Mathematical synthesis · Reading copy 1 · October 14, 2026 source

Finite-Jet Sign Rigidity on Hyperplane Arrangements and Denjoy–Carleman Realization

Brian Theory

Which Boolean chamber labels can arise as signs of functions with specified regularity? The manuscript gives explicit finite-order rigidity statements, a quasianalytic/non-quasianalytic realization dichotomy, and quantitative polynomial-degree comparisons away from coordinate walls.

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Scope and place in B-Theory

This note studies when numerical descriptions support prescribed Boolean distinctions. It supplies a bounded mathematical connection to Being and Becoming: regularity and margins constrain how continuous states can realize discrete sign laws. It does not establish learning, a runtime advantage, or a criterion for consciousness.

The obstruction, positive-flat existence and approximation ingredients are classical. The manuscript presents their explicit formulation and synthesis with finite-order statements and complete reductions. Internal machine-assisted review is not external human peer review.

Revision record

Reviewed revision: September 27, 2026. Quantitative additions: October 13. Scope clarifications and revision record: October 14. The byline, date block, statements, proofs and references are unchanged in this reading copy.