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Counterexample · quotient loss

FPRD-QA-MX-X01

Two-dimensional invariant collision

Exact statement

2I22I_2 and J2(2)J_2(2) have the same invariant quotient but different Jordan receipts, stabilizers, and Frobenius-infimum attainment.

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

All invariants, nullities, centralizers, and scaling values were recomputed 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

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

Open work

Use as the mandatory smallest hostile test for matrix quotients.