Finite trace separation

Read side by side

komorebi_math.deformation.finite_frobenius_separator works with the supplied finite trace table. If its selected trace matrix has full column rank, the constituent multiplicity vector is uniquely recoverable from those rows. Rank-deficient data does not separate every declared constituent.

from komorebi_math.deformation import finite_frobenius_separator

separator = finite_frobenius_separator({"place_a": (1, 0), "place_b": (0, 1)})
separator.certificate.require()
assert separator.recover((2, 3)) == (2, 3)

Certificate contract

The Boolean separating, certificate validity, and exact column-rank condition agree:

\[ \text{valid}\iff\text{separating}\iff\operatorname{rank}(A)=r, \]

where A is the supplied finite trace matrix and r is the constituent count. A rank-deficient result has an invalid certificate. Both certificate.require() and recover(...) reject that result.

The certificate has Exactness.EXACT because rank and recovery use exact finite algebra. Its checked assumptions concern the supplied finite table and exact column rank.

Arithmetic scope

Finite trace separation does not establish a global Galois or automorphic identification. The unchecked assumption Chebotarev density beyond the supplied table is recorded explicitly. Any global conclusion requires the relevant external arithmetic hypotheses.