Resolution: Inconclusive
Caveats: INCONCLUSIVE, stable across both readings of the guard, and the inconclusive is instructive on three levels. (1) INSTRUMENT DISCOVERY: the blind author imagined the Sectio's canon division as a number table anchored on 6:8:9:12; the actual Props. 19-20 are lettered Euclidean constructions that never instantiate a string length - the wagered arithmetic-disjointness question cannot be answered against a list that does not exist in the text; the guard and partition correctly routed this to inconclusive rather than a fake verdict. (2) THE DISCLOSED VACUITY RISK FIRED: clause 2's cross-check was too permissive exactly as the registration warned it might be - 45 and 60 are small 3-smooth multiples of the Greek five, an arithmetic coincidence, not a pathway; the discriminator proved toothless. (3) REGISTRANT-OWNED FORMALIZATION DEFECT, disclosed plainly: the p.162 apparatus footnote legibly shows a manuscript-variant diagram carrying 81/72/64/54/48 - the five Chinese pentatonic integers in a Greek source. The compute excluded it rule-faithfully (different proposition, apparatus, outside the registered core scope). But had those integers been in scope, the registered forced-set F = {1,2,3,4,6,8,9,12} would have wrongly KILLED the item on numbers whose sharedness is mathematically FORCED: both traditions must anchor at 81 = 3^4 for two integral 9:8 tone steps - the deepest instance of 'forced by the universal ratios', which the registrant's finite instance-list formalization failed to capture. LANE LESSON (candidate): when a registration formalizes an author's exclusion concept ('beyond those forced'), formalize its CLOSURE (here the 3-smooth orbit under the ratio group), never an instance list. NO V2 on this instrument (all outcomes now known); a v2 posed on a genuinely numerical Greek instrument (e.g. the canon numbers of later scholia or Boethius' division) would be a NEW registration on fresh corpora. WHAT SURVIVES: the independence thesis stands as mathematics even as the measurement goes inconclusive - the 81-anchor convergence between the traditions is arithmetical necessity, not a messenger; and the Huainanzi's position-10 anomaly (68 vs 67.42) plus its double-ascent generation step are real textual facts now cleanly extracted and quoted for any future work. Human-completable and v2-eligible only off this instrument. Blind compute claude-sonnet-5 (resume caveat in session_label); verdict claude-fable-5.
OPEN prediction (anti-connection wager): the twelve Huainanzi pitch-pipe integers and the integers of the Sectio Canonis division propositions share NO value beyond the universal-ratio terms, and at least three Chinese values carry decimal-rounding fingerprints no ratio-pair pathway produces - two mathematically comparable discoveries of the comma, zero shared arithmetic.
Resolution criteria — the registered fine print
Resolution criteria: VERBATIM PREDICTION: 'in a complete enumeration of the twelve Huainanzi lu numbers and all integers in the division propositions of the Sectio Canonis, the shared values beyond those forced by the universal ratios 2:1, 3:2, and 4:3 number exactly zero, and at least 3 of the 12 Chinese values show decimal-rounding deviations from exact 3-smooth theory that no sexagesimal or ratio-pair pathway produces; coverage guard: both numeral lists fully extracted (12 Chinese values, at least 15 Greek integers), else inconclusive.' OPERATIONALIZATION: Chinese list = the 12 lu integers of Huainanzi ch. 3 (Tianwen) as printed on ctext.org (fetch date recorded); the Shiji ch. 25 pitch-pipe numbers are extracted as the registered CONTROL, disclosed non-verdict-bearing. Greek list = every integer appearing in the Sectio Canonis's canon-division propositions in Jan's Musici Scriptores Graeci (Teubner 1895), extracted BY DIRECT READING OF THE PAGE SCANS on archive.org (identifier recorded at compute time; every integer logged with page + proposition locus) - the OCR text layer is UNUSABLE for polytonic Greek (probe recorded 2026-07-20; lesson: reachable is not readable), so page-image reading is the pinned method and OCR-layer extraction is forbidden. CLAUSE 1 (primary): I = integers appearing verbatim in both lists; forced set F = {1,2,3,4,6,8,9,12} pinned ex ante (the 2:1/3:2/4:3 ratio terms and the classical 6:8:9:12 anchor tetrad); clause 1 holds iff I minus F is EMPTY. CLAUSE 2 (secondary): generate exact 3-smooth rationals t_1..t_12 from anchor 81 by the Huainanzi's own alternating x2/3, x4/3 sequence in its stated order; among indices where t_i is non-integral, matched = count of attested v_i in {floor(t_i), round-half-up(t_i)} under base-10 arithmetic; cross-check = no such v_i appears in the Greek list nor equals any Greek integer times 2^a*3^b for |a|,|b| <= 4. Clause 2 holds iff matched >= 3 AND the cross-check holds. FULL PARTITION: guard unmet -> INCONCLUSIVE-BY-COVERAGE; clauses 1 and 2 both hold -> SUPPORTED; clause 1 fails (a shared non-forced integer) -> KILLED; clause 1 holds, clause 2 fails -> INCONCLUSIVE-BY-OPERATIONALIZATION with the failure mode recorded (the rounding discriminator proved toothless - a disclosed ex-ante vacuity risk of clause 2's design, not an occasion to re-pin).
