[zero-aska]

Fixes #28. Also carries the non-blocking findings from #27's independent review, except those in index.html, which #29 is rebuilding; those were passed to #29.

Reviews

• The first independent review (e555a3d) found three blocking errors in the note, all fixed in 790fff0:
  1. the summary read as if SDP.81 lost its black hole bound;
  2. Zhang and Yu fit Vegetti et al.'s pseudo-Jaffe plus point mass model (Δln E = −30, 1.93×10⁵ M☉), not the best fit;
  3. "test" was defined so broadly that Tamura et al. and Wong et al. qualified.
• The re-review (790fff0) confirmed all three fixes against the papers' LaTeX and found no new blocking problems. Verdict: merge.

The lensing note (notes/bh-lensing.md, #28)

Stacey et al., A&A 703, A285 (2025), re-analysed SDP.81's ALMA data. They find the ≈10⁹ M☉ sub-halo of Hezaveh et al. (2016) "most likely spurious", an artefact of poorly fitted multipoles. The note leaned on SDP.81 as the one anomaly lens with a black hole bound.

• SDP.81.
  • The summary and section 5 now say no lens in the note has both a small-scale anomaly and a bound on its black hole. SDP.81 had both until its lump was found most likely spurious.
  • Section 6 says SDP.81's anomaly is disputed and that none has been reported for PMN J1632−0033.
  • CORRECTIONS item 16 records the old claim.
• The negative claim still holds. No study tests lensing anomalies against the lens galaxy's black hole mass or spin. It is now dated 18 October 2026, with a definition of a test (fitting the anomaly itself with a model that includes the black hole) and the search method (arXiv API, INSPIRE full text, citation chasing, web search; not ADS). Work on the source quasar's black hole is set aside (Morgan et al. 2010; Reis et al. 2014).
• B1938+666.
  • Vegetti et al.'s (2026) measured profile is what every reading has to explain.
  • Oguri and Kubo read its best-fit point mass as the black hole.
  • Zhang and Yu match a less favoured fit, with self-interacting or stripped cold-dark-matter readings.
  • Zeng et al. (2026, a preprint) grow a black hole from the collapse.
• HS 0810+2554. Three models fit, and none includes a black hole:
  • wave halos (Zhou et al. 2026);
  • cold dark matter with multipoles (Miller and Williams 2025);
  • cold dark matter with subhalos (Gong et al. 2026, a preprint).
• "Central images are the only route" is gone.
  • Central images have given bounds.
  • Lensed images near the centre measured black holes of about 10¹⁰ M☉ (Nightingale et al. 2023; Melo-Carneiro et al. 2025).
• Wave dark matter models of the main lens mention its black hole only in passing (Chan et al. 2020; Palencia et al. 2025).

How it was checked. A 92-query search, with each surfaced paper confirmed against its record. Every statement was checked against the paper's full text. Two critics read the draft, then came the review and re-review above.

#27 review follow-ups

• CI. Pushes to main get a concurrency group per commit, so no main run is cancelled or left pending. A pull request's runs still cancel the superseded run.
• DOIs.
  • 18 more distinct DOIs, as 20 links, each checked on Crossref and doi.org.
  • All 72 distinct DOIs in README.md and the note resolve.
  • Bohren and Huffman stays without one, because Crossref's DOI is the 1998 reprint.
• Smaller fixes:
  • NIST is now DOI first;
  • two titles now match their published versions;
  • "pattern turns" for "circles";
  • "n = 2 Bohr speed";
  • CORRECTIONS item 9 gives the Joos–Zeh copies' published years.

CORRECTIONS numbering: #25 and #26 also add item 16. Whichever lands after this renumbers.

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https://claude.ai/code/session_01XfgH6WcwTueUFZKb6fS2s2

[zero-aska]

This is an independent review by separate agent instances that did not draft the branch. The drafting session spawned them without its drafting context. Three reviewers covered citation fidelity, physics and consistency, and CI, DOIs and small fixes. Each finding then went to one or more refuters. All three reviewers reported.

