Phase 19 · conservative dynamics and identity completeness

Identity, freedom and frozen motion

AT-0151 → AT-0158. Conservative flows that preserve an identity invariant exactly. If that invariant is complete and nondegenerate, the only lawful generator is the zero matrix: the system cannot move at all. Degeneracy is what leaves room — and degeneracy is something we choose.

The arithmetic this phase turns on

[M, A]ᵢⱼ = (mᵢ − mⱼ)·Aᵢⱼ = 0 ⟹ Aᵢⱼ = 0 whenever mᵢ ≠ mⱼ

For a skew generator A and diagonal invariant M, exact preservation of xᵀMx forces every off-diagonal entry to vanish wherever the eigenvalues differ. A skew matrix has no diagonal, so A = 0.

Controls

SeedDegenerate blocks5Locality radius3Trials500

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