Twice removed, still counting in half-degrees

Claim (verbatim)

Ptolemy's Optics is a double orphan: the Greek original is lost, the Arabic translation made from it is lost, and the work survives solely in the Latin that the amiratus Eugene of Palermo made FROM the Arabic in Norman Sicily around the 1150s - a translation of a lost translation of a lost original, and wounded at that, since Book I and the end of Book V were already missing in Eugene's Arabic exemplar and are absent from every witness (Albert Lejeune's critical edition, 1956, reissued 1989; A. Mark Smith's annotated English translation, TAPS 86.2, 1996). What makes the survivor astonishing is what two language-deaths failed to destroy: Book V carries antiquity's only systematic experimental refraction tables - air to water, air to glass, water to glass, at incidence 10 through 80 degrees - and their numerical texture is still Ptolemy's. The air-water column runs 8, 15.5, 22.5, 29, 35, 40.5, 45.5, 50: first differences stepping down by exactly half a degree each row - constant second differences, the fingerprint of Ptolemaic second-order table construction rather than of raw measurement. Tables self-protect in transmission: their redundancy makes a corrupted cell visible and repairable, so the computational DNA of a scientific work can cross two translations and a millennium of copying intact even while whole books fall off the codex. The sole-survivor Latin thus certifies, from inside, the method of a Greek original nobody has seen since antiquity.

Prediction clause (verbatim)

Prediction: in Lejeune's established text, all three refraction tables of Book V will exhibit constant second differences of half-degree magnitude, with at most two cells across the three tables breaking the pattern (primary clause: the second-difference structure with <=2 deviant cells; the verdict follows it), and no witness in any language will supply Book I - its loss being exemplar-inherited, not witness-local; cells are read from Lejeune's text with his apparatus consulted, a deviation means an edited reading that breaks the difference pattern rather than recorded variant noise, and the test voids if the apparatus shows the tables textually unstable (more than 10% of cells without a consensus reading).

Kill-dataset (verbatim)

Kill: Lejeune, L'Optique de Claude Ptolémée dans la version latine d'après l'arabe de l'émir Eugène de Sicile (1989) with Smith's TAPS 86.2 translation - a second-difference computation over every table cell plus a witness census for the missing Book I.

Novelty / leakage triage

already answered in the literature

Lejeune himself ran the analysis the primary clause pins: his 1946 study of the refraction tables and the commentary to his edition present the half-degree constant-second-difference construction, and Smith's 1996 translation states it flatly in introducing Book V - the tables are computed from a second-order progression, not raw observation, with deviant cells discussed and emended by that very rule; the absence of Book I from every witness as an exemplar-inherited loss is likewise stated in Lejeune's introduction. This is the live leak the briefing feared: the second-difference fingerprint is the published reading of these tables, not a new operation.

• A. Lejeune, Les tables de refraction de Ptolemee, Annales de la Societe scientifique de Bruxelles 60 (1946)
• A. Lejeune, L'Optique de Claude Ptolemee dans la version latine d'apres l'arabe de l'emir Eugene de Sicile, 2nd ed. (Leiden, 1989), introduction and commentary
• A.M. Smith, Ptolemy's Theory of Visual Perception, Transactions of the American Philosophical Society 86.2 (1996), introduction and Book V commentary

Predictions

No prediction registered yet.