What was verified

• Scripts and tests. node notes/bh-lensing.mjs exits 0 on Node 22.22.0 and on Node 18.20.8, and the two outputs are byte-identical. The only change from origin/main is the label "n = 2 Bohr speed" on two lines. node tests/run.mjs (npm test) prints "all 4 check file(s) pass". witness-map/table.mjs and table.mjs 1e-6 cryo both exit 0. CI run 39126537047 passed test (18), (20) and (22) on e555a3d.
• Printed numbers. Every number the script prints still matches the note: the section 1 and 2 tables, the section 3 values and the summary ranges. The PR changes none of them.
• CI concurrency (.github/workflows/test.yml:11-15). On a pull_request run the && || expression yields refs/pull/N/merge, so all runs of one PR share a group and cancel-in-progress cancels the superseded one. A push to main is keyed on github.sha, so no main run can be cancelled. PR groups and main groups never collide. PyYAML parses the file.
• DOIs. There are 72 distinct DOIs at head: 43 on main, 18 added for #27 finding 1, and 11 for the new note entries. All 72 return 302 from doi.org; a malformed control DOI returns 404.
  • All 29 new DOIs were scripted against Crossref /works/<doi> and the arXiv API. Title, journal, volume, page, year and authors match in every case.
  • For 28 of them, the arXiv record carries the same DOI. Zhang and Yu (PRD 114, 083015, 10.1103/npqp-jgrp) has no DOI in its arXiv record but matches on title and authors.
  • The NIST DOI is a DataCite dataset, which is why Crossref returns 404 for it.
  • The retitled Stott and Marsh and Mehrgan entries match Crossref.
  • Leaving out a DOI for Bohren and Huffman is justified, because Crossref's DOI is for the 1998 reissue.
• CORRECTIONS item 9. The years at CORRECTIONS.md:58 (1999, 2000, 2000, 2005) match the README's Joos-Zeh entries.
• Nothing lost from main.
  • Every removed Sources line in README.md and the note reappears as an added line once the DOI wrapper is stripped. The exceptions are the intended NIST reorder and the two retitles.
  • No URL or link from main is missing.
  • "Bohr speed" is renamed everywhere, and "circles" is gone.
  • "n = 2 Bohr speed" = αc/2 agrees with witness-map/model.js:185 and tests/bh-lensing.mjs:65.
  • The new pattern-speed wording matches BCP 2019 eq. 2.1 (ω/m < Ω_H).
  • Every "section N" reference resolves, and every Sources entry is cited in the body.
• Citations against arXiv LaTeX and abstracts. All of these match:
  • Stacey et al. 2025: "most likely spurious", poorly fitting multipoles, no evidence for the H16 or I16 sub-haloes, log Bayes factor 29. The paper says nothing about the central image or the black hole.
  • Vegetti et al. 2026: point mass of at most 10 pc and a 139 pc edge; incompatible with CDM, possibly compatible with SIDM.
  • Oguri and Kubo: 4.25×10⁵ M☉, the UD+PM point mass.
  • Zeng et al.: 5-12% within about 2 Gyr, compared against UD+PM.
  • Zhou et al.: about 3 mas against about 12 mas for NFW, from 1000 Schrödinger-Poisson halos.
  • Miller and Williams: χ = 1.59 and 2.95.
  • Gong et al.: χ² = 1.61 at 1.43×10¹² M☉.
  • Chan 2020 and Palencia 2025.
  • Nightingale 2023: 3.27 ± 2.12 ×10¹⁰ M☉ (3σ), z = 0.169.
  • Melo-Carneiro 2025: log M = 10.56, z = 0.44.
  • Morgan 2010: slope 0.80 ± 0.17.
  • Reis 2014: a = 0.87.
  • Powell 2025: 26σ, Δlog E = +348.
  • CORRECTIONS item 16 matches Stacey et al. Its 6.9σ follows Hezaveh et al.'s own abstract.
• No stale claims. git grep at e555a3d finds no leftover SDP.81 "only anomaly lens" claim. The README makes no claim that needs updating. The CORRECTIONS heading and the format of item 16 follow the file's convention, and the numbering continues from 15.

