---
conjecture: r3-b1-17
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
---

{
  "rivals": [
    {
      "mechanism": "The observed log-log slopes in the registered band are an artifact of the portal's institution-name aggregation and the ordinary-least-squares fitting procedure applied to ranks up to 500: many small or variant institution strings are collapsed, and the linear fit on log(rank) vs log(count) is forced into the [-3.0, -0.3] window by the heavy presence of singleton and near-singleton institutions that the ranking procedure always produces.",
      "why_it_explains_the_same_evidence": "Any state with at least a modest number of institutions will, after the same name-cleaning and ranking, generate a log-log plot whose OLS slope falls inside the wide [-3.0, -0.3] band simply because of the mathematical properties of ranked count data with many small values; this reproduces the training slopes and the holdout results (including the re-derived -2.71) without requiring a real accumulation-process shape.",
      "named_confounds": ["unit-of-count or string-aggregation artifact", "fitting-procedure sensitivity on ranked tails", "cataloguing practice for small institutions"],
      "discriminating_test": {
        "description": "Recompute the ranked institution counts using alternative aggregation rules (exact string match only, fuzzy match at different thresholds, or external authority control) and refit the log-log OLS slope under each rule, including and excluding the lower tail of singletons; measure how many of the resulting slopes fall outside [-3.0, -0.3].",
        "computable_on_held_data": true,
        "what_result_favors_rival": "If alternative aggregation or tail-exclusion rules push a substantial fraction of states' slopes outside the registered band while the original procedure keeps them inside, this favors the rival (fitting/aggregation artifact); if slopes remain inside the band under all reasonable alternatives, this favors the proposed accumulation-process mechanism."
      }
    },
    {
      "mechanism": "The heavy-tailed shape is produced by a small number of large state- or nationally-sponsored institutions that systematically absorb the majority of catalogued holdings in every state, combined with a long tail of minor local collections that the portal happens to include; the slope band is therefore an administrative centralization effect rather than a generic accumulation process.",
      "why_it_explains_the_same_evidence": "If every state contains one or a few dominant official repositories plus many small private or temple collections, the ranked log-log plot will exhibit slopes inside the wide registered interval for any state that has more than one institution, matching the training range and the non-degenerate holdouts.",
      "named_confounds": ["administrative or geographic classification artifact", "selection effects in what got catalogued (official vs private)", "centralization of major holdings"],
      "discriminating_test": {
        "description": "Classify each state's top-ranked institutions by type (national/state museum or library vs local temple/private/village) using any available institution metadata or external directories; recompute the log-log slope after removing the top 1-3 official institutions and after restricting only to non-official institutions. Measure whether the slope band is driven by the official institutions.",
        "computable_on_held_data": true,
        "what_result_favors_rival": "If removing the dominant official institutions flattens or steepens the remaining distribution outside the registered band, while the full distribution stays inside, this favors the rival (administrative centralization); if the slope remains inside the band even after removal of the official top ranks, this favors the proposed generic accumulation mechanism."
      }
    }
  ],
  "no_viable_rival": false,
  "notes": ""
}
