{
  "date": "2026-10-05",
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  "review_scope": "Full conclusion/status/scope/evidence/dependency register; current checkpoints and freezes; missing ledger and PR72-74. Not historical proof or certificate replay.",
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  "wall_check": "Same open gap; ZERO-GEOMETRY, NS100/101, PR74",
  "question": "Does a theta addition or lattice reindexing identity supply an original two-modulus signed comparison, rather than an elliptic-argument identity at a common modulus?",
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  "new_row": false,
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  "original_recovery_groups": "Both OPEN",
  "status": "completed; no sign candidate admitted",
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  "sources": [
    {
      "url": "https://arxiv.org/html/1502.04603v2",
      "scope": "Definitions, Sections 3.1-3.3 and 4.2; elliptic-argument identities at common modulus or tau/2tau."
    },
    {
      "url": "https://arxiv.org/html/1510.02699v1",
      "scope": "Multidimensional definition and Proposition3.1; positive integer multiples n1*tau,n2*tau with residue sum retained."
    }
  ],
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      "title": "Theta addition: the variables and boundaries matter",
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  "algebra_self_checks": [
    "bijection (n,m)<->(k,l) with same parity",
    "t=0 duplication and (n,m)=(1,0) exponent",
    "P factor by independent coordinate operators and exponential mode",
    "smooth subtraction annihilated exactly by P",
    "complete s endpoint decay on compact t ranges",
    "two integrations by parts give 2*M0; four give zero",
    "exact M0 lower bound with interior and exterior retained",
    "complete Fourier bracket factor 64*L1; no splitting growing terms"
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  "open_input": "All-height signed comparison for complete original associated kernel, or independent reference/error comparison.",
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