14]The gap survives the matched control: \(\hat{S}\)-bin gaps +0.389 / +0.14–0.18 / +0.058 \(\pm\) 0.007; but the 72/28 attribution is withdrawn (the paired refit closes only 0–27 %), cause open.^[s14]

宽度之外还有中心。低计数端，条件均值也偏高。看这张图：上排是 L0 生产的真实 PSF 图像，下排是匹配对照——同样的 PSF 栅格、掩膜、背景律、抖动、位置；黄色带标出低计数箱；右侧的条是按可观测量分箱的差距，单位是标准差。差距还在：最低计数箱高零点三八九，中间箱零点一四到零点一八，高计数箱零点零五八加减零点零零七。对照这一侧本来就是我们自己的仪器，所以这个差距量的是 L0 流水线自己的性质，不是 emldetect 的物理。但要诚实：它具体来自模板族、拟合器还是插值约定，现在开放——我们曾把它拆成七成二对二成八，后来用配对重拟合检验这个拆分，它只能补上百分之零到二十七，拆分撤回。同图同打分的配对实验也已完成：同一批图像上 emldetect 与 L0 高计数一致，DET_ML ≲ 7 处 emldetect 的中心反而比 L0 低 0.16–0.53 z、宽 0.05–0.14——所以这个超额不是 emldetect 的性质。超额本身站得住，成因未定。

Beyond the width there is the centre. At the low-count end the conditional mean is biased high too. Look at the figure: the top row is the L0 production real-PSF images, the bottom row the matched control — the same PSF raster, mask, background law, jitter and position; the yellow band marks the low-count bin; the bars on the right are the gaps in observable bins, in standard-deviation units. The gap survives: zero point three eight nine high in the lowest-count bin, zero point one four to zero point one eight in the middle bins, zero point zero five eight plus or minus zero point zero zero seven in the high-count bin. The control side is already our own instrument, so the gap measures a property of the L0 pipeline itself, not emldetect physics. But to be honest: whether it comes from the template family, the fitter or the interpolation conventions is open — we once split it seventy-two against twenty-eight per cent, then tested that split with a paired refit, which closes only zero to twenty-seven per cent, so the split is withdrawn. The paired same-images-same-scoring run is completed too: on the same images emldetect and L0 agree at high counts and at DET_ML ≲ 7 emldetect's centre is 0.16–0.53 z lower and its width 0.05–0.14 larger than L0 — so this excess is not an emldetect property. The excess stands; its cause is undetermined.

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规律阶段：四条候选全部被拒收——宽度一半在同一个位置内可推广，中心一半不能The law stage: every candidate is rejected — the width half generalises within one position, the centre half does not

候选Candidate	参数Parameters	留出格通过Held-out passes
C	0	10 / 72
D	288	48 / 72
DQ	—	42 / 72
MIX3d	—	35 / 72
完美规律（零假设）perfect law (null)	—	\(\approx\) 62–63 / 72

M2 相机、第 4 能段、67 个位置、约 10⁶ 行；一半位置拟合、一半位置打分；评分器先在“规律恰好为真”的数据上验证（K-S p 0.59）。D 最好但 p = 0.0015，仍被拒。表内通过数自此降级为历史诊断（R118 取代）：2026-10-21 的复核（R114）表明旧打分手混用三个估计对象——宽度是位置内加权 std、均值与覆盖率跨位置合并、零假设自适应；一支红队（R117）进一步证明宽度指标对逐位置偏移恒等不变（1e-15，一条带 0.30 z 逐位置偏移的规律仍通过宽度 70/72）。新打分手（R118）分开两个目标：未见位置总体上能段 4 的 D / H2 / MIX3d / C 通过 44 / 50 / 32 / 12 格（共 72）、能段 1 的 D / H2 为 36 / 43，全部被 Q 拒；逐位置上每条候选都接近 0/72，冻结位置效应 0.14 z（能段 4）/ 0.18 z（能段 1）且重尾。2026-10-22 的复核把判据与位置项又推进了一步：“每个条目都在容差 \(\varepsilon\) 内”的判据被证明噪声受限（一条完美规律在能段 4 上也只能让 21–27 % 的位置满足它），于是改成每个位置一个合并偏移，容差定为比较规律 0.05、跟踪进度 0.10，打分手冻结为 score_pooled_v1.py（18 个格、位置真值校准的 95 % 区间）；旧读数“规律就压在位置盲地板上”被地板改正推翻，改正后最好候选在 0.10 处高于地板。位置效应的来源收窄到像素级几何且两条能段共享（r = +0.936）：不是源表，导出的相位项被驳回，“像素中心把偏移放大 2 倍”的读法已撤回（打分器伪迹，同一格掩膜下比值 1.16）；第一个拟合前位置项（拟合盒背景水平）把最好候选从 0.545 抬到 0.727（p 0.003–0.004，尚未在新位置检验）。宽度侧，判据本身也被校准：一条逐行精确的方差律通过“8 箱全在 1 \(\pm\) 0.02 内”的概率只有 66.8 %，PI 于是批准“8 箱允许 1 箱失败”（完美规律通过约 95 %）；在这条判据下第一条可观测箱级宽度规律 \(\bar{V}(\hat{S}, b)\) 通过（1/8），但带宽在测试半上选定（40 个随机分半下 P(\(\leq\) 1 失败) 0.79），且同一构造迁到 emldetect 行后在全统计量下仍失败 5/5 箱。^[s19]M2 camera, band 4, 67 positions, about 10⁶ rows; fitted on half the positions, scored on the other half; the scorer was first validated on data where the law is exactly true (K-S p 0.59). D is the best but has p = 0.0015 and is still rejected. The pass counts in this table are demoted to historical diagnostics from here on (superseded by R118): a 2026-10-21 audit (R114) shows the old scorer mixes three estimands — the width is a within-position weighted std, the mean and coverage pool rows across positions, and the null adapts to the candidate; a red team (R117) further proves the width metric is identically invariant (1e-15) to per-position offsets — a law carrying a 0.30 z per-position offset still passes width 70/72. The new scorer (R118) separates two targets: on the population of unseen positions band-4 D / H2 / MIX3d / C pass 44 / 50 / 32 / 12 of 72 cells and band-1 D / H2 36 / 43, all rejected on Q; per position every candidate is near 0/72, with the frozen position effect 0.14 z (band 4) / 0.18 z (band 1), heavy-tailed. A 2026-10-22 audit advanced both the criterion and the position term: the “every entry within the tolerance \(\varepsilon\)” rule was shown to be noise-limited (even a perfect law satisfies it at only 21–27 % of positions on band 4), so it became one pooled offset per position, with tolerances of 0.05 to compare laws and 0.10 to track progress, and the scorer frozen as score_pooled_v1.py (18 cells, position-true-calibrated 95 % intervals); the old reading “the laws sit at the position-blind floor” is overturned by the floor correction, after which the best candidate sits above the floor at 0.10. The position effect's origin narrowed to pixel-level geometry shared by both bands (r = +0.936): not the source list, the derived phase term is rejected, and “pixel centres amplify the offsets 2\(\times\)” is withdrawn (a scorer artefact, ratio 1.16 under the same cell mask); a first pre-fit position term (the fit-box background level) lifts the best candidate from 0.545 to 0.727 (p 0.003–0.004, not yet tested on fresh positions). On the width side the criterion itself was calibrated too: a row-exact variance law passes “all 8 bins inside 1 \(\pm\) 0.02” only 66.8 % of the time, so the PI approved “at most 1 failing bin of 8” (a perfect law passes about 95 %); under it the first observable bin-level width law \(\bar{V}(\hat{S}, b)\) passes (1 of 8), but its bandwidth was chosen on the test half (P(\(\leq\) 1 failing bin) 0.79 over 40 random splits) and the same construction still fails 5/5 bins on emldetect rows at full statistics.^[s19]

