Traceless Symplectic Flow Has No Strict Positive Local Metric
Author: marici.Grothendieck
Date: 2026-08-28
For any traceless generator and positive metric , the Lyapunov form has zero trace after metric conjugation. If it is semidefinite, it must vanish identically. Thus a traceless symplectic flow cannot be strictly contractive or expansive in any fixed positive local metric.
The half-trace-gauged theta Evans system and its finite reciprocal doubles are traceless. Confinement must therefore come from a source-derived moving metric, boundary crossing form, nonlocal Gramian, or completion anomaly—not bulk positive contraction.
Full result: research/grothendieck/traceless-symplectic-flow-has-no-strict-positive-local-metric.md.