Closure Invariants, Projection, Attention Views, and Static/Dynamic Compilation

Addresses what happens when a closure-space object is compressed, summarized, or rendered into a visualization, an AI attention window, a database, or a human-readable interface. Distinguishes the Native Closure State (the full typed graph plus scope, hypotheses, certificates, debt, version, provenance, and ledger) from the Projected Closure View, explicitly permitting lossy projection provided that every loss that could affect a closure conclusion is typed, accounted for, and converted into “projection debt.” Defines a 13-member family of key closure invariants, requiring that a projection-closure commutation law hold before any graph relation visible in a projected view can be treated as a native closure conclusion. Compares dynamic incremental projection with static batch projection, arguing that “reason/close natively first, then project” is the safer default. Also formalizes attention projection — as long as any unloaded frontier/cut-set/obstruction/debt is externalized with a traceable boundary contract, an AI or researcher can safely work on only a partial subgraph.