Blocking findings

1. The summary says SDP.81 lost its black hole bound (notes/bh-lensing.md:23-24). All three reviewers reported this independently, and every refuter upheld it as blocking.
   • The text reads: "No anomaly lens I found has a bound on its black hole. SDP.81 had one until its dark lump was found most likely spurious (Stacey et al. 2025)." Here "one" can only mean "a bound on its black hole", so the sentence says the bound ended.
   • It did not. The bound of more than 3×10⁸ M☉ comes from the missing central image (Tamura et al. 2015; Wong et al. 2015). Both papers predate the Hezaveh lump and use smooth models only. Stacey et al.'s TeX never mentions the black hole or the central image.
   • The same PR contradicts this sentence at line 166, in the table row at line 196, at line 203 ("SDP.81 had both until …") and in CORRECTIONS item 16 ("The black hole bound stands").
   • The PR description says the summary now says "both". It does not.
   • Fix: "SDP.81 had both until its dark lump was found most likely spurious", as at line 203.
2. Zhang and Yu fit a different Vegetti model from the one the note names (notes/bh-lensing.md:154-160).
   • The note defines the profile every reading must explain as Vegetti et al.'s best fit (UD+PM): a point mass inside a uniform disc out to 139 pc. It then says "Zhang and Yu (2026) get the profile".
   • Zhang and Yu compare only with Vegetti's pseudo-Jaffe plus point mass model (PJ+PM), in both v1 and the accepted v2. They write that the profile "best matches the 'Pseudo Jaffe+Point Mass' (PJ+PM) model" and that the CDM remnant "agrees well with the PJ+PM model". They never mention the uniform disc or 139 pc.
   • Vegetti's Table 1 gives UD+PM at Δln E = 0 with a point mass of 4.25 ± 0.21 ×10⁵ M☉. It gives PJ+PM at Δln E = −30 with a point mass of 1.93 ± 0.36 ×10⁵ M☉ and a truncation radius of 266 ± 48 pc. Vegetti's line 303 says the data distinguish the two shapes.
   • Zhang and Yu's 1.9×10⁵ M☉ black hole is the PJ+PM point mass. Oguri and Kubo's 4×10⁵ M☉ is the UD+PM one. The two readings in this bullet are therefore fitted to different models, and a reader would wrongly conclude that the CDM reading needs half the black hole mass to fit the same data.
   • Fix: say that Zhang and Yu match Vegetti et al.'s PJ+PM model (Δln E = −30 against the best fit), whose 1.9×10⁵ M☉ point mass is their black hole, and drop "get the profile".
3. The new definition of a "test" is met by two papers the note cites (notes/bh-lensing.md:142-145).
   • The note says it found "none that compares anomaly data (flux ratios, image positions or imaged lumps) with a measured or modelled mass or spin of the lens galaxy's own black hole, or puts that black hole into a model fitted to such data."
   • Tamura et al. 2015 and Wong et al. 2015, cited at lines 165-167, do both. Each puts a point mass for the black hole into a lens model fitted to SDP.81 image positions: Tamura fits 46 knot images with N_DOF = 89, and Wong's likelihood L_pos covers 8 positions. Each also compares a central-image flux ratio with the modelled M_BH. So "I found no such study" is false as written.
   • The narrower claim the note means does hold. No model that fits an SDP.81 anomaly includes a black hole: not Hezaveh 2016, not Inoue 2016, not Stacey 2025.
   • Fix: count only studies that fit the anomaly itself (a flux-ratio or astrometric anomaly, or a detected lump) with a model that includes the black hole. Say explicitly that models using the black hole only for the macro-model or a central-image flux, such as Tamura's and Wong's, do not count.

