Algebraic Collapse in Nondeterministic Language Models via Deterministic Manifold Constraint (Amendment Edition v1.1)

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Theoretical framework in which the output of a nondeterministic language model is projected onto a compact Lie group (the deterministic constraint surface), and the reachable algebra of the constrained system is characterized. Amendment Edition v1.1: an author-directed mathematical audit of the v1.0 draft found and corrected six defects around the central theorem (closure of the raw projected image, a false finite-generation claim, an unproven entropy corollary, a decidability misattribution, a figure overstatement, and a conditional-to-applied leap). The corrected central result is the caging theorem: the deterministic layer confines all finite algebraic combinations of constrained outputs inside a designed lower-dimensional subgroup, regardless of sampling temperature or run length. v1.0 is preserved unaltered in version history per the append-only doctrine. Prepared with AI assistance under author direction; corrections disclosed in full.