Measurement as Center Splitting: Conditional Expectations, POVMs, and the AQM Measurement-Dynamics Closure Theorem

Measurement outcomes are not postulated as an external collapse rule. They arise as effective center splitting of a noncommutative observable algebra un der apparatus coupling, environmental decoherence, and finite-resolution coarse graining. The mathematical tools are standard: conditional expectations in operator algebras, POVM/instrument formalism in quantum operations, and environment-induced superselection in decoherence theory. The new contribu tion is to organize these tools into a center