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Varāhamihira graded five dead rivals honestly

Medieval Dated c. 100 CE – 600 CE South Asia

Status: Anticipated in print · untested

The verdict’s fine print — quoted from the resolution record: “INCONCLUSIVE-BY-DESIGN of the buildability/operationalization kind (kin to romanlaw-011 and greekastro-009/013), NOT a kill and NOT a support: Varahamihira's I,4 grading is neither vindicated nor refuted, because the digitized primary edition does not by itsel…” Read the full caveats ↓

Status is derived only from the shepherd-authored triage/prediction data above -- community submissions and claims are a separate overlay and can never change it (see the participation panel below).

This is a conjecture imagined by a language model — drawn from its trained weights and held to falsifiability, novelty, and plausibility, not to any one method: it may join two or more fields, or none. It is not an article and not evidence: it sits below the evidence/publication boundary. A quantitative prediction and a named kill-dataset are attached (when registered) so the claim stays falsifiable rather than merely evocative.
“Anticipated in print” means the direction of this claim already appears in scholarship, while this exact test has never been run — it records prior art, not proof; nothing here counts as supported or falsified until a registered resolution says so.

Claim (verbatim)

Five early astronomical systems — the Paitāmaha, Vāsiṣṭha, Romaka, Pauliśa, and Saura siddhāntas — are lost in their originals (the extant Sūryasiddhānta is a later, different text); the only quantitative access to them is Varāhamihira's Pañcasiddhāntikā (sixth century, Ujjain), a comparative digest that not only summarizes but grades them (I.4): the Pauliśa accurate, the Romaka near it, the Saura more accurate still, the remaining two far from the truth. A doxographer could rank by school loyalty at no cost; an astronomer publishing a ranking of working systems risks the sky contradicting him. If Varāhamihira's grades were empirical, then lost-text testimony can be audited a millennium and a half later: reimplement each summarized system and score it against the real sky of his own epoch. Prediction: implementing each of the five systems' solar and lunar algorithms as edited from the Pañcasiddhāntikā and scoring positional error against a modern ephemeris for dates around the treatise's epoch (505 CE, Ujjain meridian), the accuracy ordering will reproduce Varāhamihira's published grading — Saura best, Pauliśa and Romaka next, Vāsiṣṭha and Paitāmaha worst — with the Saura's mean solar-longitude error under half the Paitāmaha's (primary clause: the ordering match on the solar theory; the verdict follows it). Kill: the algorithms as edited in O. Neugebauer and D. Pingree, The Pañcasiddhāntikā of Varāhamihira (Copenhagen, 1970-71), controlled against the Kuppanna Sastri-Sarma edition (1993), run against the JPL DE ephemerides.

Prediction clause (verbatim)

Prediction: implementing each of the five systems' solar and lunar algorithms as edited from the Pañcasiddhāntikā and scoring positional error against a modern ephemeris for dates around the treatise's epoch (505 CE, Ujjain meridian), the accuracy ordering will reproduce Varāhamihira's published grading — Saura best, Pauliśa and Romaka next, Vāsiṣṭha and Paitāmaha worst — with the Saura's mean solar-longitude error under half the Paitāmaha's (primary clause: the ordering match on the solar theory; the verdict follows it).

Kill-dataset (verbatim)

Kill: the algorithms as edited in O. Neugebauer and D. Pingree, The Pañcasiddhāntikā of Varāhamihira (Copenhagen, 1970-71), controlled against the Kuppanna Sastri-Sarma edition (1993), run against the JPL DE ephemerides.

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.

Provenance

Run: Fresh agent generation · model: claude-fable-5

Fresh blind generation by claude-fable-5, 2026-07-16, breadth wave weighting India/South Asia by inferred textual production rather than survival; every item grounded in real works, authors, catalogues, and testimonia, including the real evidence of loss (citing authors, catalogue entries, translation corpora, rediscovery cases); no fabricated citations.

Novelty / leakage triage

anticipated in the literature — this exact test has never been run

Billard's programme scored Indian canons against modern ephemerides via deviation curves (including material related to the early Suryasiddhanta), and the Neugebauer-Pingree edition discusses the five systems' quality qualitatively — Varahamihira's own grading is famous. But a reimplementation of all five Pancasiddhantika systems scored against the c. 505 CE sky to audit that grading as an ordering test was not located.

