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The Bend That Doesn't Jolt

Written 2026-09-23. Claims re-read against their sources on 2026-09-27: 9 checked, 7 confirmed, 2 wrong, 0 unverifiable. By claims-audit controls 2026-09-27 (audit agent + fix agent).

Claims

• WRONG the Bernoulli sentence is quoted in "Levien's translation"
  https://www2.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-111.pdf : footnote 2: "The translation here is due to Raymond Clare Archibald [2]" (Amer. Math. Monthly 25(6), June 1917); now credited to Archibald
• WRONG dek, meta and JSON-LD: the engineers of railways and roller coasters each found the curve without knowing about the others
  https://www2.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-111.pdf : Levien counts Euler, Fresnel and Talbot as the independent discoveries; the page's own Pendrill and Stengel sources show the 1976 coaster loop adopted the known clothoid; reworded
• CONFIRMED Bernoulli's sentence reads "To find the curvature a lamina should have in order to be straightened out horizontally by a weight at one end"
  https://www2.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-111.pdf : exact wording on p. 2 of Levien
• CONFIRMED Bernoulli wrote down the equation but "did not draw its true shape"
  https://www2.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-111.pdf : "Bernoulli had written the equation for the curve, but did not draw its true shape"
• CONFIRMED at Cornu's funeral in 1902 Poincare said he "quickly replaced an unpleasant multitude of hairy integral formulas with a single harmonious figure, that the eye follows with pleasure"
  https://www2.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-111.pdf : funeral of April 16, 1902; wording matches Levien, which gives no other translator
• CONFIRMED the curve was discovered at least three times by people unaware of the earlier finds
  https://www2.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-111.pdf : abstract: "independently reinvented twice" after Euler; section 7: "The third completely independent discovery"
• CONFIRMED Levien's Euler quotations are based on Oldfather's 1933 translation with his own changes
  https://www2.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-111.pdf : "The quotes here are based on Oldfather's 1933 translation [21], with additional" changes
• CONFIRMED Stengel's clothoid loop first ran on Revolution, built by Schwarzkopf, opened 8 May 1976
  https://en.wikipedia.org/wiki/The_Great_American_Revolution : "opened to the public on May 8, 1976", manufactured by Anton Schwarzkopf, designed by Werner Stengel, first clothoid loop
• CONFIRMED the 30-digit reference values come from reference.py (mpmath), committed with its output
  research/the-bend-that-doesnt-jolt/reference.py : both files exist in the repository but only verify.mjs and mutate.mjs are served under /checks/; page now says they are not served

What was done

• [fixed] Bernoulli quotation credited as Levien's translation; now credited to Archibald (1917) as quoted by Levien, in the timeline and the Sources entry, with a dated correction line
• [fixed] dek (frontmatter, page dek, meta description, JSON-LD) said railway and roller-coaster engineers each found the curve independently; now says railway engineers did and roller-coaster loops took it up in 1976; dated correction line added
• [fixed] reader: reference.py and its output named as committed but not served; both mentions now say they are in the repository only, not served here; dated correction line added