Certified Mathematical Growth of the Chrysene Formalism: Concordance Frontiers and Minimal Scission

Abstract

We give a compact theory of certified extension for a formal presentation whose identity is constrained by an external reference structure. A protected fragment of an initial presentation is held fixed under ordinary extension, while mathematics outside that fragment may grow strictly. Candidate extensions carry proof provenance and are admitted only after passage of logically distinct mathematical, concordance, realization, and domain conditions. For a theorem with several proof routes, the inclusion-minimal sets of uncertified admission-requiring premises form a certification frontier. If ∅ ∉ Front_n(θ), then no recorded route supports assertoric certification; the corresponding frontier deficits instead yield conditional theorems. Provenance-labeled proof support prevents uncertified premises from acquiring certified status through intermediate derivations. Finally, a directed proof-support hypergraph and a least-fixed-point construction define theoretical scission: when previously certified support is invalidated, exactly the unsupported dependency region is removed while every theorem possessing a surviving grounded proof is retained. Applied to the Chrysene Formalism, the construction permits strict mathematical growth while preserving its Canonical Molecular Anchor.