机制讲完了，说把它做成规律的尝试，因为这是今天的第四条信息，也是最该诚实的一条。目标是把条件宽度和中心写成目录能用的条件律：给定测到的计数、背景和源计数斜率，检测统计量服从什么分布。我们试了四个候选：零参数基线、288 个参数的制表修正、二次斜率形式、生成式混合。每个都在一半位置上拟合、另一半上打分。打分之先，先验证评分器本身——在规律恰好为真的合成数据上，它的 p 值分布均匀。结果见表：通过数十分之七十二、四十八、四十二、三十五。作为参照，一条完美的规律在同样的噪声下平均也只通过约六十二到六十三格——所以四十八格虽然是四者最好，仍然远低于噪声底，p 值只有零点零零一五。结论是四个候选全部被拒收。把最好的那个拆开看，失败集中在中心而不是宽度：宽度格七十二个里过了六十八个，二十四个失败全在均值上，而且全部为负、集中在中计数、随斜率增长。位置也不是缺失的变量——加一个平滑的离轴项，留出失败反而从二十四个涨到五十八到七十二个；唯一能改善的是一个逐格中心截距，十八个参数，把失败降到十一个、负和从负二点二八降到负零点八零，而位置斜率不加分。所以宽度这一半在同一个位置内已经有机制也有校准，中心这一半还开着。但这里有一个今天才厘清的限定，也是我最该诚实的一点：旧打分手混用三个估计对象——宽度是位置内的加权标准差，均值与覆盖率却跨位置合并，零假设的位置散布还从候选自己的留出残差估计。红队随后给了一条精确结果：宽度指标对逐位置偏移恒等不变——一条带零点三零个标准差异常的规律，宽度格照样过百分之七十。所以"宽度可以推广"这句话，只能读作在同一个位置内。新打分手把两个目标分开：未见位置总体上，最好的候选过四十四到五十格（共七十二），逐位置上每条候选都接近零格。这也是我要强调的方法学：打分器本身错了两次，一次是零假设的通过率没算对，一次是全局统计量的尺度错了，都是先修打分器再谈结论；修好之后它的判定在多个替代零假设下全部成立，但验证带限定——位置聚落尺度由同一估计量恢复，格间相关加零点四四没有进零假设，所以最好候选的 p 值随零假设变动约一个量级，不过没有判定翻转。

The mechanism is told; now the attempt to turn it into a law, because this is today's fourth message and the one that most deserves honesty. The goal is to write the conditional width and the centre as a law a catalogue can use: given the measured counts, the background and the source-count slope, what distribution does the detection statistic follow. We tried four candidates: a parameter-free baseline, a 288-parameter tabulated correction, a quadratic-slope form and a generative mixture. Each was fitted on half the positions and scored on the other half. Before scoring, the scorer itself was validated — on synthetic data where the law is exactly true its p-values are uniform. The results are in the table: passes of ten, forty-eight, forty-two and thirty-five out of seventy-two. For reference, a perfect law passes only about sixty-two to sixty-three of the same seventy-two cells under the same noise — so forty-eight, though the best of the four, is far below the noise floor, with a p-value of only zero point zero zero one five. The verdict is that all four candidates are rejected. Taken apart, the best one fails on the centre rather than the width: sixty-eight of the seventy-two width cells pass, while all twenty-four failures are on the mean — all negative, concentrated at mid count and growing with the slope. Position is not the missing variable either: adding a smooth off-axis term raises the held-out failures from twenty-four to fifty-eight to seventy-two instead of lowering them; the only form that improves matters is a per-cell centre intercept — eighteen parameters, taking the failures to eleven and the negative sum from minus two point two eight to minus zero point eight zero, with the position slope adding nothing. So the width half within one position already has a mechanism and a calibration; the centre half is still open. But there is a qualification that only became clear today, and it is the one I most owe you: the old scorer mixes three estimands — the width is a within-position weighted standard deviation, the mean and coverage pool rows across positions, and the null's position scatter is estimated from the candidate's own held residuals. A red team then gave an exact result: the width metric is identically invariant to per-position offsets — a law carrying a zero point three standard-deviation defect still passes seventy per cent of the width cells. So the sentence "the width generalises" can only be read as within one position. The new scorer separates the two targets: on the population of unseen positions the best candidates pass forty-four to fifty of the seventy-two cells, and per position every candidate is near zero. This is also the methodological point I want to stress: the scorer itself was wrong twice — once on the null's pass rate and once on the global statistic's scale — and both times the scorer was fixed before any conclusion was drawn; after the fixes its verdicts stand under every alternative null, but the validation carries qualifications — the position-cluster scale is recovered by the same estimator, and the cross-cell correlation of plus zero point four four is not in the null, so the best candidate's p-value moves by about an order of magnitude with the null, though no verdict flips.

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一句话版本：两个几乎相等的大数相减，其中一个差 1 %，结果就差 5–16 %The one-sentence version: subtract two nearly equal large numbers, one off by 1 %, and the result is off by 5–16 %

\[ \text{term1} - 4\,\text{penalty} = V_{3p}, \qquad \text{term1} \approx 15\text{–}31 \times V_{3p} \]\[ \text{term1} - 4\,\text{penalty} = V_{3p}, \qquad \text{term1} \approx 15\text{–}31 \times V_{3p} \]

PSF 越集中、计数越低，错配越大——这就是为什么真实 PSF 的偏窄比玩具更深、更持久。the more concentrated the PSF and the lower the counts, the larger the mismatch — which is why the real PSF's narrowing is deeper and longer-lasting than the toy's.

如果今天只带走一句话，带这句。方差公式是两个几乎相等的大数之差；Fisher penalty 与有效 penalty 只差百分之一；这个百分之一被相消放大成百分之五到十六的方差高估。PSF 越集中越明显，计数越低越明显。这既是坏消息——没有简单修正——也是好消息——机制只有一个，两条流水线通用，修一次两边都受益。这句话是今天整个演讲的压缩版。接下来两页是局限与建议，然后收尾。把这句话记住，你甚至可以不听后面两页——但局限和建议对实际做目录的人同样重要，所以我还是要讲。

If you take away one sentence today, take this one. The variance formula is the difference of two nearly equal large numbers; the Fisher penalty matches the effective penalty to one per cent; that one per cent is amplified by the cancellation into a five to sixteen per cent variance over-statement. The more concentrated the PSF and the lower the counts, the worse it gets. That is the bad news — no simple fix — and the good news at once: there is one mechanism, shared by both pipelines, so fixing it once benefits both. This sentence is the entire talk in compressed form. The next two pages are caveats and advice, and then we close.Remember this sentence and you could even skip the next two pages — but the caveats and the advice matter just as much to anyone actually making catalogues, so I will go through them anyway.

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诚实的局限：模拟单场、emldetect 修正未完全检验、中心项成因开放、逐位置尚未解决Honest caveats: a single simulated field, the emldetect correction not fully tested, the centre-term cause open, no position yet solved per-position

