← CSM / 04 · Closure Dynamics, Reopening, Hysteresis, and Fixed-Point Evolution
Advances CSM from a static graph to a time-indexed dynamical system, evolving through event-driven updates. Core claim: evidence accumulation can be monotonic, but the closure state usually is not — old evidence is never deleted, but BLOCKED/CLOSED/EXHAUSTED states can be downgraded to STALE/REOPENED. Defines closure events, closure scheduling, event commutation/non-commutation, closure hysteresis (the same final evidence arriving in a different order can produce path-dependent, different outcomes), reopening waves, debt discharge, frontier drift, local closure fixed points, relative equilibrium, closure attractors/cycles, metastability, and closure oscillation. Central non-collapse principle: $\mathfrak{C}_{t+1}=\mathfrak{C}_t \not\Rightarrow \mathfrak{C}_t=\Omega^{math}$ — reaching a fixed point under a fixed theorem library/grammar/representation/bridging policy is only a relative closure fixed point, and never means “the mathematical space is complete.”
Relationship to the rest of the series, stated as closely as possible in the document's own words, not my interpretation.
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