Paper M9 — Symmetry Descent, Structure, and the Limits of Reconciliation

M9 makes explicit the role of symmetry as realized through structure in Cohesion Dynamics, building on M8’s analysis of closure-stable mismatch. Divergent branches inherit not merely state, but representations of the admissible closure algebra of their parent phase. Crucially, symmetry does not exist independently of structure: admissible symmetry representations are defined only relative to structured configurations.

Key Results:

• Structural changes that alter admissible closure operations necessarily induce symmetry descent, even when abstract symmetry labels appear unchanged
• Branching corresponds to symmetry factoring; reconciliation requires compatibility of symmetry–structure realizations
• Irreversible loss of reconciliation arises from symmetry descent rather than stochastic noise or entropy
• Explains superselection sectors, rapid decoherence, and structural arrow of time

Epistemic Role: Fully grounded in substrate mechanics of relaxation and closure. Introduces no new axioms or mechanisms; clarifies structural requirements for reconciliation and branching.

Paper ID: CD-M9 | Series: M-series (Formal Mechanisms) | Status: Draft | Dependencies: A, M1–M8 (refines M8); informed by B1–B2