Condensation Dynamics of Nested Regimes: Emergence, Safe Forgetting, and the Rate of Persistent Information

This paper develops a finite structural theory of condensation across nested declared regimes. A declared question family determines a maximal safe congruence and a terminal safe quotient; the paper asks how much distinction may be condensed along the way, how condensation composes across stages, when interacting condensations admit canonical allocation, and under what conditions a higher-level persistent unit can emerge. For a finite regime, structural condensation is defined as the logarithmic reduction in distinguishable states under a safe quotient. The resulting condensation potential is an exact path potential on the quotient order: every quotient-stage amount is a potential difference, every finite chain telescopes, and every maximal safe tower spends the same total condensation budget regardless of staging. Demand refinement is antitone in that budget: requiring more future distinctions permits weakly less safe condensation. Adding a declared clock yields a structural condensation rate. Serial nesting obeys a no-free-acceleration theorem: the total rate is a duration-weighted average of the stage rates and cannot exceed the fastest serial stage. Independent product channels, by contrast, exhibit exact parallel amplification. On shared carriers, additivity fails in both directions. The paper introduces an interaction defect that measures exactly the path-dependent allocation discrepancy across a congruence-lattice square. The defect can have either sign. For permuting congruences it admits an exact covariance formula in terms of class counts inside join blocks. Uniform and permuting congruence structure gives a broad zero-defect class; in particular, the condensation potential is a lattice valuation on the congruence lattice of every finite congruence-uniform, congruence-permutable algebra, including finite groups. The paper also distinguishes two independent forms of canonicity. In finite distributive safe-congruence intervals, Birkhoff representation yields a canonical join-irreducible condensation skeleton, but the amount assigned to an irreducible increment can remain path-dependent. Conversely, finite groups can have canonical pairwise allocation while admitting non-unique irreducible factorizations. Thus canonical total budget, canonical allocation, and canonical factorization are separate structural questions. Finally, the paper gives a regime-relative theory of emergence. A nontrivial semantic condensation of an already reduced lower-level normal form is possible exactly when the transported demand is strictly weaker; the released condensation budget bounds the amount available to the emerging level, with equality at its corresponding normal form. Persistence verdicts do not automatically transport between levels. Biological evolution, boreal ecosystems, culture, and networked information systems are therefore treated only as candidate declared instantiations. The theory does not claim that nesting causes historical acceleration; it specifies the structural quantities and common-clock conditions required for such a claim to become testable.