{
  "reported_date": "2026-11-11",
  "outcome": "No mathematical error or gap affecting the claim that at least one of beta(4), beta(6), ..., beta(32) is irrational.",
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  "reviewer_identity": "Not specified in the supplied report.",
  "reviewer_model": "Not specified in the supplied report.",
  "mathematical_scope": [
    "Complete argument in Sections 1--5 and Appendix A.",
    "Isolated-pole refinement, small-prime and dyadic costs.",
    "Arithmetic envelope, event partition and limiting prime sums.",
    "Uniform real decay and infinite-tail control.",
    "Prime dilation, local coefficient extraction and the final irrationality contradiction."
  ],
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    "arithmetic_upper": "3203914250644786841689526785574147/395150460539893383747800452300800",
    "polynomial_degree": 33,
    "phase_enclosure": "[-18.8351123668081936003718677400690 +/- 7.31e-32]",
    "seed_method": "Complete polynomial numerator and denominator with Bezout inverses modulo the powers of the pole factors.",
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