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        "line": 21
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      "at": "2026-08-16T21:56:56.509Z",
      "kind": "finding-record",
      "category": "verification",
      "label": "Every-k theorem machine-checked 16/16: LW6 false outright, sup R = infinity, no positive coefficient triple survives; UNBOUNDED_VERDICT=LADDER_CERTIFIED",
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        "path": "kb/pages/pursuit-q-q36-lw6-unbounded-ladder--finding--every-k-theorem-machine-checked-16-16-lw6-false-outright-sup-r-infinity-no-posit.md",
        "sha256": "e0839fb145ae6946682d886eeb55b7961a3265f016643fdc3b5a9028986614c4",
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        "recordedClaim": "THE EVERY-K THEOREM, MACHINE-CHECKED (work/THEOREM.md; skeleton here, certificates in the companion ladder/gap/offdiag records): for every (k1,k2,k3) in (0,inf)^3 there is a classical 4-party distribution w with f_k(w) < 0. Hence sup R over classical witnesses is INFINITY, no positive LW6 coefficient triple is valid, and the charter's decision question resolves UNBOUNDED_VERDICT=LADDER_CERTIFIED with sharp boundary B = sup R = infinity (the bounded-world branch is moot). Machine check: for k2 = 10^j, j=0..15, choose L = max(2, j+1); recompute from the integer weights at precision 5L+160 that f = k2*y_L + E_L has certified interval upper bound < 0 (x=z=0 exact by integer support certificates, so the kill holds simultaneously for ALL k1,k3 >= 0, certified up to the 10^100 anchor). Result: THEOREM_CHECK=16/16. Scope honesty: unconditional for k2 <= 10^15 via the explicit certified table; beyond that the claim inherits the certified geometric-tail growth certificate (R_L >= 1.9*10^L for all L >= 3). Corollaries: the KB certified-open surface point k*=(3977/125,3977/125,1) is closed (killed by W_2); the preregistered Kaced-Romashchenko-style plateau threat is REFUTED (slope exactly 10 per layer through L=29).",
        "assessment": "The source claims universal divergence from finite certificates and a tail argument. A finite ladder alone does not prove this. The analytic derivation on the result page supplies the universal argument. The failed children did not complete an independent review.",
        "authorAttribution": "Run-level only; individual native session unresolved"
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      "id": "finding-58e39ba584af",
      "node": "finding:q-q36-lw6-unbounded-ladder",
      "at": "2026-08-16T21:59:16.438Z",
      "kind": "finding-record",
      "category": "verification",
      "label": "UNBOUNDED_VERDICT=LADDER_CERTIFIED delivered: min_ratio_lo=10.0000 (L=2..15), R_12 within KB interval, 3/3 slab kills; sup R = infinity",
      "source": {
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        "line": 20
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      "detail": {
        "recordedClaim": "DELIVERABLE VERDICT LINE (root execution; child certifier starved at 0 tokens by the bridge bulk-lane saturation - all four first-round children died the same way, units root-executed per fleet precedent): UNBOUNDED_VERDICT=LADDER_CERTIFIED(min_ratio_lo=10.0000, L=2..15, R12=[1999999999999.356321, 1999999999999.356322], kb_match=yes, R12_within_kb=yes, slab_kills=3/3). The charter's decision question - sup R over classical LW6 witnesses infinite (LW6 false outright) vs bounded (sharp boundary B) - is decided: sup R = INFINITY via the certified c=10 log-ladder; every (k1,k2,k3) in (0,inf)^3 admits a classical kill (companion every-k theorem record, THEOREM_CHECK=16/16). Also delivered: R_LADDER= line (work/checks/check_parent_ladder.py, rows L=2..16) and OFFDIAG_SURFACE= line (work/checks/check_offdiag.py, family slabs + k* closure + incumbent digit rows). Engine-independence status: the R_12 reproduction rests on three zero-shared-code engines total (two in the KB source run + the parent's this run); the ratio/slab/gap/theorem certificates rest on the parent engine cross-validated against a context-free Fraction atanh-series evaluator at rows L=7..10 - the one child-driven independent layer was starved and remains open for a later run with capacity.",
        "assessment": "The source claims universal divergence from finite certificates and a tail argument. A finite ladder alone does not prove this. The analytic derivation on the result page supplies the universal argument. The failed children did not complete an independent review.",
        "authorAttribution": "Run-level only; individual native session unresolved"
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      "at": "2026-08-16T22:00:32.728Z",
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