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[K3] Cut the 433-1b cell-11 guard transplant - #1155

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[K3] Cut the 433-1b cell-11 guard transplant#1155
scottdhughes wants to merge 8 commits into
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scottdhughes:scott/kb-k3-433-cell11-signed-pair

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Summary

This stacks on #1154 and takes the complete signed-pair resultant on its exact
433-1b cell-11 compact tower.

The computation produces a route cut rather than a closure:

Res_w1(P,S) = N0 * D0^5 * (w0-t^2) * (w0+1) * Q2(w0),

where Q2 is quadratic. Therefore the 433-1a guard product

N0 * D0^5 * (w0-t^2)^2 * (w0-r^2) * (w0+r^2)

does not transplant to the 433-1b tower. The Q2 discriminant has square
total norm in F_p(r) but is nonsquare in the declared degree-four tower.

The packet also records and independently replays one fully guarded deployed
signed-pair point after four deterministic r fibers. At that point
N0,D0 != 0 and both complete signed-pair equations vanish exactly modulo
2130706433.

Why this matters

This prevents the remaining cell-11 orbit from being closed by copying the
433-1a factorization. It replaces that route with one explicit quadratic
cover whose owner/count is now the correct next obligation.

The result is deliberately marked YELLOW / COUNTEREXAMPLE_NEW_FLOOR. It is
not a counterexample to the KoalaBear theorem, does not close cell 11, and
makes no ledger movement.

Validation

  • complete exact Python/FLINT tower resultant and factor extraction;
  • exact tower square/nonsquare classification, including norm-sign and
    trace-zero branches;
  • deterministic deployed-fiber witness search;
  • independent SymPy replay of the predecessor source expressions at the
    witness;
  • 16/16 hostile certificate mutations rejected;
  • predecessor [K3] Reduce 433-1b cell 11 to an exact compact tower #1154 certificate replayed;
  • Wolfram PolynomialReduce independently checked the generic
    quadratic-extension square-root reconstruction identities;
  • git diff --cached --check clean before commit.

Sage 10.9 reconstructed the algebraic tower, but its built-in factorization
path rejected this characteristic above 2^29; that tool limitation is
recorded in the audit and is not used as evidence.

Dependency and review gate

Please integrate #1154 first. A fresh reviewer should audit the load-bearing
resultant/factor extraction and the interpretation of Q2 before this packet
is banked. The next research target is the exact degree/genus and rational
point projection of the residual quadratic signed-pair cover, including all
leading and denominator fibers.

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