Does an independent source corroborate Astronomia Ova's (arXiv:2610.05358) central result and its ~8-arcminute Mars equant-error figure?

physicshistory-of-scienceastronomykeplerptolemymarscorroborationsingle-source-concentrationcitation-verification

This capture answers question-corroborate-astronomia-ova-2026-mars-equant-figure-and-central-result, which named two specific gaps after three claim-notes reached the single-source concentration cap on Moore, Smith & Mertens's "Astronomia Ova" (arXiv:2610.05358): (1) the paper's ~8-arcminute Mars equant-error figure is attributed to Bracco & Provost (2009), European Journal of Physics 30(5):1063–1076, an independent peer-reviewed source not yet read directly; (2) the paper's central mathematical result is, as of capture, unreviewed and uncorroborated by any second author group.

Both gaps were chased down. The Bracco & Provost paper was located, fetched directly via extract_pdf (arXiv:0906.0484, the authors' own self-archived preprint of the published article — confirmed via Semantic Scholar's paper-metadata API to share DOI 10.1088/0143-0807/30/5/015 with the published European Journal of Physics version), and read in full. A citation search for arXiv:2610.05358 itself was run across general web search and Semantic Scholar's citation graph. No safety signals fired on any fetch in this session: all sources were third-person academic or bibliographic prose, no addressed-to-AI language, no tier self-assignment, no file-system or credential requests, no urgency framing. One route — archive_page against doi.org/10.1088/0143-0807/30/5/015 (resolving to iopscience.iop.org) — returned a Radware bot-manager CAPTCHA page, not article content; this is a new known-blocked route for iopscience.iop.org article pages, alongside this vault's existing list of blocked publisher platforms (science.org, pnas.org, academic.oup.com, journals.sagepub.com, pubsonline.informs.org, sciencedirect.com). A second route, archive_page against eric.ed.gov, failed with a dropped connection; that bibliographic record was instead read via plain WebFetch and is reported below without an archived receipt.

Claim: Astronomia Ova's own citation for the Mars-accuracy figure carries a page-range error — Bracco & Provost (2009) is at European Journal of Physics 30(5), pages 1085–1092, not 1063–1076

verifies: question-corroborate-astronomia-ova-2026-mars-equant-figure-and-central-result

Astronomia Ova cites "Bracco & Provost (2009), European Journal of Physics 30(5):1063–1076" for its 8-arcminute figure. The ETDEWEB (U.S. Department of Energy / OSTI) bibliographic record for this article — sourced from IAEA/INIS input, the kind of compiled statistical/bibliographic reference this vault treats as citable for the record itself — gives the page range as 1085–1092. The arXiv preprint (0906.0484) of the same paper runs 8 pages, consistent with a 1085–1092 range (8 pages inclusive) and inconsistent with a 1063–1076 range (14 pages). An independent bibliographic record (ERIC, eric.ed.gov/?id=EJ851828, fetched via plain WebFetch — connection dropped on the archive_page attempt, so no sha is recorded for this specific source) separately gives the same journal, volume, and issue with a page count of "8," agreeing with 1085-1092 and not 1063-1076.

• Source: ETDEWEB (osti.gov) bibliographic record for Bracco & Provost (2009)
• source_quote: "Resource Relation:Journal Name: European Journal of Physics; Journal Volume: 30; Journal Issue: 5; Other Information: PII: S0143-0807(09)19919-1; DOI: 10.1088/0143-0807/30/5/015... Size:page(s) 1085-1092"
• source_url: https://www.osti.gov/etdeweb/biblio/21304140
• source_sha: b17fb83047b1764a72d2490170ea4cda154d425d2e1059f83130559f1bfc5e25
• source_author: ETDEWEB / U.S. Dept. of Energy OSTI
• source_date: 2009 (article); record accessed 2026-10-11
• source_title: "Had the planet Mars not existed: Kepler's equant model and its physical consequences (Journal Article)"
• source_venue: "ETDEWEB (osti.gov), compiled bibliographic record, IAEA/INIS country-of-input"
• source_tier: 2
• Note: quantitative/citation-accuracy claim (a specific page range), held to the Tier 1-2 floor. Clears it via a government-maintained bibliographic compilation quoting the publisher's own PII and DOI metadata directly (verbatim quote above, quote_check-confirmed grounded against the archived fetch). This does not itself verify or refute the 8-arcminute figure — it only shows Astronomia Ova's citation locator for that figure points at the wrong pages of the right article.

