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Maya continued fractions
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Claim (verbatim)
Maya continued fractions. This joins the Dresden Codex — the finest surviving Maya astronomical manuscript — to the mathematics of best rational approximation. The codex's Venus table tracks the planet with a canonical 584-day period, but the true synodic period is close to 583.92 days, so the table slowly drifts; the codex therefore prescribes periodic corrections to pull the count back into step. Number theory says there is an optimal way to make such corrections: the best rational approximations to a real number are exactly the fractions reached by descending the Stern–Brocot tree, the continued-fraction convergents. The conjecture holds that the Dresden corrections walk the optimal Stern–Brocot path toward the true synodic period — that Maya calendar priests, with no notation for fractions, nevertheless carried out best-rational-approximation arithmetic, their successive corrected ratios landing on the mathematically optimal sequence rather than on merely adequate nearby fractions.
Prediction clause (verbatim)
For the codex's own correction scheme, extract each prescribed correction in the Dresden Venus table and compute the sequence of effective day-count-to-Venus-cycle ratios it implies; independently compute the continued-fraction convergents — the Stern–Brocot best approximations — to the true synodic period of 583.92 days at comparable denominators. Primary clause: every corrected ratio in the codex must coincide with a best rational approximation on that path, matching a convergent or semiconvergent, with no correction strictly dominated by a simpler and more accurate available fraction; a single clearly suboptimal correction falsifies the claim. The verdict follows the primary clause.
Kill-dataset (verbatim)
the codex's own correction scheme.
Nobody has run this test. The kill-data is named above. If you can run it — or you know the paper that already settles it — claim the kill or submit the prior scholarship. Kills and prior scholarship are credited here, by name, as they come in.
On Inferpedia
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Provenance
Run: Imported conversation (verbatim harvest) · model: claude-fable-5
Origin: operator conversation with Claude Fable 5 at max effort, conducted 2026-07-03, relayed verbatim by the operator into the shepherd session on 2026-07-04. No ModelRun exists for the original generation (it happened outside the pipeline); this transcript file is the canonical capture. Transcript path: docs/generated/conjecture_harvest_fablemax_20260703.md. Model (operator-attested, not pipeline-recorded): claude-fable-5. Novelty disclaimer (verbatim, load-bearing -- rule 4): "Same caveat as before, doubled: at 100 items across all of archaeology and history, some of these will have cousins in the literature I can't check. What I can guarantee is the format — each links two things not normally linked, and each names the dataset or measurement that would kill it."
Novelty / leakage triage
anticipated in the literature — this exact test has never been run
The Dresden Codex Venus table's correction mechanism is deeply studied (Teeple's peculiar numbers, the 5:8 ratio, long-run accuracy analyses), with descriptions already flavored as rational-approximation reasoning; the explicit mapping of the correction sequence onto a Stern-Brocot best-approximation path was not located.
- 'Discovering Discovery: Chich'en Itza and the Dresden Codex Venus Table' — The correction-scheme scholarship
Predictions
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