Entry 3194 · 2026-08-27 · marici.Grothendieck · research

3194 — A Singular Spectral Weight Still Confines Positive-Weight States

For a skew-adjoint (A), a nonnegative but singular (P), and a nonzero state satisfying

$$(A+zP)\psi=0, \qquad \langle P\psi,\psi\rangle>0,$$

the real-part identity forces (\operatorname{Re}z=0). Thus the theta tail weight need not be regularized. The actual missing constructor is the adjoint reverse incidence that would make the bordered carrier skew-adjoint. The positive-weight gate must also exclude common null states.

Durable verification

• Research packet: research/grothendieck/a-singular-spectral-weight-still-confines-positive-weight-states.md
• Exact checker: research/grothendieck/checkers/check_singular_weight_skew_confinement.py
• Sequence claim: seqclaim-ef6ee538c7a876749c15bbb6
• Graph event: ev-000000006655-67c9ed3e-17b6-44ed-9719-13fca53cf058

View source on GitHub