---
conjecture: r2-edh-b1-03
family: codex
model: "gpt-5.6-sol (codex-cli 0.144.0-alpha.4, ChatGPT-subscription auth)"
model_stamp_corrected: "2026-08-07 — archives were first written stamped gpt-5.5 by a runner bug (the stamper read config.toml's default instead of the -m flag actually passed). The calls themselves ran on gpt-5.6-sol throughout; only the label was wrong. Corrected in place, noted here rather than silently."
received: 2026-08-07
template: PROMPT_TEMPLATE_v1.md sha256 4344aabfacfe88362c56d89b6c89d594a7bf3a221e18a16b0e351482447e512f
rivals_parsed: 3
validation: VALID
---

{
  "rivals": [
    {
      "mechanism": "Raw province counts are heavy-tailed because provinces differ greatly in geographic area, duration, population, military presence, urbanization, and ancient use of inscriptions. These differences create unequal opportunities for inscription production even if recovery rates are similar.",
      "why_it_explains_the_same_evidence": "Large, populous, long-lived, or inscription-intensive provinces would repeatedly occupy the upper tail, while small or short-lived provinces would occupy the lower tail. Because such exposure differences occur throughout EDH's province-code order, they can produce both the training distribution and the holdout's 12 low-count and 15 high-count provinces without invoking uneven recovery.",
      "named_confounds": [
        "unequal province area",
        "unequal province duration",
        "ancient population and urbanization differences",
        "variation in military presence and epigraphic production"
      ],
      "discriminating_test": {
        "description": "Model inscription counts using province area, years of existence, and independent estimates of ancient population, settlements, or military installations as exposure variables, then examine the residual province-level distribution. The production-exposure mechanism predicts that most of the raw heavy tail and threshold crossings disappear after normalization; uneven recovery predicts substantial residual overdispersion after those opportunity differences are controlled.",
        "computable_on_held_data": false,
        "what_result_favors_rival": "Exposure variables explain most between-province count variation, and normalized or residual counts no longer show comparably many extreme low and high provinces."
      }
    },
    {
      "mechanism": "The distribution may be generated by EDH's scholarly acquisition pipeline: some provinces were populated through large, systematic corpora or institutional data imports, whereas others received sparse or selective coverage. The tail would then reflect harvesting and cataloguing intensity rather than recovery of physical inscriptions.",
      "why_it_explains_the_same_evidence": "Corpus-scale imports can place covered provinces above 1,000 records, while provinces lacking comparable source partnerships remain below 300. If these source-coverage regimes span both alphabetical halves, the same mixture naturally produces the training pattern and the even stronger high-count holdout tail.",
      "named_confounds": [
        "unequal digitization and data-import coverage",
        "dependence on province-specific publication corpora",
        "institutional cataloguing intensity",
        "selective inclusion of published finds"
      ],
      "discriminating_test": {
        "description": "Using EDH bibliographic, provenance, or import-source metadata, calculate for each province the concentration of records by source corpus and compare counts among provinces with matched source coverage. Also recompute the distribution after retaining only source series applied across many provinces. The cataloguing-pipeline rival predicts strong source-level clustering and a much weaker tail in the standardized subset; a recovery mechanism predicts the province disparities will persist across common source strata.",
        "computable_on_held_data": true,
        "what_result_favors_rival": "High-count provinces are dominated by a few bulk source corpora, low-count status tracks missing source coverage, and source-standardization substantially collapses the province-count dispersion."
      }
    },
    {
      "mechanism": "EDH's province categories may be intrinsically unequal aggregation units: broad or long-lived labels pool many findspots, while geographically small, short-lived, or finely subdivided labels split comparable material among several codes. Heavy tails can therefore arise mechanically from classification boundaries.",
      "why_it_explains_the_same_evidence": "Unequal aggregation creates many small bins and several very large bins regardless of underlying inscription or recovery intensity. Because the alphabetical split partitions labels rather than equal geographic units, this bin-size effect can operate in both training and holdout and readily generate both threshold clauses.",
      "named_confounds": [
        "unequal administrative-unit size",
        "province boundary and chronology differences",
        "split-versus-lumped geographic classification",
        "findspot-to-province coding practice"
      ],
      "discriminating_test": {
        "description": "Reassign geolocated EDH records to equal-area spatial cells, or to a single harmonized provincial map for a fixed historical period, and recompute the cell or province count distribution. The classification mechanism predicts a marked reduction in tail heaviness and threshold-equivalent extremes after harmonization; genuine uneven recovery should remain spatially overdispersed under alternative, comparably sized partitions.",
        "computable_on_held_data": true,
        "what_result_favors_rival": "The heavy tail changes sharply or largely disappears under equal-area or historically harmonized rebinning, with former extreme provinces ceasing to be extreme."
      }
    }
  ],
  "no_viable_rival": false,
  "notes": "The raw-count design does not distinguish recovery heterogeneity from unequal production opportunities, catalogue coverage, or the construction of the provincial counting units."
}
