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Eight Minutes of Arc

Written 2026-09-26. Claims re-read against their sources on 2026-09-27: 11 checked, 9 confirmed, 1 wrong, 1 unverifiable. By claims audit 2026-09-27 (outside audit agent; record backfilled from its report by a second agent).

Outside audit of the 09-26 batch, 2026-09-27. Reader check: check.zip unzipped in an empty directory and run as the page said ("node verify.mjs") exited 1 (Cannot find module); after cd eight-minutes-of-arc it passed 284/0. The report's header says 10 claims (9 confirmed, 1 wrong, 1 unverifiable), which adds to 11; the eleven items it lists are all recorded here. The Horizons claim is recorded WRONG as the report counted it. Fixes: commit 2c77f61254.

Claims

• WRONG "JPL's own Horizons service could not be the second route: it has no Mars before 1600."
  https://ssd.jpl.nasa.gov/api/horizons.api : COMMAND='499' returns "No ephemeris for target Mars prior to A.D. 1600-JAN-01", but COMMAND='4' (Mars barycenter) returns 1590 positions, and the page's own DE440 route uses the barycenter (research/eight-minutes-of-arc/reduce.py:35)
• CONFIRMED Latin of Astronomia Nova pp. 113-114: VIII / X / 8 minuta, margin "VIII minuta erroris excrescunt usque ad XXX minuta", the 1582 example (7 2/3', 9', "circa 45 gradum ab aphelio")
  https://archive.org/details/astronomianovaai00kepl/page/n154 : matches the scans served with the page
• CONFIRMED Ch. 18: twelve oppositions 1580-1604, largest difference 2'12" (1589), "intra duo scrupula"
  https://archive.org/download/astronomianovaai00kepl/page/n149_w1200.jpg : read from IA leaves n149 and n150
• CONFIRMED Ch. 16 numbers 11,332 and 7,232 from four oppositions
  https://en.wikipedia.org/wiki/Vicarious_Hypothesis : matches; by hand 7232/18564 = 0.39, bisection 9282
• CONFIRMED Pafko's mars.xls transcription from Opera Omnia, hash as in the README
  https://www.pafko.com/tycho/mars.xls : sha256 0e1c95d3...2e845 matches; all 929x21 cells equal pafko-raw.csv
• CONFIRMED Kepler met Tycho at Benatky on 4 February 1600 and stayed about two months
  https://en.wikipedia.org/wiki/Johannes_Kepler : matches, citing Caspar pp. 89-100
• CONFIRMED Carman, "Did Tycho (Or His Assistants) manipulate his observations?", Historia Mathematica 73 (2025)
  https://api.crossref.org/works/10.1016/j.hm.2025.09.006 : exists as cited
• CONFIRMED Frisch, Opera Omnia vol. 3
  https://archive.org/details/joanniskeplerias03kepl : exists; the HathiTrust record returns 403 to curl (bot blocking, not a broken link)
• CONFIRMED Christophe Yamahata's Observable notebooks on Tycho and Mars
  https://observablehq.com/collection/@christophe-yamahata/tycho-brahe-and-mars : exist
• CONFIRMED Dek, card, seoTitle, body and verifier agree on 882, 0.87', 1.19', 8.4', 1.8'/2.4%, 74', 77', 23' and 23 Pafko disagreements
  public/strata/eight-minutes-of-arc/index.html : internally consistent
• UNVERIFIABLE Tycho's clock ran 17 minutes slow in January 1585 (credited to Gingerich and Voelkel)
  https://api.crossref.org/works/10.1177/002182869802900101 : the paper exists (JHA 29:1-34, 1998) but is paywalled; search found nothing on the detail

What was done

• [fixed] MED the run instruction failed as written (the zip unpacks into a subfolder): the page now says unzip it, cd eight-minutes-of-arc, and run node verify.mjs (2c77f61254).
• [fixed] MINOR Horizons "has no Mars before 1600": the page and research/eight-minutes-of-arc/cross_check.py now say Horizons serves the same JPL integration, so it would not be independent; its Mars body 499 stops at 1600 while the barycentre 4 reaches further back (2c77f61254).
• [fixed] MINOR "changing one digit on this page makes it fail" overstated the check: now scoped to every marked figure, with the unmarked prose counts said to be checked by hand (2c77f61254).
• [declined] MINOR the placard names research/eight-minutes-of-arc/verify.mjs, which is 404 on the site: left as is; the path is printed by scripts/check-placard.mjs by design as the repository name of the check, and the page's own check section points readers to check.zip, which runs.
• [fixed] MINOR stale comment in the zip's cross_check.py ("883 readings"): now 887, matching cross-check.json and the page (2c77f61254; check.zip rebuilt in the same commit).