Center-Free Co-Articulation Load: A Sharp Dynamic Symmetry-Information Theorem

This preprint establishes a sharp information-theoretic lower bound for history-dependent finite continuation fibers carrying transitive symmetry. For a realized continuation Y_t, a full collection of perspectival contributions Z_t, and maximal information λ_t available to any proper subcoalition, the irreducible full-coalition advantage satisfiesK_t ≥ [\,b(m_t,ε_t)-λ_t\,]_+,whereb(m,ε)=log_2 m-h_2(ε)-εlog_2(m-1).The bound follows from transitive-orbit uniformity and the conditional Fano inequality and is shown to be sharp on regular cyclic fibers by explicit constructions across the full admissible leakage range. The paper further derives a cumulative history-dependent bound, proves invariance under history-dependent injective recoding, and establishes a finite-information pre-specification obstruction: a single pre-existing variable of finite Shannon entropy cannot support arbitrarily large cumulative continuation load at prescribed error levels. The result is deliberately narrower than a general theory of synergistic information. Its invariant measures the information advantage of the full coalition over its most informative proper subcoalition. Standard ingredients—including Fano’s inequality, transitive group actions, additive secret sharing, the mutual-information chain rule, and data processing—are not claimed as novel. The contribution lies in their sharp coupling within a dynamic, history-relative theorem architecture. The formal result is operational and information-theoretic. It does not by itself establish ontological claims about consciousness, potentiality, causation, or metaphysical freedom.