Claim: A direct read of Bracco & Provost (2009) finds no "8 arcminutes," "13% of a degree," or "quarter of the width of the Moon" figure anywhere in its text

verifies: question-corroborate-astronomia-ova-2026-mars-equant-figure-and-central-result

The paper Astronomia Ova names for its Mars-accuracy figure — read here in full via extract_pdf against the authors' own arXiv self-archive, confirmed by DOI match to be the same work as the published journal article — is an 8-page kinematics exercise showing that Kepler's equant model, to first order in eccentricity, reproduces Kepler's second law, Hamilton's hodograph, and an inverse-square centripetal acceleration. It discusses why Kepler abandoned the equant model (Mars's eccentricity exposed a mismatch with Tycho Brahe's observational precision) only in general qualitative terms, in a single footnote, and states no specific numerical error figure for Mars's predicted position anywhere in its introduction, body, or footnotes. Neither "8" nor "arcmin" nor any arcminute symbol, nor "13%," nor any reference to the Moon's angular width, appears in the extracted text.

• Source: Christian Bracco and Jean-Pierre Provost, "Had the Planet Mars Not Existed: Kepler's Equant Model and Its Physical Consequences"
• source_quote: "it is from the equant parameters e,R of the Earth, that he derived accurate distances of Mars to the Sun, and was led to abandon his equant model since these distances did not fit it at the precision of Tycho Brahe's observations."
• source_url: https://arxiv.org/pdf/0906.0484
• source_sha: 3fd088befb727487eff2a4d53d33d8587c3e7f2176f88099a37980190fd06330
• source_author: Christian Bracco, Jean-Pierre Provost
• source_date: 2009
• source_title: "Had the Planet Mars Not Existed: Kepler's Equant Model and Its Physical Consequences"
• source_venue: "European Journal of Physics 30(5):1085-1092 (2009); author-deposited arXiv:0906.0484"
• source_tier: 1
• quote_check: quote verified grounded: true against the extracted PDF text.
• Note: this is a claim about the absence of a figure in a directly-read Tier 1 primary, which is itself the strongest form of evidence available for a negative claim of this kind — a full first-hand read, not a search failure. It does not establish that the 8-arcminute figure is false, only that Astronomia Ova's specific attribution of it to this paper does not hold up against the paper's own text.

Claim: Independent corroboration for the 8-arcminute figure itself traces to Kepler's own primary text, not to Bracco & Provost — but this capture has not yet read that primary text at first hand

verifies: question-corroborate-astronomia-ova-2026-mars-equant-figure-and-central-result

A search for the 8-arcminute Mars figure outside Astronomia Ova and outside Bracco & Provost locates it in Kepler's own Astronomia Nova (Heidelberg, 1609), Chapter 19 — as relayed (in two slightly different English renderings, both unattributed beyond "trans. J. V. Field unless otherwise noted") by the University of St Andrews' MacTutor History of Mathematics archive, which cites the passage to page 113–114 of the original and to Kepler, gesammelte Werke (KGW) volume 3, pages 177–178. Both renderings state the error is 8 arcminutes, specifically for Mars, and specifically deduced from Tycho Brahe's observations — independently corroborating the figure's existence, size, and Mars-specificity, but by a route (Kepler's Chapter 19) distinct from the citation Astronomia Ova gives (Bracco & Provost 2009).

• Source: MacTutor History of Mathematics, "Quotations by Johannes Kepler," quoting Kepler's Astronomia Nova (1609), Chapter 19
• source_quote: "To us, on whom Divine benevolence has bestowed the most diligent of observers, Tycho Brahe, from whose observations this eight-minute error of Ptolemy's in regard to Mars is deduced, it is fitting that we accept with grateful minds this gift from God, and both acknowledge and build upon it."
• source_quote_2: "Since divine goodness has bestowed on us Tycho Brahe the most diligent observer, from whose observations this error of 8 minutes in Ptolemy's calculation for Mars has been deduced; it is right that with grateful minds we acknowledge and profit by God's good gift."
• source_url: https://mathshistory.st-andrews.ac.uk/Biographies/Kepler/quotations/
• source_url_2: https://mathshistory.st-andrews.ac.uk/Biographies/Kepler/quotations/
• source_sha: 74991f1fa7fe15aab2a34008d5be3e1487f99f309e2c2f036514774455b3989f
• source_sha_2: 74991f1fa7fe15aab2a34008d5be3e1487f99f309e2c2f036514774455b3989f
• source_author: Johannes Kepler (quoted); page compiled by MacTutor / University of St Andrews
• source_date: "1609 (original text); page accessed 2026-10-11"
• source_title: "Quotations by Johannes Kepler"
• source_venue: "MacTutor History of Mathematics Archive, University of St Andrews — relaying Kepler, Astronomia Nova (Heidelberg, 1609), Ch. 19, pp. 113-114; KGW 3, 177-178"
• source_tier: 3
• quote_check: both passages verified grounded: true against the archived page text.
• [unverified-quant — needs primary]: this is a quantitative, load-bearing historical figure and MacTutor is Tier 3-4 (an encyclopedic/educational relay, not the primary itself per sources.md's rule against grading an encyclopaedia article Tier 1). It corroborates that the 8-arcminute Mars figure genuinely traces to Kepler's own hand, independent of both Astronomia Ova and Bracco & Provost — but a direct read of Donahue's 1992 Cambridge University Press translation of Astronomia Nova (already flagged as a lead in the parent question) is needed before this figure clears the floor at Tier 1-2 on its own. Until then, the 8-arcminute number stands independently attested but not yet independently verified at primary tier by this vault.

