A Zipf-like rank-size slope in the papyri place record, stable across three normalizations

Provenance notice. This article exists because ONE conjecture, tested three times against the same underlying growing dataset under three successively refined place-name normalizations, was pre-registered and resolved as SUPPORTED all three times on the Inferpedia conjectures campaign's 1001-blind lane. The conjecture, cj-079, "Zipf in the archive", concerns Mesopotamian tablet-archive volumes under imperial integration; ALL THREE tests reported here are an explicitly labelled ADJACENT-VARIANT calibration test on a different dataset — papyri.info's Egyptian documentary-record counts by origin place — and say nothing about the conjecture's actual Mesopotamian claim, which remains untested. The conjecture itself remains at its own recorded verdict and L1 lead status; nothing here reopens or revises it. All three resolutions are calibration- flagged (triage: adjacent). This article was published in beta after a recorded Fable publication judgement (docs/generated/publication_judgement_618_20260716.json); every figure was recomputed from the three committed rank-size extracts 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.

All three fitted slopes in this article are direct OLS (ordinary least squares) regression outputs on place-record counts; nothing about them is inferred from indirect traces. What makes this article worth promoting as a single unit rather than three separate one-line facts is the SEQUENCE: the same underlying question, asked three times as the place-name mapping that turns raw text strings into a canonical place list was progressively refined, with each refinement's criteria fixed and committed before that round's numbers were seen. That the answer barely moves across three independent remappings is itself the finding; what it means about Egyptian documentary survival, publication, or excavation practice — and, doubly, what it does NOT mean about Mesopotamian city sizes, the conjecture's actual subject — is stated plainly below and repeated because it is easy to lose track of across three rounds of numbers.

Summary

papyri.info records Egyptian documentary papyri with a free-text origin-place field. Ranking places by record count and fitting a power law to the top 50 (log10(count) on log10(rank), by ordinary least squares) gives a slope near −1, the signature of Zipf's law, three times over as the place-name handling improved: raw, unnormalized origin-place strings give a slope of −0.8983 (R² 0.9748, 79,215 total records, 42 unknown/ambiguous buckets excluded); a first structural normalization mapping strings to canonical places (built blind to the resulting counts) gives −1.0077 (R² 0.9734, 77,606 records, 12,608 excluded as unknown or ambiguous); a second normalization adding comma-split parsing, homonym guards, and a residual-place tier (also built blind to counts) gives, on its pre-registered binding series, −1.0561 (R² 0.9527, same 77,606-record population, 12,634 + 5,226 records excluded as unknown/ambiguous or residual). All three clear the same pre-registered support band (slope between −1.4 and −0.8, R² at least 0.90). The movement from raw strings to the first normalization (−0.898 to −1.008) is toward canonical Zipf, driven by consolidating a real place split across multiple strings (Oxyrhynchos, the top-ranked site, appeared separately at rank 2 and rank 5 under different string formattings before consolidation, then at rank 1 after). The further movement from the first to the second normalization is small (−1.008 to −1.056), and a version of the second normalization's own comparison computed without excluding the residual-place tier gives −1.0532 — nearly identical to the binding −1.0561 — showing the result is not sensitive to that particular modelling choice either.

What is being inferred

This is stated three times in this article because it is the article's most important caveat and the easiest one to lose: NONE of these three tests concern Mesopotamian city sizes, tablet archive volumes, or ancient political integration, which is what the underlying conjecture actually claims. All three are explicitly registered, adjacent-variant calibration tests asking a narrower, prior question — does a Zipf-like rank-size pattern appear at all in a large documentary-survival record, using a workable in-house dataset — on Egyptian papyri, a different place, medium, and time depth than the conjecture's own Mesopotamian tablet claim. Nothing here should be read as evidence about the conjecture's actual subject. Separately: that the papyri.info place-record counts follow this pattern is directly measured; WHY they do — ancient administrative/economic geography, versus modern excavation intensity, preservation bias (papyrus survives disproportionately well in Egypt's dry Fayum region), and publication practice, all of which the resolution records name as live, untested alternatives — is not established by a rank-size fit alone.

What is attested

One conjecture (cj-079, "Zipf in the archive") carries three separately pre-registered predictions on the papyri.info adjacent-variant test, resolved in sequence as the place-name mapping improved.

Raw strings (registered 2026-07-04T12:47:03Z; computed 2026-07-04T12:50:32Z): OLS of log10(count) on log10(rank), top 50 ranks, after excluding 42 unknown-type buckets ('unbekannt'/'unknown'/'sine loco'/'?'). SUPPORTED if slope in [−1.4, −0.8] and R² ≥ 0.90; KILLED if slope outside [−2.0, −0.5] or R² < 0.80. Result: slope −0.8983, intercept 3.954, R² 0.9748 — inside the band, near its shallow (−0.8) edge. Verdict: SUPPORTED.