PSF、背景律、抖动取自一个场（M31）；外推到其他场需重新验证。The PSF, background law and jitter come from one field (M31); extrapolating to other fields needs re-validation.
emldetect 的宽度缺口已由机制解释（0.89）；按计数修正的 \(V_{3p}\) 在 emldetect 输出上校准时成立（留出 0.976 [0.956, 0.993] 是一次偏低的分半，40 个按半径分层的分半平均 0.998；6 参数修正只通过 25/72 个宽度格），但换独立模拟就过修、未定稿。emldetect's width deficit is explained by the mechanism (0.89); the count-corrected \(V_{3p}\) works when calibrated on emldetect output (the held-out 0.976 [0.956, 0.993] is one low split — the average over 40 radius-stratified splits is 0.998, and the 6-parameter correction passes only 25/72 width cells) but over-corrects when transferred from an independent simulation and is not final.
低计数中心项超额的成因开放（72/28 归因已撤回）。The low-count centre excess's cause is open (the 72/28 attribution is withdrawn).
同图同打分的配对实验（只让拟合器不同）已完成（3 个试点位置）：L0 超额不是 emldetect 的性质，但 67 位置的推广尚未做。The paired same-images-same-scoring run (only the fitter differing) is completed (3 pilot positions): the L0 excess is not an emldetect property, but the 67-position extension has not been done.
第一个拟合前位置项把最好候选从 0.545 抬到 0.727，但它在同一批位置上拟合并打分，尚未在未见位置上检验；冻结打分手的宽度区间仍欠覆盖（0.941 / 0.946 对一个 0.950 的接受带），所以每个已解决比例都要连这个限制一起引用；可观测箱级宽度规律的通过也依赖估计量细节：宽度检验的行自助标准误忽略了 \((\mathrm{pid}, S_{true})\) 聚类设计（中位设计效应 1.26），聚类标准误下玩具 1/8 变 0/8、“匹配统计量 1/5 通过”按种子运气撤回（P(\(\leq\) 1 失败) 0.067），“窄核靠误差相消通过”的读法也被改判为粗锚伪迹（细锚下次序在每个分半里都反过来）；而 1.16 的臂间残余本身是真的（\(\chi^2\) 312 于 12 个自由度），两臂还在盒表起点、注入取整像素与一次 PSF 存档错配上有别，这一段没有解释。The first pre-fit position term lifts the best candidate from 0.545 to 0.727, but it was fitted and scored on the same positions and has not been tested on unseen positions; the frozen scorer's width interval still under-covers (0.941 / 0.946 against a 0.950 acceptance band), so every solved fraction must be quoted with that limit attached; the observable bin-level width law's pass also depends on estimator detail: the width test's row-bootstrap SE ignores the \((\mathrm{pid}, S_{true})\) cluster design (median design effect 1.26), under a cluster SE the toy's 1/8 becomes 0/8 and the “matched-power pass (1 of 5)” is withdrawn as seed luck (P(\(\leq\) 1 fail) 0.067), and the “narrow kernel passes by error cancellation” reading is itself re-interpreted as a coarse-anchor artefact (with fine anchors the ordering reverses in every split); and the 1.16 arm-to-arm residual is itself real (\(\chi^2\) 312 on 12 degrees of freedom), with the two arms also differing in boxlist start, injection rounding pixel and one PSF staging error, so that part is unexplained.
普适性只在冻结合并口径下、且只在有信息量的块上检验过：M2 能段 1 的中心通过（0.7273），M1 能段 1 是一个已分辨的中心失败（0.381），M1 其余能段与高计数锚点（能段 4 为 0/12）分辨不了或失败，Tier 1 因此压住等 PI；位置项在新位置上的检验是 AMBIGUOUS（+0.148 [−0.037, +0.333]），且 27 个新位置里 8 个受源拥挤污染，所以它不能读作位置项的检验；宽度判据的零假设（k* 2–3）与掩膜规则（中位 MASKFRAC_EML < 0.98，代价约 10 % 的位置）都还是 Provisional，等 PI 决定。Universality has been tested only under the frozen pooled convention and only on the informative blocks: M2 band 1's centre passes (0.7273), M1 band 1 is a resolved centre failure (0.381), the remaining M1 bands and the high-count anchors (band 4 at 0/12) either cannot be resolved or fail, so Tier 1 is held for the PI; the position term's test at fresh positions is AMBIGUOUS (+0.148 [−0.037, +0.333]) and 8 of the 27 fresh positions are source-crowded, so it cannot be read as a test of the position term; the width rule's null (k* 2–3) and the mask rule (median MASKFRAC_EML < 0.98, at a cost of about 10 % of positions) are both Provisional and await the PI.
普适性 Tier 1 的第一臂只在留出能段块上打过分：M2 能段 1 的中心确认（0.727 [−0.152, +0.061]），宽度旗标 AMBIGUOUS（超出真实、单侧约 2 %、箱边敏感），锚 8/12，没有合并判定；M1 各能段只作描述。背景通道的定律非普适（估计背景下 +0.174 z）意味着任何用到估计背景的结论都要带这个系统差；候选参数 C2 只在一个观测、9 个留出位置上暂定。代价锚实测 0.97 CPU-s/行（区间 0.86–1.3），旧 0.4 作废；星表侧 DET_ML 有序结构是标注同义反复、断幂律 5/6（M2 低 \(\mu_0\) 的事后补丁不是确认性证据）、eta 振幅修合并宽度但逐格形状失败。Universality Tier 1's first arm has been scored only on the held-out band blocks: M2 band 1's centre is confirmed (0.727 [−0.152, +0.061]), the width flag is AMBIGUOUS (the excess real, one-sided about 2 %, edge-sensitive), the anchor 8/12, and there is no combined verdict; the M1 bands stay descriptive. The background channel's non-universality (+0.174 z under an estimated background) means every conclusion that uses an estimated background carries that systematic; the candidate parameter C2 is provisional on one observation and 9 held positions. The cost anchor is measured at 0.97 CPU-s/row (band 0.86–1.3), superseding the old 0.4; on the catalogue side the DET_ML-ordered structure is a labelling tautology, the broken power law is 5/6 (M2's low-\(\mu_0\) patch is not confirmatory evidence), and the eta amplitude restores the pooled width while the per-cell shape fails.

四条局限，按大小排。第一，所有结论来自可控模拟，且 PSF、背景与抖动取自单一场——M31；换场要重新验证。第二，emldetect 的宽度缺口虽然被机制解释了百分之八十九，但按计数修正的方差还没做出来并通过独立检验，所以今天不能给你修正方案。第三，低计数中心项的成因开放。第四，把两条流水线放在同一批图像、同一套打分下的配对实验已经完成（三个试点位置）：结论是 L0 超额不是 emldetect 的性质、单图 emldetect 规律必须在 emldetect 输出上建立，但六十七个位置的推广还没做。我特意把局限放在结果之后、建议之前——它们的顺序就是它们的重量。如果你只信一条局限，信第一条：单场模拟是所有数字的地基。

Four caveats, in order of size. First, all conclusions come from a controlled simulation whose PSF, background and jitter are taken from a single field — M31; another field needs re-validation. Second, although the mechanism explains eighty-nine per cent of emldetect's width deficit, the count-corrected variance has not been built and independently tested yet, so I cannot hand you a correction today. Third, the low-count centre term's cause is open. Fourth, the paired run that puts both pipelines on the same images with the same scoring is completed (three pilot positions): the conclusion is that the L0 excess is not an emldetect property and the single-image emldetect law must be built on emldetect output, but the sixty-seven-position extension has not been done. I put the caveats after the results and before the advice on purpose — their order is their weight. If you trust only one caveat, trust the first: the single simulated field is the foundation under every number you have seen.

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对你做 X 射线巡天的实际建议：分区间的三条规则Practical advice for X-ray survey work: three rules by interval

区间Interval	做法What to do
DET_ML \( \geq \) 50	直接用零参数公式给误差use the parameter-free formula's errors directly
DET_ML 6–20	按 \(\hat{S}\) 分箱的 std z 表经验校准，报告校准来源与区间calibrate empirically with a per-\(\hat{S}\)-bin std z table, reporting the source and interval
跨流水线across pipelines	不要把一条流水线的校准搬到另一条；先做同图同打分的配对比较never carry one pipeline's calibration to another; run the paired same-image comparison first

落到实践，三条规则，按检测似然分区。第一，五十以上，直接用零参数公式给误差——零参数、零校准，这是锚区间的红利。第二，六到二十的目录区间，用按可观测量分箱的标准差比表做经验校准，并且写明校准的来源与适用区间——因为错配随计数、背景、PSF 变，一张表只在它的区间内有效。第三，跨流水线比较时，千万不要把一条流水线的校准搬到另一条上——打分与振幅估计量都不同；先做同图同打分的配对比较再下结论。如果你今晚就要处理一个 XMM 目录，这三条就是你能直接用的输出。第二条还有个容易忽略的细节：校准表要跟着你的 PSF 版本与能段走，换能段就是换表。

Down to practice, three rules, partitioned by detection likelihood. First, above fifty, use the parameter-free formula's errors directly — zero parameters, zero calibration; that is the anchor interval's dividend. Second, in the catalogue interval six to twenty, calibrate empirically with a standard-deviation-ratio table binned in observables, and state the calibration's source and interval — because the mismatch varies with counts, background and PSF, a table is valid only inside its interval. Third, across pipelines, never carry one pipeline's calibration to another — the scoring and the amplitude estimands differ; run the paired same-image, same-scoring comparison before concluding anything. If you have an XMM catalogue to process tonight, these three rules are the directly usable output of this talk. One easily missed detail on the second rule: the calibration table must follow your PSF version and your band — change the band and you change the table.