Sources cited by the triage

O. Neugebauer and D. Pingree, The Pancasiddhantika of Varahamihira, 2 vols. (Copenhagen, 1970-71)
R. Billard, L'astronomie indienne: investigation des textes sanskrits et des donnees numeriques (EFEO, Paris, 1971)

Predictions

Inconclusive registered 2026-07-17 calibration prediction (parent triage: leaked/adjacent)

Resolution: Inconclusive

Caveats: INCONCLUSIVE-BY-DESIGN of the buildability/operationalization kind (kin to romanlaw-011 and greekastro-009/013), NOT a kill and NOT a support: Varahamihira's I,4 grading is neither vindicated nor refuted, because the digitized primary edition does not by itself pin two of the five systems' solar algorithms unambiguously, and the registration explicitly forbids reconstructing them from secondary paraphrase -- which is precisely what filling the Vasistha remainder-to-degrees rule (Kharegat 1895 / Kuppanna Sastri, cited not reproduced) and the Paulisa solar apogee (absent from text and index alike) would require. The registrant HONESTLY FLAGGED exactly this risk ex ante ('may resolve INCONCLUSIVE_BY_DESIGN -- algorithms not openly buildable'), and the resolution lands on the flagged limb, though not the flagged sub-reason: availability was fine (the 1970 volume is on archive.org in full), and the void is one level deeper -- the open text itself underdetermines two algorithms. This verdict is a claim about what the digitized edition alone can support, NOT a claim about Varahamihira's honesty or the true accuracy ordering of the five siddhantas. Blind hygiene held: I,4's ranking was recorded by the compute for transparency only and used in no direction; no error figures, date grids, or orderings were produced for any system, including the three cleanly extractable ones. Secondary notes: (a) the sidereal-vs-tropical ayanamsa frame choice (~3 deg around 505 CE) is a real methodological judgment but, being a near-constant additive offset across systems, would likely not reorder them and was not the decisive obstacle; (b) OCR of the Sanskrit text and critical apparatus is unusable (English translation and Introduction only), so a relevant garbled footnote cannot be fully excluded; (c) Part 2 of the edition (mathematical commentary) was deliberately not consulted, consistent with the guard -- it plausibly resolves both gaps. The conjecture is therefore human-completable and v2-eligible: a re-registration that either permits the published Kharegat/Kuppanna reconstructions as declared inputs, or scopes the ordering to the three fully-specified systems (Paitamaha, Romaka, Saura -- which happen to include both ends of the wagered 0.5x comparison), would be resolvable on the same digitized source.

Registered against the five siddhanta solar algorithms as edited in the Pancasiddhantika, scored vs a modern ephemeris. Claim under test (primary clause): the empirical solar-accuracy ORDERING of the five systems reproduces Varahamihira's own published grading (Saura best; Pauliza, Romaka next; Vaziztha, Paitamaha worst), with the Saura's mean solar-longitude error under HALF the Paitamaha's.

Resolution criteria — the registered fine print

Resolution criteria: DATA: the solar-longitude algorithms of the Paitamaha, Vaziztha, Romaka, Pauliza and Saura siddhantas as edited in O. Neugebauer & D. Pingree, The Pancasiddhantika of Varahamihira (Copenhagen 1970-71), controlled against Kuppanna Sastri-Sarma (1993); true solar longitudes from a JPL DE ephemeris at the Ujjain meridian. FEASIBILITY GUARD (evaluate FIRST): the Neugebauer-Pingree edition is a PRINT critical edition; if the five systems' solar algorithms are NOT available in an open/digitized form sufficient to implement them faithfully, the kill-dataset is not buildable as registered -> INCONCLUSIVE_BY_DESIGN (do not reconstruct the algorithms from secondary paraphrase). METRIC (if buildable): implement each system's solar-longitude computation; compute mean absolute error vs the ephemeris over a set of dates spanning ~505 CE (the treatise epoch). PRIMARY: does the best->worst ordering match Varahamihira's grading AND is mean_error(Saura) < 0.5 * mean_error(Paitamaha)? CLAUSE PRECEDENCE: (1) INCONCLUSIVE_BY_DESIGN per the feasibility guard, or if the algorithms cannot be implemented unambiguously. (2) SUPPORTED if the ordering matches and the Saura<0.5*Paitamaha condition holds. (3) KILLED otherwise. Report each system's mean error, the ordering, and the algorithm source actually used. computed_at postdates registered_at.

