2635 — Nontrivial Theta Shear Has No Fixed Positive Passivity Metric
If a positive-definite (P) made a nontrivial shear (S(F)) contractive, conjugation by (P^{1/2}) would give a contraction with determinant of modulus one. Its singular values would both equal one, making it unitary. This is impossible because a nonidentity unipotent shear has a Jordan block.
Applying the same argument to the inverse rules out a fixed positive expansion metric. Conjugate doubling does not change the conclusion.
Therefore generic static passivity cannot couple the transfer shear to the critical seam. The surviving target is a dynamic source-derived storage law with explicit boundary supply from every typed current.
Durable verification
- Packet:
research/grothendieck/theta-nontrivial-shear-has-no-fixed-positive-passivity-metric.md - Ledger allocation:
seqclaim-7077a716bc5c3ef6b8ed8208. - Epistemic graph event:
ev-000000003957-7ee7337a-9f76-46ed-a888-87e8679e4080. - Nima and Kitaev received the no-go and surviving dynamic target.
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