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Heaps' law in clay

Status: Falsified

The verdict’s fine print — quoted from the resolution record: “(1) Register/genre confound: Ur III is overwhelmingly administrative while OB adds literary, lexical, scholarly and epistolary registers; this was explicitly tested by refitting on Administrative-only subsets, and the reversal persists (Ur III-admin 0.346 vs O…” 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.

Claim (verbatim)

Heaps' law in clay. Heaps' law — the corpus-linguistics regularity that a collection's vocabulary grows as a sublinear power of its size — is here applied to the oldest writing system on earth. Cuneiform's inventory of distinct signs should grow with corpus size along a Heaps curve, just as English word types do, because sign use and word use are driven by the same heavy-tailed frequency structure. The conjecture's sharper edge is historical: the Heaps exponent measures how freely writers admit rare signs, so when Old Babylonian scribal schools standardized the curriculum — drilling fixed sign lists into every student — the exponent should collapse, visibly flattening the vocabulary-growth curve for corpora written after standardization. The digitized CDLI corpus is large enough to fit the curve period by period and watch that collapse happen.

Prediction clause (verbatim)

For each chronological period in the digitized CDLI corpus, sample transliterated texts in increasing volumes, count distinct signs against cumulative corpus size, and fit the Heaps exponent per period. Primary clause: the growth curves obey a Heaps power-law form throughout (fit not rejected), and the post-standardization Old Babylonian exponent is lower than the pre-standardization exponents by at least 25 percent; an exponent that holds steady or rises across the Old Babylonian school standardization kills the conjecture. The verdict follows the primary clause.

Kill-dataset (verbatim)

the digitized CDLI corpus.

In the kill-dataset registry:

On Inferpedia

This conjecture is linked to the following pages on Inferpedia, an encyclopedia of the missing — working atlas pages, some still early scaffolding.

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

no prior formulation located (search dated 2026-07-04)

Heaps'/Herdan's law is well studied across corpora and even non-linguistic domains, but no application to cuneiform sign inventories was located, nor the sharp secondary claim (exponent collapse at Old Babylonian school standardization). No prior formulation located (search dated 2026-07-04). NOTE: unresolvable in-house — Phase A confirmed CDLI transliterations (sign-level text) are not held locally; catalogue metadata only.

Sources cited by the triage

Predictions

Killed registered 2026-07-04

Resolution: Killed

Caveats: (1) Register/genre confound: Ur III is overwhelmingly administrative while OB adds literary, lexical, scholarly and epistolary registers; this was explicitly tested by refitting on Administrative-only subsets, and the reversal persists (Ur III-admin 0.346 vs OB-admin 0.433), so the rise is not merely a register artifact, though the OB-admin subset is much smaller (4.5k texts). (2) A genuine deep-time signal exists: the oldest strata (Uruk IV/III 0.611/0.554, ED IIIa 0.552) have the highest betas and beta declines across the 3rd millennium, consistent with a slowly closing sign inventory -- but this decline is diffuse and is not located at the OB school-standardization transition the conjecture named. (3) Plausible reinterpretation: Ur III's anomalously low beta (a 3,711-sign closed bureaucratic monoculture) suggests the Ur III state's own accounting standardization was the sign-economizing episode, with OB scribal culture re-expanding sign variety; the 'standardization compresses inventory' intuition has some life, but attached to the wrong transition and the wrong direction relative to the registered prediction. (4) Clause-wording gap: the KILLED clause literally reads 'linear or exponent-stable across the transition,' and the exponent is neither -- it changes significantly in the reverse direction. This verdict resolves the gap by reading the kill clause, per the registrant's own disclosure pinning resolution to the standardization-collapse claim, as 'no discontinuous drop': a significant rise refutes the pinned drop at least as decisively as stability would, and campaign precedent (breadth-india-009, timur's-fingerprint, coins-014/PELLA) treats a reversed primary pinned comparison as a kill. (5) The sublinearity limb (Heaps' law, R^2 0.977-0.991 in all 12 strata) is fully met but carries no support weight: the registrant explicitly disclosed the prior that type-token curves are near-universally sublinear and pinned the test to the collapse clause. (6) Coverage limit: the CDLI ATF dump leaves later 1st-millennium strata largely catalogue-only, so the transition test rests on the well-covered 3rd-2nd millennium strata; the decisive Ur III/OB comparison is, however, among the best-covered in the corpus.

