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Theorem · classical import and exact adapter

FPRD-QA-MX-T01

Invariant quotient and balanced core

Exact statement

The characteristic polynomial is the affine quotient for one matrix; every fibre has one closed semisimple orbit, and its normal representatives form one unitary orbit.

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

Kempf–Ness and invariant-theory inputs are separated from the elementary one-matrix specialization.

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

  • A balanced representative is a unitary orbit, not a canonical matrix.

Open work

Compare simultaneous-conjugation fibres where traces of words replace one characteristic polynomial.