[K3] Cut the 433-1b cell-11 guard transplant - #1155
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…3 closed; universal structure (204 nodes pinned) Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01EaFM28YvmBtkP3JEgeiBuC
This was referenced Aug 10, 2026
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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:
where
Q2is quadratic. Therefore the 433-1a guard productdoes not transplant to the 433-1b tower. The
Q2discriminant has squaretotal 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
rfibers. At that pointN0,D0 != 0and both complete signed-pair equations vanish exactly modulo2130706433.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 isnot a counterexample to the KoalaBear theorem, does not close cell 11, and
makes no ledger movement.
Validation
trace-zero branches;
witness;
PolynomialReduceindependently checked the genericquadratic-extension square-root reconstruction identities;
git diff --cached --checkclean before commit.Sage 10.9 reconstructed the algebraic tower, but its built-in factorization
path rejected this characteristic above
2^29; that tool limitation isrecorded 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
Q2before this packetis 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.