Exact theorem · real 2×2 matrices

Finite matrix root

Direct integer multiplication for the declared commutator G = [Q, Ω].

This record is a reproducible calculation on the displayed inputs. It preserves the scope of CA-ALG-001 in the public claim register.

Deterministic check

Declared input and output

The computation is performed locally in the browser from the integers below.

CA-ALG-001

Recompute the exact root

The result must agree with the record before it can be used as this record’s output.

[[1, 1], [1, 0]]

[[0, 1], [-1, 0]]

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Procedure	Compute QΩ − ΩQ; square the resulting matrix; compute trace and determinant.
Expected output	G = [[−2, 1], [1, 2]], G² = 5I, tr(G) = 0, det(G) = −5.
Receipt	Machine-readable record; browser calculation above.
Boundary	Displayed real 2×2 matrices and their direct algebraic consequences.

Boundary. The calculation establishes the stated finite matrix identities. It does not itself establish a physical identification, measured constant, or model calibration.