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下一步：把机制变成产品——单图 emldetect 条件律 \(p(\mathrm{DET\_ML} \mid \hat{S}, b, \mathrm{index})\)Next: turning the mechanism into a product — the single-image emldetect conditional law \(p(\mathrm{DET\_ML} \mid \hat{S}, b, \mathrm{index})\)

\[ p(\mathrm{DET\_ML} \mid \hat{S}, b, \mathrm{index}), \qquad \mathrm{index} = \text{slope of } dN/dS \]\[ p(\mathrm{DET\_ML} \mid \hat{S}, b, \mathrm{index}), \qquad \mathrm{index} = \text{slope of } dN/dS \]

范围：3 仪器（PN、M1、M2）× 5 能段；\(b\) 取 4XMM 星表出现过的 \(b\) 的 10–90 % 区间；任意视场位置。PI 于 2026-10-22 10:44 EDT 定下推进顺序：普适性 Tier 0 先跑（跨能段 / 跨仪器打分），Tier 1 的条目 1–2 等它的结果。Tier 0 已跑完（A0-RESCORE，冻结合并口径、零新参数）：星表轴上冻结的宽度律在 \(\mu_0 \lesssim\) 120 / 250 域内通过、以上失败；能段/仪器轴上起初报的失败已撤回（打分口径错误），但重新打分给出新的图景——M2 能段 1 的中心通过（24/33 = 0.7273），M1 能段 1 是一个已分辨的中心失败（8/21 = 0.381），M1 其余能段在现有设计下分辨不了（MDS 约 0.30），高计数锚点只部分通过（M1 能段 4 为 0/12）；次要目标是 3 仪器 \(\times\) 5 能段、完备性与流量后验、论文、普适性验证。后续：多仪器 → 多能段 → 多次观测。Domain: 3 instruments (PN, M1, M2) × 5 bands; \(b\) in the 10–90 % range of the \(b\) values occurring in the 4XMM catalogue; any field-of-view position. The PI set the order on 2026-10-22 10:44 EDT: universality Tier 0 runs first (cross-band / cross-instrument scoring), with Tier 1 items 1–2 after its results. Tier 0 has now run (A0-RESCORE, frozen pooled convention, zero new parameters): on the catalogue axis the frozen width law passes within \(\mu_0 \lesssim\) 120 / 250 and fails above; on the band/instrument axis the first reported failure is withdrawn (a scoring-convention error), but the re-score gives a new picture — M2 band 1's centre passes (24/33 = 0.7273), M1 band 1 is a resolved centre failure (8/21 = 0.381), the remaining M1 bands cannot be resolved under the present design (MDS about 0.30), and the high-count anchor passes only in part (M1 band 4 at 0/12); the secondary goals are 3 instruments \(\times\) 5 bands, completeness and the flux posterior, the paper, and universality validation. Later: multi-instrument → multi-band → repeat observations.^[s15]

最后说下一步。机制已知之后，目标是把它变成目录用户能直接用的产品：单图 emldetect 的条件律——看上方的公式：给定测到的计数、背景、以及源计数分布的斜率，检测统计量服从什么分布。为什么带斜率？因为弱源处对真实流量的依赖，经斜率这个变量表达，而不是条件在真实流量上——后者是目录用户拿不到的。范围是三个仪器乘五个能段，背景取星表里实际出现过的区间，位置覆盖整个视场。之后才谈完备性和流量后验。这一步已经在做，而且今天可以报告一个否定的结果：四个候选形式（零参数基线、288 参数的制表修正、二次斜率、生成式混合）在留出位置上被一支先在“恰好为真”数据上验证过的评分器全部拒收——失败集中在中心而不是宽度。当天下午的复核厘清了边界：评分器混用估计对象，宽度指标对逐位置偏移恒等不变，所以"宽度可推广"只能读作在同一个位置内；新打分手分开两个目标后，未见位置总体上最好的候选过四十四到五十格（共七十二），逐位置上每条候选都接近零格。项目负责人当天把进度指标定为已解决位置的比例（与面积），可以从零开始增长，不设阈值；第一个点已经测出：能段 4 上 D 与 H2 各只有 4/33 个位置的条目通过比例达到 0.90（均值 0.643 / 0.651），能段 1 只有 1/33——这就是进度曲线的起点。所以下一步不是再拟合一个规律，而是先解决中心项：一个正在进行的符号回归试点（两条臂，其中一条的模型后端是本地推理服务）在中心残差面上找一个短解析式，再用同一支评分器留出打分、并测试跨能段迁移；另有一个混合规律任务在跑——用最好的宽度形式配上生成式混合的中心。这一切都建立在今天的机制上——机制统一了，产品才有正确的骨架。还有一件当天定下的顺序：普适性分两层——先跑 Tier 0（跨能段、跨仪器打分），Tier 1 的两个条目等它的结果，避免在没搞清一条规律能迁移多远之前就铺开。条件律不是又一个理论练习：它是完备性曲线和流量后验的输入，做目录的人最终拿到的应该是它。

Finally, next steps. With the mechanism known, the goal is to turn it into a product a catalogue user can apply directly: the single-image emldetect conditional law — look at the formula at the top: given the measured counts, the background, and the slope of the source-count distribution, what distribution does the detection statistic follow? Why carry the slope? Because the faint-end dependence on the true flux is expressed through that variable, not by conditioning on the true flux — which a catalogue user never has. The domain is three instruments times five bands, backgrounds spanning the range that actually occurs in the catalogue, positions across the whole field of view. Completeness and flux posteriors come after. That step is already under way, and today I can report a negative result: four candidate forms (a parameter-free baseline, a 288-parameter tabulated correction, a quadratic slope and a generative mixture) are all rejected on held-out positions by a scorer first validated on exactly-true data — the failures concentrate on the centre rather than the width. An afternoon audit drew the boundary: the scorer mixed estimands and the width metric is identically invariant to per-position offsets, so "the width generalises" can only be read as within one position; with the new scorer separating the two targets, the best candidates pass forty-four to fifty of the seventy-two cells on the population of unseen positions, and per position every candidate is near zero. The principal investigator set the progress metric that same day as the solved fraction (and solved area) of positions, allowed to grow from zero with no threshold; the first point is already measured: on band 4 only 4/33 positions have an entry pass fraction of 0.90 or more for D and for H2 (means 0.643 / 0.651), and only 1/33 on band 1 — that is where the progress curve starts. a symbolic-regression trial now running (two arms, one with a local inference service as the model backend) searches the centre residual surface for a short analytic form, then scores held-out with the same scorer and tests transfer across bands; a hybrid-law task is running too — the best width form paired with the generative mixture's centre. All of it rests on today's mechanism — with the mechanism unified, the product has the right skeleton.One more order was set that day: universality runs in two tiers — Tier 0 first (cross-band, cross-instrument scoring), with Tier 1's two items waiting for its results, so that we do not spread out before knowing how far one law transports. The conditional law is not another theoretical exercise: it is the input to completeness curves and flux posteriors — it is what catalogue users should eventually hold in their hands.

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总结：三条带回家的信息Summary: three take-home messages

零参数条件宽度在高计数锚是对的（std z 0.98–1.00，DET_ML \(\gtrsim\) 20–50）。The parameter-free conditional width is right at the high-count anchor (std z 0.98–1.00, DET_ML \(\gtrsim\) 20–50).
目录区间（DET_ML 6–20）它系统性偏窄 8–16 %，且没有任何可观测的点修正能闭合。In the catalogue interval (DET_ML 6–20) it is systematically narrow by 8–16 %, and no observable point correction closes it.
偏窄的机制只有一个且两条流水线共享：约 1 % 的 penalty 错配被相消放大；emldetect 侧它解释 0.89 [0.84, 0.93] 的缺口。把机制做成条件律的四个候选形式被一支验证过的评分器全部拒收：宽度一半在同一个位置内可推广，中心一半不能。2026-10-22 起这句话有了刻度：进度判据从“每个条目都在容差内”改成每个位置一个合并偏移（容差 0.05 比较 / 0.10 跟踪），打分手随之冻结；第一个拟合前位置项把最好候选从 0.545 抬到 0.727（p 0.003–0.004），但尚未在新位置检验；宽度判据校准为“8 箱允许 1 箱失败”后第一条可观测箱级规律通过，却仍过不了 emldetect 的全统计量；冻结打分手的宽度区间还欠覆盖（0.941 / 0.946 对 0.950），每个已解决比例都要连这个限制一起引用。The mechanism is one and shared by both pipelines: a ~1 % penalty mismatch amplified by the cancellation; on the emldetect side it explains 0.89 [0.84, 0.93] of the deficit. Four candidate forms of the conditional law are all rejected by a validated scorer: the width half generalises within one position, the centre half does not. Since 2026-10-22 that sentence has a scale: the progress criterion moved from “every entry within the tolerance” to one pooled offset per position (tolerance 0.05 to compare / 0.10 to track), with the scorer frozen with it; a first pre-fit position term lifts the best candidate from 0.545 to 0.727 (p 0.003–0.004), but it has not been tested on fresh positions; after the width rule was calibrated to “at most 1 failing bin of 8” the first observable bin-level law passes, yet still fails emldetect's full statistics; and the frozen scorer's width interval under-covers (0.941 / 0.946 against 0.950), so every solved fraction must be quoted with that limit attached.