Non-blocking findings

• notes/bh-lensing.md:179-181: the χ = 3.0 usual-order fit to HS 0810+2554 is given without its condition. Two reviewers reported this.
  • That fit uses pairing P3, which swaps A1 and A2 between the two sources relative to Hartley et al.'s P1. The abstract says "with two images being assigned to opposite sources". With P1 and the usual order, the best fit is χ = 3.35.
  • The note gives the caveat for the χ = 1.6 fit but not this one, and the wave dark matter fits it is compared with use P1.
  • Suggested addition: "but with two of the eight images assigned to the other source".
  • Also, "0.4 to 0.9%" describes the χ = 1.59 model. The χ = 2.95 fit has a1 ≈ 0, a3 = 0.53% and a4 = 0.45%, so the range is loose there, not wrong.
• notes/bh-lensing.md:207-211: the section 5 weighing sentence.
  • "Through a central image or lensed images near the centre. These have weighed … so far only black holes of about 10¹⁰ M☉" credits central images with weighings that used none. Nightingale 2023 says "without a central image being observed", and Melo-Carneiro models a radial arc plus kinematics.
  • Line 165 and table rows 196-197 also use "weigh" for the one-sided bounds (below 2×10⁸ and above 3×10⁸ M☉), so "only about 10¹⁰" contradicts them.
  • Suggestion: say that central images have so far given bounds, and that lensed images near the centre have measured two black holes, both about 10¹⁰ M☉.
• CORRECTIONS.md:110: item 16's title says "with a weighed black hole". The claim it corrects and its body describe a lower bound. Suggest "with a bound on its black hole".
• notes/bh-lensing.md:222-224: "neither now has a confirmed small-scale anomaly" implies that PMN J1632−0033 once had one. Its table row (line 197) says "None found", and no anomaly has been reported for it. Drop "now", or treat the two lenses separately.
• notes/bh-lensing.md:198, 287: the "as cited by Oguri and Kubo" hedge on Powell et al. 2025 is out of date. Powell's own text gives 26σ (Δlog E = +348), and the PR adds the DOI, checked on Crossref (Nat Astron 9, 1714-1722). This is optional cleanup.
• tests/checks.mjs:55-56: the Joos-Zeh comment still uses preprint years (Kiefer & Joos 1998, Joos 1999, Kiefer 1999). CORRECTIONS.md:58 now uses the published years (1999, 2000, 2000). The arXiv ids keep each reference unambiguous, and the PR does not touch this file. Consistency nit.
• notes/bh-lensing.md:211, 224: two inserted sentences were not rewrapped. They leave lines of 127 and 125 characters, each followed by a short line (45 and 22 characters). Lines 54, 153, 236 and 250 are 117-118 characters, against the usual 110-115. Rendering is unaffected.
• PR description: "20 more" and "All 72 DOIs" count different things. "20 more" counts DOI links, while "72" counts distinct DOIs. Finding 1 added 18 distinct DOIs, because Baumann and Planck are in both files: 43 + 18 + 11 = 72. This affects only the description.
• Reported and refuted: README.md:183-184 ("the lens systems with anomaly and black hole data") was said to conflict with the note's "no system has both". The refuter showed that the phrase describes the section 5 table, which still lists both kinds of data, and that pointing to issue #1 matches the note's header.

Verdict: do not merge until the SDP.81 summary sentence (notes/bh-lensing.md:23-24), the Zhang and Yu attribution (notes/bh-lensing.md:154-160) and the definition of a test (notes/bh-lensing.md:142-145) are fixed

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[zero-aska]

Re-review of fix commit 790fff0. Separate agent instances that did not draft the branch did the checking. The drafting session spawned them without its drafting context: one adversarial checker for each of the three blocking findings of the earlier review, and one for the whole delta. All four checks returned.

