Heavy-tailed survival without a shared universality class

Provenance notice. This article exists because TWO conjectures on the same underlying datasets — Pinakes' Greek-works witness counts and DBBE's Byzantine book-epigram witness counts — were pre-registered and resolved on the Inferpedia conjectures campaign's 1001-blind lane, and read together they measure a pattern neither states alone: survival is heavy-tailed in both corpora, but the two corpora do not share a common tail exponent. The first, cj-021, "Manuscript Yule process", was SUPPORTED (the heavy-tail family, not the specific power-law form, is confirmed in both datasets). The second, fresh-fablemax-b3-20260705-004, "The universality class of survival", was KILLED (the two datasets' tail exponents do not agree). Both remain at their own recorded verdicts and L1 lead status; nothing here reopens or revises either. cj-021 is calibration-flagged (triage: adjacent, citing Cisne 2005 and unseen-species-loss modelling of manuscript demography); the universality test's triage verdict is technically "novel_unlocated" (no prior comparison of these two catalogues was found), though — as this article foregrounds rather than hides — the registrant had already computed both exponents before registering it. This article was published in beta after a recorded Fable publication judgement (docs/generated/publication_judgement_617_20260716.json); every figure was recomputed from the two committed fit artifacts before publication.

Epistemic status

This article reports a measured pattern in surviving records: the numbers are directly attested in the cited datasets; what they mean is an open interpretation.

Both halves of this article are direct model fits — maximum-likelihood exponents and AIC (Akaike Information Criterion, a model-comparison score where lower is better) scores computed once against two in-house witness-count datasets — not inferences from indirect traces. What is inferred is the JOINT reading: that "heavy-tailed" and "one universality class" are two different, separable claims, and that this record supports the first while rejecting the second. One further honesty point governs the second half specifically and is foregrounded, not buried: the test that rejected a shared universality class was registered by an author who had already seen both fitted exponents from the first test. That is disclosed in the pre-registration itself, and this article treats the second result as a formalization of already-known evidence, not as an independent, blind confirmation.

Summary

Two in-house witness-count datasets were fit with three candidate statistical models each (a discrete power law, a discretized lognormal, and a geometric distribution), by maximum likelihood, compared by AIC. Pinakes (21,513 Greek works, 245,592 witness links): power-law exponent (alpha) 1.559, AIC 125,138.21; lognormal AIC 123,129.09 (better by about 2,009 AIC); geometric AIC 145,854.89 (worse by roughly 22,726 AIC than the best heavy-tailed model). DBBE (4,898 Byzantine book-epigram type-groups, 12,123 witnesses): power-law exponent 2.3652, AIC 11,207.86; lognormal AIC 11,251.83 (worse, so the power law wins here); geometric AIC 16,358.60 (worse by roughly 5,151 AIC than the best heavy-tailed model). Both datasets clearly reject the thin-tailed geometric model in favor of a heavy-tailed one (power law or lognormal) — the "manuscript Yule process" conjecture's calibration test is SUPPORTED. But the two datasets' heavy tails are not the same tail: a direct exponent-equality test (asymptotic standard errors: 0.00381 for Pinakes, 0.01951 for DBBE) puts the gap between 1.559 and 2.3652 at 40.6 pooled standard errors — far past the 3-SE kill threshold — and Pinakes' own best-fitting model is the lognormal, not the power law, beating it by about 2,009 AIC, past the 10-AIC threshold that itself kills a universality claim. The "universality class of survival" conjecture is KILLED on both of its registered clauses.

What is being inferred

Nothing about the specific mechanism of manuscript survival — preferential attachment, genre-specific copying incentives, or anything else — is established by these fits alone; a statistical model winning a model-comparison contest is not the same as a causal account of why copies accumulate the way they do. Nothing is asserted about the "superlinear over-survival of bestsellers" half of the original Yule-process conjecture either: that requires joining catalogue counts (the living population of a text, as recorded in medieval library inventories) against extant counts (the fossils, what actually survives today), a join this article's two source resolutions do not attempt. What these two witness-count datasets measure is EXTANT survival, already convolved with centuries of loss, not original production.

What is attested

Two conjectures were pre-registered against the same underlying extract artifacts (Pinakes and DBBE works-by-witnesses counts).

cj-021, "Manuscript Yule process" (registered 2026-07-04T12:47:03Z): fit three models by maximum likelihood to each dataset's copies-per-work distribution; SUPPORTED if the best heavy-tailed model (power law or lognormal) beat the geometric model by more than 10 AIC in BOTH datasets AND works with 10+ witnesses comprised at least 0.5% of works in both; KILLED if the geometric model came within 10 AIC of the best model in EITHER dataset. Computed (2026-07-04T12:50:32Z): Pinakes power-law alpha 1.559 (AIC 125,138.21), lognormal AIC 123,129.09, geometric AIC 145,854.89 (margin over geometric: 22,725.8); DBBE power-law alpha 2.3652 (AIC 11,207.86), lognormal AIC 11,251.83, geometric AIC 16,358.60 (margin: 5,150.74). Tail share (works with 10+ witnesses): 24.195% in Pinakes, 2.817% in DBBE, both clearing the 0.5% floor. Verdict: SUPPORTED — with the recorded nuance that the pure power law wins only in DBBE (alpha 2.3652, inside the pre-registered plausible range of 1.5–4.0); in Pinakes the lognormal beats the power law by about 2,009 AIC, so the conjecture's specific "power-law copy counts" wording is only partially vindicated even where the broader heavy-tail family is confirmed.