总结，三条，也是开头承诺的三条。第一，零参数条件宽度在高计数锚是对的——标准差比零点九八到一点零零，那里不需要校准。第二，在目录最关心的弱源区间，它系统性偏窄百分之八到十六，而且没有任何可观测的点修正能闭合——必须经验校准。第三，偏窄的机制只有一个，两条流水线共享：两个几乎相消的大项里约百分之一的 penalty 错配，被相消放大；emldetect 一侧它解释百分之八十九的缺口。第三条里还有一个今天才有的新结果：把机制做成条件律的四个候选形式，被一支先在“恰好为真”数据上验证过的评分器全部拒收——失败集中在中心而不是宽度。当天下午的复核厘清了这句话的边界：评分器混用了估计对象，宽度指标对逐位置偏移恒等不变，所以"宽度可推广"只能读作在同一个位置内；新打分手分开两个目标后，未见位置总体上最好的候选过四十四到五十格（共七十二），逐位置上每条候选都接近零格。所以宽度这一半在同一个位置内已经有机制也有校准，中心这一半还开着。这三条分别回答了“哪里可信、哪里要校准、为什么”。这就是全部。谢谢——欢迎提问，这张幻灯片会一直留着。

To summarise, three points — the three I promised at the start. First, the parameter-free conditional width is right at the high-count anchor — standard-deviation ratio zero point nine eight to one point zero zero; no calibration needed there. Second, in the faint-source interval catalogues care about most, it is systematically narrow by eight to sixteen per cent, and no observable point correction closes it — empirical calibration is required. Third, the mechanism is one and shared by both pipelines: a one-per-cent penalty mismatch inside two nearly cancelling large terms, amplified by the cancellation; on the emldetect side it explains eighty-nine per cent of the deficit. The third point also carries a result that is new today: four candidate forms of the conditional law were all rejected by a scorer first validated on exactly-true data — the failures concentrate on the centre rather than the width. An afternoon audit drew the boundary of that sentence: the scorer mixed estimands and the width metric is identically invariant to per-position offsets, so "the width generalises" can only be read as within one position; with the new scorer separating the two targets, the best candidates pass forty-four to fifty of the seventy-two cells on the population of unseen positions, and per position every candidate is near zero. So the width half within one position already has a mechanism and a calibration; the centre half is still open. These three answer, in order, "where can it be trusted, where must it be calibrated, and why". That is the whole story. Thank you — I am happy to take questions, and this slide stays up.

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致谢Acknowledgments

模拟构造基于 XMM-Newton（ESA 科学任务，仪器与贡献由 ESA 成员国与 NASA 直接资助）。本报告的整理由 AI 代理辅助完成（按 AAS 政策声明）。数据与代码将在定稿后发布（PI 决定）。The simulation construction is based on XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA. AI agents assisted in preparing this talk (stated per AAS policy). Data and code will be released after the draft is settled (PI to decide).

致谢：模拟构造基于 XMM-Newton，欧空局的科学任务，仪器与贡献由欧空局成员国与 NASA 直接资助。本报告的整理由 AI 代理辅助完成，按期刊政策如实声明。原始数据来自 XMM 科学档案，产品与代码将在定稿后由项目负责人安排发布。这一页也留在屏幕上。再次感谢大家——问答开始。

Acknowledgments: the simulation construction is based on XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA. AI agents assisted in preparing this talk, disclosed per journal policy. The raw data come from the XMM-Newton Science Archive; products and code will be released as the principal investigator decides once the draft settles. This page stays on the screen too. Thank you all again — let us begin the questions.

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备用页从此开始（问答时可跳转）Backup slides start here (jump as questions come)

B1 数据表：构造与流水线参数Data table: construction and pipeline parameters
B2 逐格宽度表（L0，目录区间）Per-cell width table (L0, catalogue interval)
B3 emldetect 逐箱表与错配随计数的下降emldetect per-bin table and the mismatch falling with counts
B4 位置混合：按拟合偏移分箱的均值梯度Position mixture: the mean gradient in fitted-offset bins
B5 先验作用域：宽度无关，均值要先验Prior scope: width independent, mean needs the prior
B6 为什么逐格平均吃掉信号（R083 → R086 的教训）Why per-cell averaging eats the signal (the R083 → R086 lesson)
B7 覆盖率的净效应：宽度与中心项相消Net coverage: the width and centre terms cancel
B8 约定清单（ln、ΔC/2、ecut、BG 单位）The convention checklist (ln, ΔC/2, ecut, BG units)

（此页不占报告时间。）从这一页起是备用页：B1 数据表、B2 逐格宽度表、B3 emldetect 逐箱表与错配随计数的下降、B4 位置混合、B5 先验作用域、B6 逐格平均为什么吃掉信号、B7 覆盖率净效应、B8 约定清单。问答时我会按问题直接跳到对应页。

(This page costs no talk time.) From here on are the backup slides: B1 the data table, B2 the per-cell width table, B3 emldetect's per-bin table and the mismatch falling with counts, B4 the position mixture, B5 the prior scope, B6 why per-cell averaging eats the signal, B7 the net coverage effect, and B8 the convention checklist. During questions I will jump straight to the relevant page.

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25 / B0

B1 · 数据表：构造与流水线参数Data table: construction and pipeline parameters

项Item	值Value
源密度Source-count density	\( dN/dS \propto S^{-2.5} \) 于 [5.58, 51.20]\( dN/dS \propto S^{-2.5} \) on [5.58, 51.20]
位置数Positions	67, 离轴 0–13′off-axis 0–13 arcmin
L0	全局网格 + Nelder–Mead，\(\nu = 3\)，真实 PSF 模板族global grid + Nelder–Mead, \(\nu = 3\), real-PSF template family
L1	SAS emldetect（位置自由，替代核，名义位置）SAS emldetect (position free, surrogate kernel, nominal position)
复算Replays	每条记录级结论一次独立复算，逐位一致one independent replay per record-grade conclusion, bit-identical

^[s4][s5]

（备用页。）

(Backup.)