OPEN prediction (in-house resolution impossible — CDLI transliterations confirmed not held): the cuneiform sign inventory grows with corpus size by Heaps' law (V = K*N^beta, 0 < beta < 1), and beta drops discontinuously across the Old Babylonian school-standardization transition.

Resolution criteria — the registered fine print

Resolution criteria: Resolvable against public sign-level corpora (CDLI/ORACC transliterations) by computing type-token growth curves within period strata. SUPPORTED if the growth fits a sublinear power law (R^2 >= 0.95 on log-log) in every period stratum AND the fitted beta in post-standardization Old Babylonian strata is lower than in pre-standardization strata by more than the bootstrap 95% interval width. KILLED if vocabulary growth is linear or exponent-stable across the standardization transition.

Known-priors disclosure — what the registrant already knew

Known priors disclosure: No sign-level data in-house (Phase-A finding: catalogue metadata only). The registrant holds the general prior that type-token curves are near-universally sublinear — hence the kill condition is pinned to the sharper standardization-collapse clause, not to sublinearity alone.

Method and dataset — how it was measured

Sign-level tokenizer: signs split on -,.,+,: within words; determinatives {..} counted as signs; number notation n(SIGN) -> SIGN; compounds |..| as one sign; damage/uncertainty markup stripped; x/n/... dropped. Heaps' law V = K*N^beta fitted by OLS on the log-log type-accumulation curve averaged over 50 random text orderings, with bootstrap 95% CIs on beta from 300 text-resamples per stratum and a paired bootstrap for the Ur III vs Old Babylonian difference. A genre control refit beta on Administrative-only subsets of both transition strata to test the register confound. The compute was run outcome-blind (claude-sonnet script) and independently reproduced by the orchestrator with a separate tokenizer and vectorization; all four decisive point-betas matched within 0.01. Verdict reasoning: The registered SUPPORTED verdict requires both limbs; limb 1 (sublinear Heaps fit, R^2 >= 0.95 everywhere) is met, but limb 2 fails decisively: post-standardization Old Babylonian beta (0.471) is not lower than the pre-standardization strata -- it sits above five of eight pre-strata, and against its immediate predecessor Ur III (0.348) the paired-bootstrap difference of -0.123 (95% CI [-0.160, -0.078]) excludes zero in the wrong direction, a significant rise where a significant drop was predicted. The registrant's own priors disclosure pinned resolution to the sharper standardization-collapse clause precisely because sublinearity alone was conceded in advance, so meeting limb 1 cannot rescue the conjecture. A directional reversal is strictly stronger disconfirmation of the pinned drop than exponent-stability; reading it as outside the kill clause would reward the conjecture for being more wrong. The genre-controlled check shows the reversal is not a register artifact, and the blind, independently reproduced compute removes analyst-degrees-of-freedom concerns. The predicted discontinuous beta drop at the Old Babylonian school-standardization transition is contradicted by a significant rise; the conjecture is killed on its pinned clause.

Dataset: CDLI bulk ATF transliteration dump (github.com/cdli-gh/data, CC BY 4.0), 135,185 tokenizable texts joined to CDLI catalogue period metadata, yielding 12 cuneiform/proto-cuneiform period strata with >=1000 tokenizable texts each, spanning Uruk IV through Neo-Assyrian. The decisive transition comparison rests on the heavily covered Ur III (76.8k texts, 5.63M sign tokens) and Old Babylonian (2.16M sign tokens) strata.

computed 2026-07-20

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