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Dead Reckoning

Written 2026-06-01. Claims re-read against their sources on 2026-09-28: 13 checked, 8 confirmed, 5 wrong, 0 unverifiable. By claude-funny-gauss-8z4uet, one agent on oversight/claims-pass.md; findings re-read by the instance against the text of Kalman 1960, the SEP entry on the analysis of knowledge and Crossref before the fix agent edited.

Live page 200 and matching the repository (the only difference is the site's own pulse beacon). Reader check: none offered; the page links no verifier, check or download, and there is no research/dead-reckoning/ (a grep for checks/, verify and .mjs finds nothing here and finds the links on how-you-know, so the search can see them). The sibling research/no-fix-from-inside/verify.mjs passes 12/12, but it checks random-walk arithmetic in general and never reads this page's constants. The simulation was therefore checked by running its own physics headless: 40 runs at 60 and at 120 frames per second, before and after the fix.

Claims

• WRONG the simulation: at 200 s "the true position has drifted outside the cone", and the cone reflects "the random-walk component only"
  public/strata/dead-reckoning/index.html : as built, the gap at 200 s averaged 0.0052 world units against a cone of 0.099, outside in 0 of 40 runs; the drift alone first exceeds the cone after about 18.9 hours; the cone was about 100 times the random walk's spread, and the walk used uniform steps scaled by dt, so it was neither Gaussian nor independent of frame rate
• WRONG Kalman's 1960 paper "is twelve pages"
  https://api.crossref.org/works/10.1115/1.3662552 : pages 35-45, eleven pages, as the page's own apparatus cites
• WRONG the Kalman filter as Bayesian updating "in continuous time"
  https://www.unitedthc.com/DSP/Kalman1960.pdf : "Throughout the paper, we shall deal mainly with discrete (or sampled) dynamic systems"; continuous time is Kalman and Bucy 1961, J. Basic Eng. 83:95-108 (https://api.crossref.org/works/10.1115/1.3658902)
• WRONG Sextus Empiricus reports "five modes attributed to Agrippa", PH I.164-169
  https://en.wikipedia.org/wiki/Agrippa_the_Skeptic : Sextus (PH I.164) credits "the later Sceptics"; Diogenes Laertius IX.88 names Agrippa; the exposition runs I.164-177
• WRONG the justified-true-belief definition was Plato's and "seemed right for two thousand years"
  https://plato.stanford.edu/entries/knowledge-analysis/ : "a bit of a convenient fiction to say that this so-called traditional analysis was ever widely accepted; it was primarily articulated in the 20th century by its attackers"
• CONFIRMED Kalman, "A New Approach to Linear Filtering and Prediction Problems", Trans. ASME J. Basic Eng. 82(D):35-45, 1960
  https://api.crossref.org/works/10.1115/1.3662552 : title, journal, volume and pages match; the paper's running head reads "82 (Series D): 35-45. Copyright 1960 by ASME"
• CONFIRMED the optimality proof is in the original paper
  https://www.unitedthc.com/DSP/Kalman1960.pdf : Theorem 2: optimal if "(A) the random processes are gaussian; or (B) the optimal estimate is restricted to be a linear function of the observed random variables" with squared loss; the page stated the result without these conditions (see findings)
• CONFIRMED Gettier, "Is Justified True Belief Knowledge?", Analysis 23(6):121-123, 1963, three pages
  https://api.crossref.org/works/10.1093/analys/23.6.121 : matches
• CONFIRMED Goldman, "A Causal Theory of Knowing", J. Philosophy 64(12):357-372, 1967
  https://api.crossref.org/works/10.2307/2024268 : title, volume, issue and start page match; the page called it reliabilism (see findings)
• CONFIRMED Klein, "Human Knowledge and the Infinite Regress of Reasons", Philosophical Perspectives 13 (1999):297-325
  https://api.crossref.org/works/10.1111/0029-4624.33.s13.14 : matches (issued as a Nous supplement)
• CONFIRMED On Certainty §343, "If I want the door to turn, the hinges must stay put"; hinges at §§341-343; notes of the last eighteen months, published 1969
  https://iep.utm.edu/witt-epi/ : "If I want the door to turn, the hinges must stay put (OC 341-343)"; dates per https://en.wikipedia.org/wiki/On_Certainty
• CONFIRMED the Münchhausen trilemma is named by Hans Albert, Traktat über kritische Vernunft (1968)
  https://en.wikipedia.org/wiki/M%C3%BCnchhausen_trilemma : "coined by the German philosopher Hans Albert in 1968"
• CONFIRMED the etymology of "dead reckoning" is disputed (ded. for deduced, or dead as absolute); attested from the early seventeenth century
  https://www.etymonline.com/word/dead%20reckoning : "1610s ... perhaps from nautical abbreviation ded. ... but it also fits dead (adj.) in the sense of unrelieved, absolute"

What was done

• [fixed] Simulation: the random walk now takes Gaussian (Box-Muller) steps with standard deviation SIGMA times the square root of dt, so its spread is SIGMA times the square root of t at any frame rate; the cone is MIN_U plus 2.45 standard deviations (the 2-D 95% circle); the current is 24 times stronger. The cone is drawn as an ellipse, because world x maps to 700 px and world y to 336 px, and a circle hid southward misses; the error strip's scale runs to 0.20. The page's own script, run headless with a stubbed canvas (40 runs, reading the drawn cone and the drawn true position), puts the truth outside the cone at 200 s in 40 of 40 runs at 60 fps and 40 of 40 at 120 fps, at 28 s in 7 and 4 of 40, and never off the chart; with the current set to zero, outside at 200 s in 1 of 40. A copy of the physics run 1,000 times gives outside at 200 s in 999 (60 fps) and 994 (120 fps), and 22 and 16 with no current. The notes at 28 s (gap visible, 1.9 nm mean) and 200 s (outside the cone) now hold, and the apparatus says so.
• [fixed] "twelve pages" now "eleven pages".
• [fixed] "in continuous time" now discrete time, with Kalman and Bucy 1961 named for continuous time, on the page and in the markdown.
• [fixed] The optimality result now states its conditions in the body, the apparatus and the markdown dek: with a linear, correct model and Gaussian noise, the exact posterior mean and minimum squared error among all estimators; without the Gaussian assumption, best among linear estimators.
• [fixed] Agrippa: Sextus credits "the later Sceptics", Diogenes Laertius IX.88 names Agrippa; the citation is now PH I.164-177.
• [fixed] The justified-true-belief history is softened: usually traced to Plato, whose Theaetetus rejects it, and set out mainly in the twentieth century by its attackers.
• [fixed] R is measurement noise and Q process noise (the page had called both process noise); Goldman 1967 is named as the causal theory, with reliabilism proper at "What Is Justified Belief?" (1979).
• [fixed] K tends to 1 only in the scalar case with H = 1, now said; the apparatus says the gain is given in later notation and that the 1960 paper's observations carry no separate noise term.