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B2 · 逐格宽度表：L0 在目录区间按可观测量分箱Per-cell width table: L0 in the catalogue interval, binned in observables

典型 DET_MLTypical DET_ML	\( \approx \) 4.6	7.9	11.1	22.8	36.8
合并 std zpooled std z	0.840	0.894	0.909	0.959	0.984

67 位置合并，比单一位置低约 0.02；DET_ML \(\approx\) 36–60 才回到 1。^[s9]Pooled over 67 positions, about 0.02 below the single position; back to 1 only by DET_ML \(\approx\) 36–60.^[s9]

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B3 · emldetect 逐箱表；错配随计数下降emldetect per-bin table; the mismatch falls with counts

DET_ML	6–10	10–20	20–50	50–100	>100
错配mismatch	+1.19 %	+0.63 %	+0.64 %	+0.42 %	\( \approx \) 0

箱内宽度缺口被解释 0.89 [0.84, 0.93]（6–10）；按行合并宽度 0.940 [0.922, 0.958]，比预测宽 0.021（位置/b 混合）。^[s13]The within-cell deficit is explained to 0.89 [0.84, 0.93] (6–10); the row-pooled width is 0.940 [0.922, 0.958], 0.021 wider than predicted (position/b mixing).^[s13]

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B4 · 位置混合：按拟合偏移分箱，均值从 +0.26 降到圆壁处的 −2.76Position mixture: in fitted-offset bins the mean runs from +0.26 down to −2.76 at the wall

L0 生产表 DET_ML 6–10 窗口，按 \(\hat{r}\) 分箱的 \(z\) 均值；\(\hat{r} \gtrsim\) 14.9 px 处骤降（支撑墙）。^[s16]The L0 production table's DET_ML 6–10 window, \(z\) means in \(\hat{r}\) bins; a sharp drop at \(\hat{r} \gtrsim\) 14.9 px (the support wall).^[s16]

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B5 · 先验作用域：宽度与先验无关（\(\leq\) 0.6 SE），均值要源计数先验Prior scope: the width is prior-independent (\(\leq\) 0.6 SE), the mean needs the source-count prior

先验扫描：宽度不变，均值随 \(\alpha\) 单调移动——这就是条件律要带 index 变量的原因。^[s17]A prior scan: the width is unchanged while the mean moves monotonically with \(\alpha\) — the reason the conditional law carries an index variable.^[s17]

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B6 · 为什么逐格平均吃掉信号：R083 → R086 的教训Why per-cell averaging eats the signal: the R083 → R086 lesson

估计量Estimator	L1 错配（DET_ML 6–10）L1 mismatch (DET_ML 6–10)
逐格比值再平均mean of per-cell ratios	−0.14 % [−0.91, +0.45] （不显著）(not significant)
合并估计量pooled estimators	+1.19 % [+1.03, +1.35]

两个估计量的差不是统计涨落：逐格比值被格间散布支配，合并估计量保留信号（恒等式闭合到 1e-15）。^[s13]The gap between the two is not a fluctuation: per-cell ratios are dominated by the between-cell scatter, pooled estimators keep the signal (the identity closes to 1e-15).^[s13]

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B7 · 覆盖率的净效应：宽度项（+5–11 pp）与中心项（−1–10 pp）相消Net coverage: the width term (+5–11 pp) and the centre term (−1–10 pp) cancel

\[ \text{net over-coverage} = +2\text{–}5\ \text{pp} \quad (\text{DET\_ML}\ 3.5\text{–}15), \qquad \text{width-only fix} \Rightarrow -2.9\ \text{pp at } 4.9 \]\[ \text{net over-coverage} = +2\text{–}5\ \text{pp} \quad (\text{DET\_ML}\ 3.5\text{–}15), \qquad \text{width-only fix} \Rightarrow -2.9\ \text{pp at } 4.9 \]

只修宽度反而欠覆盖；所以目标是区间覆盖率误差 \(\leq\) 2 pp，宽度与中心一起校准。^[s18]Closing the width alone under-covers; so the goal is interval-coverage error \(\leq\) 2 pp, calibrating width and centre together.^[s18]

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B8 · 约定清单：ln、\(\Delta C/2\)、ecut、BG 单位——每个都造成过 2–50 倍的假信号The convention checklist: ln, \(\Delta C/2\), ecut, BG units — each caused a 2–50× spurious signal

DET_ML \( = -\ln Q(\nu/2, \Delta C/2) \) ——自然对数，第二参数是 \(\Delta C/2\)。— natural log, second argument \(\Delta C/2\).
单图 3 参数：\(\nu = 3\)（shape 1.5）。Single image, 3 parameters: \(\nu = 3\) (shape 1.5).
ecut / scut / 拟合半径ecut / scut / fit radius: 截断比值随 \((S, b)\) 跨 0.49–0.91，引用必须带全条件。truncation ratios span 0.49–0.91 over \((S, b)\); quote only with the full conditions.
BG 单位 counts/像素（4″ 像素）。units counts/pixel (4 arcsec pixels).

^[s1]

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预期问答（10–15 分钟）Anticipated Q&A (10–15 minutes)