Blocking findings from the earlier review

1. Summary sentence on SDP.81: fixed. notes/bh-lensing.md:23-24 now reads "No lens I found has both a small-scale anomaly and a bound on its black hole. SDP.81 had both until its dark lump was found most likely spurious (Stacey et al. 2025)." This matches section 5 (line 207-208), the table row (line 200) and CORRECTIONS item 16 ("The black hole bound stands"). Stacey et al.'s TeX (arXiv 2508.02776) never mentions a black hole or a central image, so the Tamura/Wong bound (above 3×10⁸ M☉) still holds.
2. Zhang and Yu matched to the wrong Vegetti model: fixed. Lines 161-165 now say Zhang and Yu match the pseudo-Jaffe plus point mass (PJ+PM) model. Their TeX (arXiv 2606.12909, lines 143 and 212) says the same, and the M_BH = 1.9×10⁵ M☉ they adopt (line 194) is the PJ+PM point mass in Vegetti Table 1 (1.93 ± 0.36 ×10⁵, Δln E = −30). Oguri and Kubo's 4×10⁵ is the UD+PM point mass, so the new sentence "come from different fits to the same data" is correct.
3. Definition of a test: fixed. In lines 143-147, Tamura (yt.tex:249) and Wong (lines 314, 386-395) put the black hole in the smooth macro-model only to predict the central image's flux, and neither paper fits an anomaly. The Hezaveh 2016 and Stacey 2025 models of the lump contain no black hole. The checker grepped all 20 lensing sources plus Inoue 2016. None fits a flux-ratio anomaly, an astrometric anomaly or a dark lump with a model that contains the lens galaxy's own black hole, so "I found no such study" stands.

New problems

Blocking: none. The whole-delta check found that node notes/bh-lensing.mjs and node tests/run.mjs both exit 0, and that no script changed. A whitespace-insensitive diff of e555a3d against 790fff0 shows only the intended edits and no lost source or URL.

Non-blocking (all optional):

• notes/bh-lensing.md:170: Section 4 still says central images "weigh lens-galaxy black holes directly", then gives one-sided bounds. Section 5 (line 211) now says central images "have so far given bounds". The earlier review flagged this line too. Two checkers raised it. Suggested: "Central images bound lens-galaxy black holes directly".
• notes/bh-lensing.md:161-162: "which fits less well (Δln E = −30 against the best fit)" is softer than Vegetti et al.'s own "significantly disfavored" (ms.tex:299). The number is right. Suggested: "which the data disfavour (Δln E = −30 against the best fit)". Also, "instead match" reads better than "match instead".
• notes/bh-lensing.md:163, 165: The PJ+PM point mass appears as 1.9×10⁵ M☉ at line 163 and as 2×10⁵ M☉ at line 165, which could read as two different masses. Using 1.9×10⁵ in both places would match Vegetti Table 1 and Zhang and Yu.
• notes/bh-lensing.md:24, 143-147, 207-208: SDP.81 had a second reported sub-halo, from Inoue et al. 2016 (arXiv:1510.00150), which the repo never mentions. Stacey et al. dismiss that one too (main.tex:421, 452), and Inoue's model has no black hole, so every conclusion holds and only the coverage is incomplete. Optional fix at lines 24 and 207-208: "its dark lumps (Hezaveh et al. 2016; Inoue et al. 2016) were found not robust". Inoue could also be added to the models named at lines 143-147.
• notes/bh-lensing.md:23-24, 207-208 and CORRECTIONS.md:116 against notes/bh-lensing.md:227-228: The summary, section 5 and CORRECTIONS item 16 drop SDP.81 as an anomaly lens, while section 6 and the PR title call its anomaly "disputed". Stacey et al.'s "most likely spurious" and "not robust" support either wording, and each categorical sentence keeps that hedge, so this is a judgment call.
• PR description: it says section 6 now says no lens in the note has both. Section 6 instead says SDP.81's anomaly is disputed and that none has been reported for PMN J1632−0033. The meaning is the same; only the description is off.

Verdict: merge

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