---
conjecture: r2-edh-b1-08
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": "The floor may be generated by EDH's material taxonomy: synonymous, uncertain, compound, or overly specific labels can turn a smaller number of physical substances into five or more distinct recorded values. Because the same cataloguing conventions govern both alphabetical halves, this inflation would reproduce both minima.",
      "why_it_explains_the_same_evidence": "With at least 50 typed records, even a province containing only a few basic substances can accumulate several label variants. A uniform database-wide thesaurus or shared data-entry practice therefore explains the training minimum of 7 and holdout minimum of 8 without requiring genuinely broad provincial material repertoires.",
      "named_confounds": [
        "data-entry synonymy and spelling variation",
        "taxonomic granularity differences",
        "compound or uncertain material labels",
        "cataloguer-specific terminology"
      ],
      "discriminating_test": {
        "description": "Construct a documented equivalence map that collapses spelling variants, regional names, uncertain alternatives, and material subtypes into coarse physical substances; then recompute each eligible province's richness. Also test whether uncollapsed richness varies by cataloguer or contributing source after controlling for row count.",
        "computable_on_held_data": true,
        "what_result_favors_rival": "The rival is favored if one or more provinces fall below five after normalization, or if most excess richness consists of label variants strongly associated with particular cataloguers or sources."
      }
    },
    {
      "mechanism": "The province-level floor may be an aggregation effect: each province pools inscriptions from numerous sites, centuries, and object functions, while the 50-typed-row eligibility rule preferentially retains aggregates containing several such contexts. Diversity would then arise from mixing contexts rather than from vocabulary breadth within a typical provincial epigraphic setting.",
      "why_it_explains_the_same_evidence": "Both training and holdout provinces were evaluated using the same coarse geographic unit and support threshold. Eligible provinces would consequently combine enough heterogeneous contexts to exceed five labels in either alphabetical half, even if individual sites or periods used only a narrow material repertoire.",
      "named_confounds": [
        "province-level aggregation across sites",
        "chronological pooling",
        "object-function mixture",
        "minimum-support selection effect"
      ],
      "discriminating_test": {
        "description": "Using EDH row metadata, compare material richness in equal-sized samples drawn from single site-period strata with samples of the same size pooled across multiple sites and periods. Model richness as a function of row count and the number of represented contexts, then test whether province identity contributes after context mixture is controlled.",
        "computable_on_held_data": true,
        "what_result_favors_rival": "The rival is favored if pooled samples reliably exceed five while many equally large single-context samples do not, and if the number of pooled contexts largely accounts for provincial richness."
      }
    },
    {
      "mechanism": "A small empire-wide core of standardized inscription substrates, reinforced by preferential survival and cataloguing of durable monuments, may guarantee the floor. On this account, the result is driven by the ubiquity of a few common materials rather than by the corpus's long tail of 118 material values.",
      "why_it_explains_the_same_evidence": "Roman monumental and administrative practices could distribute the same handful of common stone, metal, and ceramic substrate categories across many provinces, while durable examples are disproportionately preserved and catalogued. Every sufficiently sampled province in both halves would therefore exceed five even if the remaining material vocabulary were strongly regional or sparse.",
      "named_confounds": [
        "empire-wide standardization of inscription substrates",
        "substrate-dependent preservation bias",
        "cataloguing preference for durable monumental objects",
        "object-type composition"
      ],
      "discriminating_test": {
        "description": "Using training data only, identify the material values with the highest province-level prevalence. In the holdout, recompute provincial richness after removing this pre-specified common core and compare the resulting incidence patterns with a model in which diversity is broadly distributed across the 118-value vocabulary.",
        "computable_on_held_data": true,
        "what_result_favors_rival": "The rival is favored if nearly every province's passage is supplied by the same small core and removing that core causes widespread sub-five residual richness; broadly distributed, province-specific residual diversity would instead favor the stated vocabulary-breadth account."
      }
    }
  ],
  "no_viable_rival": false,
  "notes": ""
}