“为什么不直接在真实 XMM 观测上做？”"Why not just do this on real XMM observations?" 真实数据同时变仪器、背景、源群、流水线，四个因子纠缠；模拟基准让每层只有一个变量。配对实验（同图同打分）已经完成：它回答“拟合器贡献多少”的方式，是证明 L0 的低计数超额不是 emldetect 的性质——所以单图 emldetect 规律要在 emldetect 自己的输出上建。（用 B1。） Real data change instrument, background, population and pipeline at once — four entangled factors; the benchmark isolates one per layer. The paired run (same images, same scoring) is completed: it answers "how much is the fitter" by showing the L0 low-count excess is not an emldetect property — so the single-image emldetect law must be built on emldetect's own output. (Uses B1.)
“把 \(\sqrt{V}\) 换成模拟校准表不就行了？”"Why not just replace \(\sqrt{V}\) with a simulation-calibrated table?" 这正是实用路线；但要报告校准的来源与适用区间，且不能跨流水线搬。我们的贡献是告诉你表必须随 (计数, 背景, PSF) 变——因为机制如此。（用 B2、B3。） That is the practical route; but the calibration's source and interval must be reported, and it must not be carried across pipelines. Our contribution is telling you the table must vary with counts, background and PSF — because the mechanism does. (Uses B2, B3.)
“这个 1 % 错配是不是你们打分方式的伪迹？”"Is this 1 % mismatch an artefact of your scoring?" 它随 PSF 的翼结构走、随计数走，在两条独立流水线上都出现，且 emldetect 侧解释 0.89 的缺口——伪迹不会这样跨流水线自洽。同图同打分的配对实验已经完成，它确认了这个超额不是 emldetect 的性质。（用 B6。） It follows the PSF's wing structure and the counts, appears in both pipelines independently, and explains 0.89 of the deficit on the emldetect side — an artefact would not be cross-pipeline self-consistent. The paired same-images-same-scoring run is completed and confirms the excess is not an emldetect property. (Uses B6.)
“为什么之前测到 emldetect 错配约等于零？”"Why was emldetect's mismatch previously measured as about zero?" 逐格比值再取平均被格间散布支配；合并估计量保留信号。同一批数据、两种估计量，差不是涨落（恒等式闭合到 1e-15）。（用 B6。） Averaging per-cell ratios lets the between-cell scatter dominate; pooled estimators keep the signal. Same data, two estimators — the gap is not a fluctuation (the identity closes to 1e-15). (Uses B6.)
“结果对其他场、其他能段普适吗？”"Does this generalise to other fields and bands?" 机制（相消放大）应当普适，因为它只依赖方差公式是两项之差；错配的数值不普适——它随 PSF 翼结构与计数变。所以条件律产品按 3 仪器 × 5 能段做，每格自己校准。（用 B3。） The mechanism — cancellation amplification — should generalise, since it only needs the variance to be a difference of two terms; the mismatch's value does not, as it follows the PSF's wings and the counts. Hence the conditional-law product is built per 3 instruments × 5 bands, each cell calibrated on its own. (Uses B3.)
“位置自由会不会才是罪魁？”"Isn't the free position the real culprit?" 位置自由不改变宽度，但带来中心项问题：按拟合偏移分箱，均值从 +0.26 平滑下降到支撑墙处的 −2.76。宽度与中心是两个可分离的问题。（用 B4。） A free position leaves the width unchanged but brings the centre term: in fitted-offset bins the mean runs from +0.26 down to −2.76 at the support wall. Width and centre are separable problems. (Uses B4.)
“均值那边怎么办？宽度讲了半天。”"What about the mean? This was all width." 均值需要源计数先验（宽度不需要）：先验扫描里宽度不动、均值随斜率单调移动。这就是条件律带 index 变量的原因——弱源处对真实流量的依赖经斜率表达。（用 B5。） The mean needs the source-count prior (the width does not): in prior scans the width is fixed while the mean moves monotonically with the slope. That is why the conditional law carries an index variable — the faint-end dependence on the true flux is expressed through the slope. (Uses B5.)
“覆盖率受多少影响？”"How much does coverage suffer?" 净效应只有 +2–5 pp 过覆盖，因为宽度项与中心项相消；只修宽度反而欠覆盖 −2.9 pp。所以目标是联合校准到 2 pp。（用 B7。） The net effect is only +2–5 pp over-coverage, because the width and centre terms cancel; closing the width alone under-covers by −2.9 pp. Hence the joint 2 pp goal. (Uses B7.)
“为什么不拟合一个二阶修正项？”"Why not fit a second-order correction term?" 试过：解析候选拒绝（Bartlett 符号反、beyond-Fisher 过修 1.3–7.4 倍且低计数出负方差）。拟合一个项当然可以，但那变成经验校准，而且必须逐 (计数, 背景, PSF) 格做——零参数路线到此为止是负结果。（用 B2。） Tried: analytic candidates are rejected (Bartlett wrong sign; beyond-Fisher over-corrects 1.3–7.4× and gives negative variance at low counts). Fitting a term is of course possible, but that is empirical calibration and must be done per counts-background-PSF cell — the parameter-free route ends in a negative result here. (Uses B2.)
“这些结论的统计把握多大？”"How statistically solid are these conclusions?" 每箱 \(\geq\) 10,000 行、判据 \(1 \pm 0.02\) 预注册；关键数字带区间（如 +1.19 % [+1.03, +1.35]、0.89 [0.84, 0.93]）；每条记录级结论有一次独立复算。红队专门攻击过这些推导，其中一次推翻了我们自己的读数（逐格平均那条）。（用 B6。） At least 10,000 rows per bin, a pre-registered \(1 \pm 0.02\) key; headline numbers carry intervals (e.g. +1.19 % [+1.03, +1.35], 0.89 [0.84, 0.93]); every record-grade conclusion has an independent replay. Red teams attacked these derivations specifically and once overturned our own reading (the per-cell average). (Uses B6.)
“目录用户明天能拿走什么？”"What can a catalogue user take away tomorrow?" 三条规则：DET_ML \(\geq\) 50 直接用公式；6–20 用按 \(\hat{S}\) 分箱的经验校准并报告来源；跨流水线先做同图同打分配对比较。条件律产品在制。（用主报告第 21 页。） Three rules: above DET_ML 50 use the formula; in 6–20 use the per-\(\hat{S}\)-bin empirical calibration and report its source; across pipelines run the paired same-image comparison first. The conditional-law product is in progress. (Uses slide 21.)
“你们怎么知道不是打分器又在骗人？”"How do you know the scorer is not fooling you again?" 因为它今天错了两次，都是我们自己抓出来并修好的：一次是零假设的通过率没算对（一条完美规律平均也只通过约 61/72，所以 10/72 远在噪声底之下），一次是全局统计量的尺度错了（288 项的观测统计量对 72 项的零假设，p = 0.000 不是 p 值）。修好之后，评分器先在“规律恰好为真”的合成数据上验证（p 值均匀，K-S p 0.59），再打分。这也是我们强调的方法学：先验证打分器，再谈结论。（用 B6。） Because it was wrong twice today, and both times we caught and fixed it ourselves: once on the null's pass rate (a perfect law passes only about 61/72 on average, so 10/72 is far below the noise floor) and once on the global statistic's scale (a 288-term observed statistic against a 72-term null, so p = 0.000 is not a p-value). After the fixes, the scorer is validated on synthetic data where the law is exactly true (uniform p, K-S p 0.59) before it scores anything. That is the methodology we stress: validate the scorer first, then draw conclusions. (Uses B6.)
“还有什么你不知道的？”"What do you still not know?" 四件：条件律的中心项——四个候选形式全部被拒，宽度一半在同一个位置内可推广而中心一半不能（宽度指标对逐位置偏移恒等不变，1e-15），且位置不是缺失的变量；低计数中心项超额的成因（72/28 拆分已撤回，配对实验已证明它不是 emldetect 的性质）；按计数修正的 \(V_{3p}\) 在 emldetect 输出上校准时给留出 0.976 [0.956, 0.993]（一次偏低的分半，40 个分半平均 0.998），但换独立模拟仍过修；规律能否迁到其他能段（能段 1 上重拟合 37/72，原样迁移 17/72；新打分手给出能段 1 的 D / H2 通过 36 / 43 格）。我们如实标开放。 Four things: the conditional law's centre term — all four candidate forms are rejected, the width half generalises within one position while the centre half does not (the width metric is identically invariant to per-position offsets, 1e-15), and position is not the missing variable; the cause of the low-count centre excess (the 72/28 split is withdrawn and the paired run has shown it is not an emldetect property); the count-corrected \(V_{3p}\), which gives a held-out 0.976 [0.956, 0.993] when calibrated on emldetect output (one low split — 0.998 averaged over 40 splits) but still over-corrects when transferred from an independent simulation; and whether the law transfers to other bands (on band 1 the refit passes 37/72 and the unchanged transfer 17/72; the new scorer gives band-1 D / H2 36 / 43). We keep them labelled open, honestly.
“你说‘已解决位置的比例’——现在怎么量、量到多少？”“You say ‘the solved fraction of positions’ — how is it measured now, and where does it stand?” 判据本身被校准过一次：“每个条目都在容差 \(\varepsilon\) 内”是噪声受限的——一条完美规律在能段 4 上也只能让 21–27 % 的位置满足它，因为每个条目自身的抽样误差约 0.12 z，而位置效应本身是 0.14 z。所以现在每个位置只报一个合并偏移，容差比较规律用 0.05、跟踪进度用 0.10，打分手冻结（18 个格、位置真值校准的 95 % 区间）。在这把尺子上，最好候选在 0.10 处是 0.545，高于改正后的地板 0.469；加上第一个拟合前位置项（拟合盒背景水平）到 0.727（p 0.003–0.004），但那是同一批位置的拟合并打分，尚未在新位置检验。还有一个必须连带的限制：冻结打分手的宽度区间欠覆盖（0.941 / 0.946 对一个 0.950 的接受带），所以任何比例都要连这个区间一起引用。（用主报告第 19 页。） The criterion itself was calibrated once: “every entry within the tolerance \(\varepsilon\)” is noise-limited — even a perfect law satisfies it at only 21–27 % of positions on band 4, because each entry's own sampling error is about 0.12 z while the position effect itself is 0.14 z. So each position now reports one pooled offset, with tolerances of 0.05 to compare laws and 0.10 to track progress, and the scorer is frozen (18 cells, position-true-calibrated 95 % intervals). On that ruler the best candidate sits at 0.545 at 0.10, above the corrected floor of 0.469; adding the first pre-fit position term (the fit-box background level) takes it to 0.727 (p 0.003–0.004), but that was fitted and scored on the same positions and is not yet tested on fresh ones. One limit must travel with every such number: the frozen scorer's width interval under-covers (0.941 / 0.946 against a 0.950 acceptance band), so any fraction is quoted together with that interval. (Uses slide 19.)

