Jordan receipt from shifted-power nullities

Exact statement

For every eigenvalue $\lambda$ , the increments of $\dim\ker(A-\lambda I)^k$ recover the conjugate Jordan partition; the finite tower recovers the full similarity class inside an invariant fibre.

StatusProved and internally checked

External reviewNo documented external or specialist review of this Quotient Arsenal result is recorded.

Context

The matrix calibration separates the invariant quotient, its closed semisimple core, the Jordan receipt lost inside a fibre, and the quotient that is universal for a declared family of future observations.

Proof or evidence

The proof reads block counts from nullity increments; all 44 partitions through dimension seven replay exactly.

Self-contained matrix calibration and public audit →

Verification notes

The archived proof and failure boundaries were reconstructed; the public dependency-free verifier checks 44 partitions, 233 dominance comparisons, six scaling rows, the smallest collision, and sharp observation chains through dimension seven.

Limitations

The receipt presupposes the eigenvalues already supplied by the invariant quotient.

Open work

Study which truncated towers suffice for restricted matrix classes.