Known-priors disclosure — what the registrant already knew

Known priors disclosure: Held: the conjecture's reasoning (Varahamihira graded five now-lost systems and the grading should be empirically checkable) and general knowledge the Pancasiddhantika is the sole quantitative access to the lost originals. NOT computed: any accuracy figure. HONESTLY FLAGGED at registration: the edition is print, so this may resolve INCONCLUSIVE_BY_DESIGN (algorithms not openly buildable) rather than supported/killed.

Method and dataset — how it was measured

Feasibility-first protocol per the registration: a firewalled blind compute (claude-sonnet-5, blind to the predicted ordering and to the 0.5x Saura/Paitamaha threshold) fetched the digitized N-P Part 1 and assessed, system by system, whether each solar-longitude algorithm is unambiguously implementable from the digitized edition itself, returning feasible_to_implement_unambiguously = false with per-verse evidence and no error figures computed (the guard's ELSE branch). The compute also confirmed the true-sky side (pure-Python Meeus-style low-precision solar longitude) is computable in principle, and flagged the sidereal-vs-tropical ayanamsa frame choice as a real but secondary, non-decisive complication. Verdict authored by claude-fable-5 applying the registered clause precedence: clause (1) has two limbs -- the availability limb is NOT met (the print edition is digitized and open), but the 'algorithms cannot be implemented unambiguously' limb IS met (2 of 5 systems underdetermined by the digitized edition; the PRIMARY claim is a FIVE-way accuracy ordering, which a 3-of-5 partial build cannot underwrite; filling the Vasistha remainder-rule and Paulisa apogee gaps would require exactly the secondary-paraphrase/expert reconstruction the registration forbids). Clause (1) therefore fires: INCONCLUSIVE_BY_DESIGN. Clauses (2) and (3) were not reached and no positional-error computation was performed.

Dataset: Neugebauer & Pingree, The Pancasiddhantika of Varahamihira, Part 1 (Text, Translation, Introduction), Copenhagen 1970, archive.org djvu.txt full text (sha256 e360696bbdd2b71fe11056fc769b1abc343d8f4390ce2b958896ba0c1d001408, 443186 bytes) -- the edition IS digitized, so the guard's availability limb is met. Per-system solar-algorithm extractability from that digitized edition alone: Paitamaha (Ch. XII) cleanly extractable (mean-motion-only; the absence of a manda term is the system's documented design, not a gap; internal check 1830x9/122 = exactly 135 nakshatras); Romaka (Ch. VIII) cleanly extractable (mean motion, apogee 75 deg, six-value equation table, explicit 7-1/3-nadi Yavanapura-Avanti desantara, all numeric in-text); Saura/Suryasiddhanta (Ch. IX) cleanly extractable (mean motion, apogee 80 deg, Sine-equation amplitude 14, epoch already at Avanti). Two blockers: Vasistha (II,1) gives a 12-unequal-sector mean-longitude table (subtrahends verified to sum to exactly 1461 quarter-days = one solar year) but states no rule converting the terminal-sector remainder to degrees, and the edition's own Introduction records that this passage required external published reconstruction (Kharegat 1895; Kuppanna Sastri) which is cited, not reproduced (orchestrator independently confirmed the citations at djvu lines 3682-3730); Paulisa (III,1-3) gives a fully numeric equation-of-centre table but the solar APOGEE longitude needed to form its input anomaly is stated nowhere in the chapter or the whole digitized volume -- 'diminished by the apogee' is the translators' bracketed interpretive insertion, and the book's own index lists ucca (apogee) only for Ch. VI (Moon) and Ch. IX (Surya), never Ch. III.

computed 2026-07-20

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