{
  "title": "When Checking Takes Time: An Exact Two-Probe Stopping Frontier",
  "abstract": "We solve a finite Bayesian prediction problem in which each diagnostic probe reads a hidden binary mechanism and then permits a random transition before delivering its reading. A point forecast may subsequently be disclosed to the mechanism, which responds through a specified COPY/NOT evaluator. For initial fault probability and observation error both 1/4, at most two probes, transition probability h in [0,1/2], disclosure probability lambda in [0,1], and probe cost c >= 0, we obtain the exact minimum expected prediction error plus probe cost. A branch-dominance proof reduces all policies to immediate stopping or a single contingent two-probe plan. The latter can improve the objective even though its first probe alone makes prediction worse. We give exact examples of beneficial contingent diagnosis and harmful mandatory continuation, and distinguish executing a check from having the option to check. This is a worked specialization of classical Bayesian filtering and optimal stopping, with a reproducible finite certificate. Historical priority, architectural advantage, and consciousness conclusions are not claimed.",
  "version": "1.0",
  "date": "2026-11-09",
  "timezone": "Asia/Bangkok",
  "document_type": "Technical addendum; local release candidate",
  "destination": {
    "site": "https://www.b-theory.com",
    "index": "https://www.b-theory.com/papers/",
    "suggested_slug": "when-checking-takes-time",
    "relationship": "Addendum to reflective self-model study; cross-link with self-diagnosis paper at central editorial discretion",
    "status": "Prepared locally; not uploaded, pushed or published; central publication remains single writer"
  },
  "review_status": "Fresh independent AI proof and hostile reviews; minor edits resolved; final hostile re-review found no supported major objection within addendum scope. Not human peer review.",
  "verification": {
    "primary_exact_cases": 160,
    "independent_exact_cases": 160,
    "policies": 38,
    "outcomes": 64,
    "continuum_proof": "Analytic branch dominance and finite policy reduction",
    "pdf_pages": 5,
    "pdf_build": "ReportLab, successful; not a TeX compilation",
    "visual_review": "All five final Poppler PNG renders inspected; no clipping, overlap or missing text observed",
    "renderer_warning": "Poppler printed missing display-font warnings for unused font aliases; rendering exited0 and all pages were inspected"
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  "limits": [
    "At most 2 probes; prior=noise=1/4",
    "Known symmetric independent per-probe flip h in [0,1/2]",
    "Independent disclosure lambda in [0,1]; c>=0",
    "Read then transition; no final delay; policies act at their own stopping times",
    "Historical priority unverified; Monahan abstract-only and 2013 Ahmad/Yu abstract-only comparison",
    "No physical validation, architecture advantage or consciousness conclusion"
  ],
  "release_recommendation": "Ready for central editorial publication as a modest technical addendum; do not market as independently established novel general theory.",
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