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Counterexample · boundary case

FPRD-QA-MX-X02

Three-dimensional repeated-eigenvalue collision

Exact statement

Repeated-eigenvalue semisimple and nonsemisimple 3-by-3 matrices collide in polynomial invariants while their receipts and stabilizers differ.

StatusExact and reproduced
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 independent certificate checks the repeated-eigenvalue boundary directly.

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

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

Open work

Retain as the repeated-eigenvalue regression fixture.