Normalized places, v1 (registered 2026-07-04T14:51:42Z, criteria fixed in a committed document before the mapping existed; computed 2026-07-04T14:52:30Z): the same OLS specification over 1,062 canonical places after a structure-based mapping (built blind to counts) folded 2,864 distinct strings together, excluding 12,608 records (16.2%) as unknown or ambiguous. Result: slope −1.0077, intercept 4.1214, R² 0.9734, a shift of −0.1094 from the raw-string baseline; Oxyrhynchos consolidated to rank 1 (7,660 records) from its previously split rank-2/rank-5 appearance. Verdict: SUPPORTED. The underlying population also grew from 79,215 to 77,606 records between the two tests via a concurrent, sanctioned data-cleanup pass (a mis-tradition retag), so this result measures normalization and population cleanup jointly, not normalization alone — disclosed in the pre-registration itself.

Normalized places, v2 (registered 2026-07-05T10:32:11Z, criteria fixed in a second committed document before the v2 mapping was built; computed 2026-07-05T10:33:00Z): a further-refined mapping adding comma-split parsing, an Arsinoe-name consolidation with homonym guards, and a residual-place tier for tokens too coarse to count as a settlement, over the same 77,606-record population. The pre-registered BINDING series (excluding unknown, ambiguous, and residual-tier keys) gives slope −1.0561, intercept 4.1363, R² 0.9527 across 978 canonical keys — inside the same [−1.4, −0.8] support band. Verdict: SUPPORTED. Reported alongside, as pre-registered non-binding narrative: a strict comparison series computed WITHOUT excluding the residual tier gives slope −1.0532 (R² 0.9593), nearly identical to the binding figure; Arsinoe consolidates to rank 10 (1,333 records); and 6 of the top-50 identities changed between v1 and v2.

Why infer this entity

This article promotes a directly fitted statistical pattern tested three times for robustness to a specific, disclosed source of measurement error — free-text place-string fragmentation — rather than once. It is included in the promotion ladder because the sequence itself, not any single fit, is the disciplined result: each mapping was built and its criteria committed BEFORE that round's rank-size numbers were seen, so the near-stability of the slope across three rounds (−0.898, −1.008, −1.056) is evidence about the underlying record's structure, not about a modeller's ability to tune a mapping toward a preferred answer.

Evidence ledger

Six primary records, all committed to this site's own repository, were read directly: the pre-registration and resolution/verdict records for the raw-string test (docs/generated/conjecture_predictions_shepherd_20260704.json, row 1; docs/generated/conjecture_resolutions_shepherd_20260704.json, row 1), for the v1-normalized test (docs/generated/conjecture_prediction_f1_normalized_20260704.json; docs/generated/conjecture_resolution_f1_normalized_20260704.json), and for the v2-normalized test (docs/generated/conjecture_prediction_v2_normalized_20260705.json; docs/generated/conjecture_resolution_v2_normalized_20260705.json). These in turn point to the full rank lists and regression outputs in docs/generated/conjecture_extracts/resolution_analysis_20260704.json, docs/generated/conjecture_extracts/f1_normalized_ranksize_20260704.json, and docs/generated/conjecture_extracts/v2_normalized_ranksize_20260705.json. No live model call read or summarized any external web page for this promotion.

Counterarguments

Record counts per place proxy excavation intensity, preservation, and publication practice at least as much as ancient documentary output — a caveat disclosed at every one of the three registrations and not resolved by any of them; Egypt's Fayum region in particular is known to have preservation conditions (arid climate favoring papyrus survival) that are not representative of Egypt generally, let alone of the ancient Mediterranean world. None of the three normalizations settles what a "place" should mean at the boundary between a settlement and a larger administrative unit: the v2 mapping retains nome-level (district-level) keys by design, so "Arsinoites" (grown to 5,515 records by comma-split folding) sits in the same top-50 list as individual named towns, and a settlement-only re-test — excluding district-level entries entirely — has not been performed. A rank-4 "Egypt" bucket in the v1 series (4,084 records, a country-level residual carrying no finer toponym) was not excluded by that round's pre-registered criteria, though the v2 mapping's residual tier addresses a version of the same problem for later rounds. The CDLI (cuneiform) lane was abstained by pre-registration across this whole conjecture, because the in-house cuneiform batch is ID-ordered and non-random — a caveat that does not affect the papyri result reported here but is a reminder that this test could not be run on the conjecture's own subject dataset. And most fundamentally: excavation and publication bias in the underlying record is untouched by any of the three place-name normalizations, which only fix how existing records are grouped, not which records exist to be counted in the first place.

Confidence scores

• Direct attestation of the three fitted slopes and their stability: 90
• Existence warrant (this is a real, reportable pattern in papyri.info's place-record counts): 84
• Specificity: 88
• Reconstruction dependence (how much rests on interpretation beyond the three regression outputs): 20
• Counterevidence pressure: 30

What would change the score

A settlement-only re-test, excluding district- and country-level entries such as "Arsinoites" and "Egypt" from the ranked list entirely, would close the article's largest remaining definitional caveat and could move the slope in either direction. An independent excavation-and-publication-intensity dataset, if one could be constructed, would let a future test separate "how many documents survive from this place" from "how large this place actually was" — the step this article deliberately does not take. And, most directly relevant to the conjecture this calibration test was registered against: an actual Mesopotamian tablet-archive-volume dataset, tested under the same rank-size specification, would be the first test that bears on cj-079's real claim rather than on this adjacent Egyptian-papyri stand-in.