---
conjecture: r2-edh-b1-03
family: grok
model: "Grok 4.5 expert (chat paste-back via orchestrator window)"
received: 2026-08-06
template: PROMPT_TEMPLATE_v1.md sha256 4344aabfacfe88362c56d89b6c89d594a7bf3a221e18a16b0e351482447e512f
rivals_parsed: 2
note: "Unlabeled paste; matched to 03 by its own deciding numbers (18/9 vs 12/15, floors 12 and 5). ge symbols transcribed as unicode escapes. NB rival 1's random-partition test is the partition-imbalance diagnostic amendment #8 already ordered — convergent."
---

{
"rivals": [
{
"mechanism": "EDH's province list is a fixed, already heavy-tailed collection of administrative units of widely varying historical size and modern cataloguing intensity; any roughly balanced alphabetical (or random) partition of that fixed list will tend to place comparable numbers of small and large provinces into each half, reproducing the observed counts of provinces under 300 and over 1,000 without any deeper unevenness-of-recovery process operating on the holdout specifically.",
"why_it_explains_the_same_evidence": "Because the underlying set of 65 real provinces is static and already exhibits many small units and a minority of large ones, splitting it alphabetically yields 18 small and 9 large in the first half and 12 small and 15 large in the second half simply by the statistics of partitioning a heavy-tailed list; the registered floors are therefore satisfied by the partition itself rather than by a recurring recovery pattern.",
"named_confounds": ["unit-of-count or administrative classification artifact", "fixed heavy-tailed list of province definitions", "alphabetical partition of a static set"],
"discriminating_test": {
"description": "Generate multiple random balanced partitions of the full set of 65 real provinces and, for each partition, count how many units fall under 300 and how many fall at or above 1,000 in the second half. Measure the fraction of random partitions that satisfy both registered floors (\u226512 under 300 and \u22655 at \u22651,000).",
"computable_on_held_data": true,
"what_result_favors_rival": "If the great majority of random partitions also satisfy both floors, this favors the rival (statistical property of partitioning a fixed heavy-tailed list); if only the alphabetical split (or a small minority of partitions) does so, this favors the proposed unevenness-of-recovery shape claim."
}
},
{
"mechanism": "The observed counts of small and large provinces are produced by EDH's own long-term cataloguing coverage, which systematically recorded a large number of minor provinces at low volume while concentrating effort on a smaller number of major ones; the alphabetical holdout simply inherits the same coverage pattern that already existed in the training half.",
"why_it_explains_the_same_evidence": "A database built by many contributors over decades will naturally contain many sparsely represented provinces and a handful of densely represented ones; both the training counts (18 under 300, 9 at \u22651,000) and the holdout counts (12 under 300, 15 at \u22651,000) then reflect that same internal coverage structure rather than a general recovery process that independently recurs across an alphabetical cut.",
"named_confounds": ["selection effects in what got catalogued", "cataloguing or data-entry practice of a multi-contributor project", "digitization priorities across provinces"],
"discriminating_test": {
"description": "Compare the EDH province-size distribution against independent tallies of published Roman inscriptions for the same provinces (national corpora, CIL, other epigraphic databases). Measure whether the external distributions show a markedly different number of provinces under 300 and at or above 1,000.",
"computable_on_held_data": false,
"what_result_favors_rival": "If external counts produce substantially fewer small provinces or a different balance of large ones, this favors the rival (EDH-specific coverage pattern); if the external distributions closely match EDH's heavy-tailed shape, this favors the proposed general unevenness-of-recovery mechanism."
}
}
],
"no_viable_rival": false,
"notes": ""
}
