[K3] Close two fixed 112 cells and cut quadratic frontier - #1149
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scottdhughes wants to merge 63 commits into
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[K3] Close two fixed 112 cells and cut quadratic frontier#1149scottdhughes wants to merge 63 commits into
scottdhughes wants to merge 63 commits into
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This was referenced Aug 6, 2026
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Stack and review boundary
This PR is stacked on #1144 at exact head
05ff2348de8f2c0f99683875ff12a9a79dcf21ec. The net review is commit55ac3e074: the exact eighteen-cell fixed-moving frontier packet. Parent noise will collapse when the stack integrates.Result
F00/F01 x R02/R11/R20cells on their exact named opensF00-R11andF01-R11empty (full localizer nilpotence index three)F04/F05/F06/F07cells through the exact quadratic dichotomyRes_w(P,Q)=U^2-VZ, withw=-U/Vonly onV!=0V=0rank-drop branch instead of dividing it away18 -> 16; no owner, charge, K3 value, or KoalaBear row bound movesWolfram Language independently returned five zero identities for the generic resultant/reconstruction algebra. The fail-closed Python verifier independently replays them in SymPy and rejects 11/11 hostile mutations. Fresh cell-specific proof review is still required, so this PR is intentionally draft.
Upstream relation
PR #1143 now closes
433-1a -> O0band positive433-1brole cell 14, and asks next for the six aligned-positive unramified cells; this packet attacks the literalF00/F01six-cell block. PR #1148 is M31 fixture-specific affine-hull rigidity and lacks the containment theorem needed here. PR #1147 is a separate Paper-D reduction. No open PR duplicates this packet.Validation
The exact quadratic compressor was also replayed successfully for all twelve literal high-complexity cells. Optimized Python execution is refused. A monolithic four-variable basis and a high-degree generic three-variable basis were nonterminal and are not used as evidence.
Next exact action
Derive full
J/Iquotient parity for the fourF00/F01-R02/R20survivors. For each of the six quadratic orbits, splitV!=0fromU=V=0, substitute into the remaining quartics only on the generic branch, and terminate each component in emptiness, a named owner, or an explicit primitive route. Do not retry the raw monolithic four-variable basis or discard degree-drop components.