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Taylor's law of the nomes
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).
Claim (verbatim)
Taylor's law of the nomes. Taylor's law — fluctuation scaling from statistical physics and ecology — says that across populations, variance grows as a power of the mean: exponent 1 for independent Poisson noise, 2 for perfectly synchronized fluctuation. This conjecture applies it to the geography of documentary survival across the attested places of Greco-Roman Egypt. The mechanism is that the shocks governing document production and survival — floods, plagues, administrative reforms — were regionally correlated, hitting neighbouring districts together, yet never perfectly global, so no place's fortunes were either independent of or identical to the rest. The variance of each place's per-25-year documentary output should therefore scale with its mean at an exponent strictly between 1 and 2 — well above the Poisson value that pure accidents of survival would give, well below the full-synchrony value of one shared shock — with a tight power-law fit across all substantially documented places.
Prediction clause (verbatim)
For all attested places with >= 50 dated documents, regressing the log variance of 25-year-bin document counts on the log mean count yields a slope in [1.35, 1.85] with R^2 >= 0.8; a slope <= 1.1 (pure survival noise) or >= 1.95 (full synchrony) kills it.
Kill-dataset (verbatim)
Kill: papyri.info dates and places (~77k records, in house).
In the kill-dataset registry:
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.
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: Fresh agent generation · model: claude-fable-5
Generated by a fresh Fable-tier instance at maximum effort with generation-first blindness (no repo/web/DB access); titles-only knowledge of existing items, embedded in titles_supplied per the batch-2 lane rule; prompt pre-committed in docs/GOAL_CONJECTURES_BATCH3_20260705.md (b043140). Novelty unverified by construction. titles_supplied stripped to the committed sidecar conjecture_fresh_fablemax_batch3_titles_supplied_20260705.md at import (schema additionalProperties:false; relaxation queued).
Novelty / leakage triage
no prior formulation located (search dated 2026-07-05)
Taylor's law has a rich transplant tradition (crime, epidemiology, finance, number theory — Cohen's survey) but no located application to archaeological/documentary survival data, and the specific interpretive claim (exponent between 1 and 2 as regionally-correlated shocks in a pre-modern record) appears unmade. No prior formulation located (search dated 2026-07-05). In-house computable.
Sources cited by the triage
- Cohen, 'Taylor's Power Law: Before and After 50 Years of Scientific Scrutiny' (arXiv 1505.02033) — The transplant tradition; no documentary-survival case
Predictions
No prediction registered yet.
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