fresh-fablemax-b3-20260705-004, "The universality class of survival" (registered 2026-07-05T18:57:20Z): using the same committed extract artifacts, fit power laws by maximum likelihood to both distributions and compute a two-sided z-test for exponent equality using asymptotic standard errors; KILLED if the exponent gap exceeds 3 pooled standard errors OR if either dataset's power law is beaten by the lognormal by more than 10 AIC; SUPPORTED if the exponents agree within 2 pooled SEs AND the power law is the best model in both. Computed (2026-07-05T18:58:54Z): alpha_pinakes 1.559 (SE 0.00381), alpha_dbbe 2.3652 (SE 0.01951), gap 40.6 pooled SEs; Pinakes lognormal beats the power law by 2,009.12 AIC. Both kill clauses fire independently. Verdict: KILLED. The pre-registration for this second test carries an unusual, explicit disclosure: the registrant had ALREADY computed both exponents in the cj-021 resolution the day before, and states plainly that the test is expected to reject collapse — in the disclosure’s own words, "the verdict’s value is honest bookkeeping (the conjecture should not remain 'open' when the lane's own prior computation effectively falsifies it)." This is not a blind test; it is a documented formalization of a result the registrant already knew.

Why infer this entity

This article promotes two directly computed statistical comparisons, read together as one story: survival is heavy-tailed in both a large classical-Greek-works catalogue and a much smaller Byzantine epigram catalogue, but the two corpora's heavy tails are quantitatively different enough to reject a single shared generative process. It is included in the promotion ladder because the pairing — one SUPPORTED calibration test and one KILLED, disclosed-non-blind test on the same underlying fits — is itself a useful, honestly documented example of how the same numbers can license a broad claim (heavy tails exist) while refuting a narrower one (the tails are the same tail), and of how a registrant's own prior knowledge should be disclosed rather than hidden when a test is not, in fact, blind.

Evidence ledger

Four primary records, all committed to this site's own repository, were read directly: the pre-registration and resolution/verdict records for cj-021 (docs/generated/conjecture_predictions_shepherd_20260704.json, row 0; docs/generated/conjecture_resolutions_shepherd_20260704.json, row 0), and the pre-registration and resolution/verdict records for fresh-fablemax-b3-20260705-004 (docs/generated/conjecture_predictions_b3_20260705.json, row 0; docs/generated/conjecture_resolutions_b3_20260705.json, row 0). Both resolutions point to the same underlying computation artifacts (docs/generated/conjecture_extracts/resolution_analysis_20260704.json for the original fits; docs/generated/conjecture_extracts/b3_resolutions_20260705.json for the exponent-equality test and its "universality" key, which itself notes it draws its AIC figure from the committed cj-021 artifact). No live model call read or summarized any external web page for this promotion.

Counterarguments

The universality-class test's own known-priors disclosure is the strongest available objection to treating it as independent confirmation of anything: the registrant knew both exponents (1.559 and 2.3652) and the Pinakes lognormal-beats-power-law result before writing the kill/support clauses, so a KILLED verdict here provides essentially no additional evidential weight beyond what the cj-021 resolution already showed — its value is bookkeeping honesty (closing an otherwise-open conjecture with a formal verdict), not discovery. Both datasets measure EXTANT witness counts, already convolved with centuries of copying and loss, not original production; a shared production-side process could in principle exist even where the surviving-witness exponents differ, if loss rates differ systematically between a large classical corpus and a smaller medieval epigram corpus. Genre and catalogue-scope caveats from the underlying extracts carry over unresolved: Pinakes' Byzantine Greek catalogue coverage and DBBE's book-epigram genre scope are not general models of "manuscript survival," only of these two specific, bounded catalogues. And the "superlinear over-survival of bestsellers" half of the original Yule-process conjecture — the part that would connect these witness-count fits to an actual claim about WHY copies accumulate this way — remains untested by either resolution reported here.

Confidence scores

• Direct attestation of the fitted exponents, AIC margins, and the SE-based gap: 88
• Existence warrant (this is a real, reportable pattern in both catalogues): 82
• Specificity: 85
• Reconstruction dependence (how much rests on interpretation beyond the fitted numbers, including the known-priors caveat on the second test): 35
• Counterevidence pressure: 35

What would change the score

An independent, genuinely blind replication of the exponent-equality test — registered by someone who has not seen either fitted exponent — would settle the standing objection that the KILLED verdict on universality is not independent evidence. A catalogue-vs-extant join, of the kind the original Yule-process conjecture's untested half calls for, would move this article from a survival-side measurement toward an actual test of the size-biased over-survival mechanism. And a third heavy-tailed corpus, from a different textual tradition entirely, would show whether the Pinakes/DBBE exponent mismatch is a two-corpus idiosyncrasy or a more general finding that heavy-tailed survival does not imply a shared universality class.