Known-priors disclosure — what the registrant already knew
Known priors disclosure: Triaged adjacent 2026-07-20. Deferred from batch 1 until the intersection rule could be designed properly - done here; the registrant has computed no intersection and no rounding table. Disclosed from triage: the claim antedates explicit Chinese engagement with fifth-stacking non-closure (standardly Jing Fang, 1st c. BCE, not 3rd c. BCE) - a framing error that does not touch the numeral test; any resolution write-up must carry the correction. The registrant knows the standard qualitative facts (the Huainanzi list begins at 81; the Sectio works in ratio pairs) - that is the wager's premise; whether any larger integer coincides across the enumerated lists is genuinely unknown to the registrant. Instrument probe disclosed: Jan OCR unusable, page-scan reading pinned instead - the first registration to apply the B-005 lesson-4 refinement at pin time.
Method and dataset — how it was measured
Register-before-compute held (registration 18:04:34Z, packet 9290244). Guard: 12 Chinese values extracted; Greek 'at least 15 integers' - 25 occurrences (literal reading: met) but only 7 distinct small values (distinct reading: unmet); the registration did not say 'distinct', so both readings are adjudicated. CLAUSE 1 (literal-guard path): intersection of {42..81} with {1..9} is EMPTY; I minus F trivially empty - holds, near-vacuously (the ranges do not overlap because the Greek text contains no large numbers at all). CLAUSE 2: 7 non-integral positions, 6 matched to floor/round (all but position 10, Jiazhong 68 vs exact 67.42 - a genuine attested anomaly); cross-check FAILS: 45 = 5 x 3^2 and 60 = 5 x 2^2 x 3 are reachable from the Greek integer 5 within the registered 2^a*3^b bounds. Registered partition: clause 1 holds + clause 2 fails -> INCONCLUSIVE-BY-OPERATIONALIZATION; the distinct-guard reading gives INCONCLUSIVE-BY-COVERAGE. The verdict is INCONCLUSIVE on both readings - stable across the ambiguity.
Dataset: Chinese: Huainanzi ch. 3 (Tianwen) 12 lu integers in the text's own generation order from ctext.org (81, 54, 72, 48, 64, 42, 57, 76, 51, 68, 45, 60 - orchestrator-confirmed against independent knowledge), plus the Shiji ch. 25 pentatonic control (81, 54, 72, 48, 64). Greek: the Sectio Canonis's division propositions (Props. 19-20, Jan 1895 pp. 163-166, archive.org bub_gb_Q_gkcPDBpAYC) read DIRECTLY FROM PAGE SCANS per the registered pin (OCR layer never consulted; IIIF gateway failed, legacy image endpoint used; all pages fully legible): 25 integer occurrences, distinct values {1,2,3,4,5,8,9}, all as number-words and ratio-terms - the division construction is Euclidean letter-geometry and NEVER numerically instantiates a string length.
computed 2026-07-20