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[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#1149
scottdhughes wants to merge 63 commits into
przchojecki:mainfrom
scottdhughes:scott/kb-k3-m2-112-fixed-frontier-route-cut

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@scottdhughes

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Stack and review boundary

This PR is stacked on #1144 at exact head 05ff2348de8f2c0f99683875ff12a9a79dcf21ec. The net review is commit 55ac3e074: the exact eighteen-cell fixed-moving frontier packet. Parent noise will collapse when the stack integrates.

Result

  • reconstructs all six literal F00/F01 x R02/R11/R20 cells on their exact named opens
  • proves F00-R11 and F01-R11 empty (full localizer nilpotence index three)
  • retains the four crossed/identity charts as two-dimensional q-slice schemes
  • compiles all twelve F04/F05/F06/F07 cells through the exact quadratic dichotomy
    Res_w(P,Q)=U^2-VZ, with w=-U/V only on V!=0
  • retains the complete V=0 rank-drop branch instead of dividing it away
  • collapses the twelve literal high-complexity cells to six exact two-cell fingerprint orbits
  • moves the aligned-positive frontier 18 -> 16; no owner, charge, K3 value, or KoalaBear row bound moves

Wolfram 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 -> O0b and positive 433-1b role cell 14, and asks next for the six aligned-positive unramified cells; this packet attacks the literal F00/F01 six-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

python3 experimental/scripts/verify_kb_mca_v4_m2_aligned_positive_fixed_frontier_v1.py --check --tamper-selftest
env HOME=/private/tmp/rs_mca_sage_home /usr/local/bin/sage experimental/scripts/compile_kb_mca_v4_m2_aligned_positive_fixed_frontier_v1.sage --cell F00-R11 --check --summary
env HOME=/private/tmp/rs_mca_sage_home /usr/local/bin/sage experimental/scripts/compile_kb_mca_v4_m2_aligned_positive_fixed_frontier_v1.sage --cell F00-R02 --check --summary
env HOME=/private/tmp/rs_mca_sage_home /usr/local/bin/sage experimental/scripts/compile_kb_mca_v4_m2_aligned_positive_fixed_frontier_v1.sage --cell F04-R02 --check --summary
python3 -m py_compile experimental/scripts/verify_kb_mca_v4_m2_aligned_positive_fixed_frontier_v1.py
git diff --check 05ff2348de8f2c0f99683875ff12a9a79dcf21ec..HEAD

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/I quotient parity for the four F00/F01-R02/R20 survivors. For each of the six quadratic orbits, split V!=0 from U=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.

scottdhughes and others added 30 commits July 29, 2026 11:16
@scottdhughes

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Superseded and absorbed by #1152: its c112 coverage certificate includes the literal crosswalk, upstream imports, independent replays, and closes the remaining rank-drop/full-J branches. Closing this draft avoids duplicate review; the mathematical content is retained in #1152.

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