来源对照表Source Map

标记Marker	记录Record
[s1]	`cognition-os/CLAUDE.md — DET_ML Convention; Catalog Convention Traps (I041)`
[s2]	`physics.html §5 (boundary-corrected null law)`
[s3]	`07_REVISION_LOG.md R030 (Ŝ-binning artefact withdrawn)`
[s4]	`cognition-os/PARETO_BENCHMARK_V2.md`
[s5]	`07_REVISION_LOG.md R062; reviews/RT-58_triage_claude.md`
[s6]	`07_REVISION_LOG.md R067; reviews/RT-64_triage_claude.md`
[s7]	`cognition-os/CLAUDE.md — IRON RULE (ML Analysis Methodology)`
[s8]	`07_REVISION_LOG.md R076`
[s9]	`07_REVISION_LOG.md R062, R065; reviews/RT-62_triage_claude.md`
[s10]	`07_REVISION_LOG.md R068, R072, R080`
[s11]	`07_REVISION_LOG.md R077; reviews/RT-72_triage_claude.md`
[s12]	`07_REVISION_LOG.md R078, R080, R081`
[s13]	`07_REVISION_LOG.md R086 (reversing R083); reviews/RT-81_triage_claude.md`
[s14]	`07_REVISION_LOG.md R082, R084, R085, R087`
[s15]	`04_DECISION_LOG.md 2026-10-20 04:51 EDT (main line and domain)`
[s16]	`07_REVISION_LOG.md R075, R076`
[s17]	`07_REVISION_LOG.md R063; reviews/RT-59_triage_claude.md`
[s18]	`07_REVISION_LOG.md R073`
[s19]	`07_REVISION_LOG.md R093–R104 (the law stage: LAW-1/2/3/4, M2B1, D-M2B1, NULL-1, RT-87–RT-94, CENTRE-POS)`
[s21]	07_REVISION_LOG.md R125–R156 (the 2026-10-22 re-calibration: the pooled-offset criterion and the frozen scorer, the floor correction, the pixel-geometry position effect, the first pre-fit position term, the calibrated width rule and the observable bin-level law, the width-CI coverage limit, the error-compensation reading, the 1.16 arm ratio); R157–R161 (the cluster-SE and seed-luck withdrawals, the Tier 0 band/instrument FAIL (withdrawn in R162) and catalogue-axis PASS within domain, the coarse-anchor re-interpretation, the B011 sign defect at 0 % of the failures); 04_DECISION_LOG.md 2026-10-22 (the PI's tolerances and the universality order); R162–R185 (the Tier 0 convention correction and A0-RESCORE, the fine width anchors and the cluster-bootstrap CI, the catalogue \(\mu_0\) domains and bias forms, the fresh-position AMBIGUOUS verdict and the crowding, the width-rule null recalibration, the mask rule, the three M1 positions, the clean population, and the revised Tier 1 plan); R189–R229 (the T1-e held-out block scoring and its three separate verdicts, the background channel's non-universality and candidate C2, the cost-anchor correction and the T1-a launch, the catalogue tautology, the broken power law and the eta amplitude, the refuted PSF-weighted reference, and the withdrawn cross-fit inflation)
[s20]	`07_REVISION_LOG.md R114–R120 (the 2026-10-21 re-scoping: R114 the expert's estimand critique, R115 the width split ensemble, R116 the centre decomposition, R117 RT-98's width-invariance result, R118 SCORER-CONTRACT v2's two targets, R119 RT-101's seed-range qualification, R120 RT-100's first progress point)`

致谢：本页的整理工作由 AI 代理完成（按 AAS 政策声明）。基于 XMM-Newton（ESA 科学任务，仪器与贡献由 ESA 成员国与 NASA 直接资助）的模拟构造。Acknowledgments: AI agents assisted in preparing this page (stated per AAS policy). The simulation construction is based on XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA.

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报告讲稿Seminar

XMM-Newton 点源检测似然比的零参数条件宽度：机制与边界A parameter-free conditional width for the XMM-Newton point-source detection likelihood ratio: mechanism and limits

你从目录里拿到的每一个误差棒，都假设了一个条件宽度Every error bar you take from a catalogue assumes a conditional width

承诺：听完这个报告，你会知道 (1) 零参数宽度在哪个区间可信 (2) 哪个区间必须校准 (3) 为什么Promise: by the end you will know (1) where the parameter-free width can be trusted, (2) where it must be calibrated, and (3) why

大纲：背景 → 方法 → 三条结果 → 局限 → 这对做 X 射线巡天的人意味着什么Outline: background → method → three results → caveats → what it means for anyone doing an X-ray survey

检测似然 DET_ML：把“这里有没有源”折成一个数的似然比检验DET_ML: a likelihood-ratio test that folds "is there a source here" into one number

教科书说 \(\Delta C\) 应该是 \(\chi^2_3\)——但目录恰恰关心它最不可信的地方The textbook says \(\Delta C\) should be \(\chi^2_3\) — but catalogues care exactly where that is least reliable

条件化决定一切：理论只能条件于可观测量 \((\hat{S}, b)\)，永远不能条件于模拟标签Conditioning decides everything: theory may condition on the observables \((\hat{S}, b)\), never on the simulation label

已有的经验校准路线给得出“差多少”，给不出“为什么”Existing empirical-calibration routes can tell you "how much" but not "why"

基准的构造：真实 PSF、逐像素背景、抖动——同一批图像喂两条流水线The benchmark construction: a real PSF, per-pixel background, jitter — one batch of images fed to two pipelines

两条流水线：L0（我们自己的拟合器）与 L1（SAS 的 emldetect）Two pipelines: L0 (our own fitter) and L1 (SAS's emldetect)

检验统计量：逐行 \(z\)，按可观测量分箱，判据 \(1 \pm 0.02\)The test statistic: per-row \(z\), binned in observables, key \(1 \pm 0.02\)

结果一（先说好消息）：高计数锚处，零参数公式就是答案Result one (the good news first): at the high-count anchor, the parameter-free formula is the answer

结果二：目录区间里，同一公式在真实 PSF 下系统性偏窄Result two: in the catalogue interval the same formula is systematically narrow under the real PSF

没有任何可观测的点修正能闭合它——三条修正路线全部关闭No observable point correction closes it — three correction routes are all closed

结果三（核心）：偏窄来自两个几乎相消的大项——\(V_{3p} = \mathrm{term1} - 4\,\mathrm{penalty}\)Result three (the core): the narrowing comes from two nearly cancelling large terms — \(V_{3p} = \mathrm{term1} - 4\,\mathrm{penalty}\)

错配不是常数：它随 PSF 的翼结构（低计数翼像素）与计数上升The mismatch is not a constant: it rises with the PSF's wing structure (low-count wing pixels) and the counts

同一个机制也决定 emldetect 的宽度——两条流水线，一个机制The same mechanism sets emldetect's width too — two pipelines, one mechanism

低计数端的中心项也偏高——它是 L0 流水线自己的性质，成因开放At the low-count end the centre term is biased high too — a property of the L0 pipeline itself, cause open

规律阶段：四条候选全部被拒收——宽度一半在同一个位置内可推广，中心一半不能The law stage: every candidate is rejected — the width half generalises within one position, the centre half does not

一句话版本：两个几乎相等的大数相减，其中一个差 1 %，结果就差 5–16 %The one-sentence version: subtract two nearly equal large numbers, one off by 1 %, and the result is off by 5–16 %

诚实的局限：模拟单场、emldetect 修正未完全检验、中心项成因开放、逐位置尚未解决Honest caveats: a single simulated field, the emldetect correction not fully tested, the centre-term cause open, no position yet solved per-position

对你做 X 射线巡天的实际建议：分区间的三条规则Practical advice for X-ray survey work: three rules by interval

下一步：把机制变成产品——单图 emldetect 条件律 \(p(\mathrm{DET\_ML} \mid \hat{S}, b, \mathrm{index})\)Next: turning the mechanism into a product — the single-image emldetect conditional law \(p(\mathrm{DET\_ML} \mid \hat{S}, b, \mathrm{index})\)

总结：三条带回家的信息Summary: three take-home messages

致谢Acknowledgments

备用页从此开始（问答时可跳转）Backup slides start here (jump as questions come)

B1 · 数据表：构造与流水线参数Data table: construction and pipeline parameters

B2 · 逐格宽度表：L0 在目录区间按可观测量分箱Per-cell width table: L0 in the catalogue interval, binned in observables

B3 · emldetect 逐箱表；错配随计数下降emldetect per-bin table; the mismatch falls with counts

B4 · 位置混合：按拟合偏移分箱，均值从 +0.26 降到圆壁处的 −2.76Position mixture: in fitted-offset bins the mean runs from +0.26 down to −2.76 at the wall

B5 · 先验作用域：宽度与先验无关（\(\leq\) 0.6 SE），均值要源计数先验Prior scope: the width is prior-independent (\(\leq\) 0.6 SE), the mean needs the source-count prior

B6 · 为什么逐格平均吃掉信号：R083 → R086 的教训Why per-cell averaging eats the signal: the R083 → R086 lesson

B7 · 覆盖率的净效应：宽度项（+5–11 pp）与中心项（−1–10 pp）相消Net coverage: the width term (+5–11 pp) and the centre term (−1–10 pp) cancel

B8 · 约定清单：ln、\(\Delta C/2\)、ecut、BG 单位——每个都造成过 2–50 倍的假信号The convention checklist: ln, \(\Delta C/2\), ecut, BG units — each caused a 2–50× spurious signal

预期问答（10–15 分钟）Anticipated Q&A (10–15 minutes)

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