Claim: No independent citation, review, or replication of Astronomia Ova's central result has appeared in the week since its 2026-10-04 posting

verifies: question-corroborate-astronomia-ova-2026-mars-equant-figure-and-central-result

A search across general web search and Semantic Scholar's citation-graph API for arXiv:2610.05358, "Astronomia Ova," and combinations with the authors' names (Moore, Smith, Mertens) and with "Legendre polynomials" + "equant" returned no citing paper, review, commentary, or independent replication of the orbit-family result. This is consistent with the paper's youth (one week old at the time of this search) rather than with any judgment on the result's correctness; a preprint this recent would not typically have accrued citations yet regardless of validity. The central mathematical result therefore remains, as the parent question anticipated, unreviewed and uncorroborated by any second author group or venue as of this capture.

• Source: this session's own search record (negative result)
• source_url: "N/A — absence-of-citation finding across arxiv.org, general web search, and api.semanticscholar.org/graph/v1/paper/arXiv:2610.05358, searched 2026-10-11"
• source_tier: "N/A (negative search finding, not a positive claim resting on a document)"
• Note: per the operating instructions, a genuine search failure to find corroborating or disconfirming material is a valid, reportable outcome, not a gap to paper over. Marked [unverified — could not confirm or deny after search] for the central-result half of the parent question specifically; the Mars-figure half is addressed by the three claims above instead.

Further leads

• Donahue's 1992 Cambridge University Press translation of Kepler's Astronomia Nova, Chapter 19 (pp. 113-114 in the original German-collected-works pagination cited by MacTutor) — the one remaining read that would move the 8-arcminute figure itself to Tier 1-2, and would also let a future session cross-check MacTutor's J. V. Field translation against Donahue's wording for the same passage.
• The Semantic Scholar paper record for Bracco & Provost (2009) confirms paperId ee654f40d67e863ae613f314d58af85daa2ecac8, bridging arXiv:0906.0484 and DOI 10.1088/0143-0807/30/5/015 — useful if a future session wants to check that record's own citation count or "cited by" list for later uses of the equant-model paper.
• iopscience.iop.org's DOI-resolved article pages now join this vault's list of publisher platforms that block archive_page/direct fetch (Radware CAPTCHA, this session, 2026-10-11) — a candidate addition to sources.md's known-blocked list alongside science.org, pnas.org, academic.oup.com, journals.sagepub.com, pubsonline.informs.org, and sciencedirect.com.
• eric.ed.gov's article-record pages dropped the connection on archive_page in this session (one data point, not yet a pattern) — the record was still readable via plain WebFetch, just without an archived sha; worth a retry in a future session.
• Donahue's and MacTutor/J. V. Field's two Chapter 19 translations differ slightly in wording ("this eight-minute error of Ptolemy's in regard to Mars" vs. "this error of 8 minutes in Ptolemy's calculation for Mars") — both appear on the same MacTutor page without clear attribution of which is whose; worth sorting out once Donahue is read directly.

Entity candidates

• Christian Bracco — person — co-author of the paper Astronomia Ova cites (with a page-range error) for its central Mars-accuracy figure; the independent-source check this capture ran landed on him and Provost first, per the instruction to flag the older/foundational comparison figure before the newer paper's own authors.
• Jean-Pierre Provost — person — co-author alongside Bracco; the 2009 paper the corroboration question specifically named as the independent source to verify.
• Johannes Kepler — person — already has a vault entity (entity-johannes-kepler); not re-flagged as a new candidate, but worth noting explicitly that his own Chapter 19 text, not Bracco & Provost's 2009 paper, turns out to be the true foundational source the 8-arcminute figure actually traces to.
• J. V. Field — person — historian of mathematics credited as translator for most of MacTutor's Kepler quotations page, including (probably) one of the two Chapter 19 renderings quoted above; unattributed as to which specific passage is hers vs. another translator's.
• William H. Donahue — person — translator of the 1992 Cambridge University Press New Astronomy; the remaining unread Tier-1-eligible source for the 8-arcminute figure's primary wording (already flagged as a lead in the parent question).