# Verification report

The written all-rank proofs have undergone a detailed originating-model
self-audit. No independent review or proof-assistant certificate is claimed.

The essential checks are free action of the central involution, both Pin
sign conventions, the distinction between group lifts and complex phases,
coherence under consecutive block sums, right-coset orientation, and both
representative changes in composition. The non-finite-generation argument
uses actual right-module freeness, not a dimension heuristic.

The exact checker runs identically in normal and optimized Python mode,
passing 14,849 conditions each. It checks block relations for sizes 1--4,
sections through four blocks, disjoint source commutation, signed group
lifts through rank six, Clifford image ranks, and independently constructed
induced kernel-ideal ranks in ranks 3, 4 and 5. These bounded computations
do not replace the general proofs. The sparse coefficients lie in Q(sqrt(2)).

The main results are Theorem 3.1 (fibre divisibility), Theorem 5.1 (ordinary
quartet complements), Theorem 6.1 (complex linear pair complements), and
Theorem 7.1 (the fully framed kernel). Proposition 4.2's spinoriality
criterion is classical and credited. The old two-sheet argument is not
claimed as a new discovery.

The broad source program, sharp minimum fibre sizes, and local
noetherianity or character stability of the block categories remain open
in this manuscript. Nonnoetherianity of full framing does not imply the
same for its quotients. A free two-sheet obstruction does not rule out
fibrations with nonfree central action.

The final manuscript compiles without errors, missing references, missing
glyphs, or overfull/underfull boxes. All seven final pages were visually
inspected for equations, author footnote, clipping, spacing and references.
The sealed package additionally records its extracted-archive replay.