Negative result

FPRD-QA-MX-F2

Nonsemisimple orbit floor is not attained

Exact statement

A nonsemisimple conjugacy orbit approaches but never reaches its balanced Frobenius floor.

StatusProved
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

Jordan scaling approaches the floor and equality would force normality, hence semisimplicity.

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

  • No novelty or specialist-review claim is made; the statement is limited to the displayed presentation and hypotheses.

Open work

Measure approximation cost together with conditioning.