R2 — Recursive Field Dynamics and the Conservation of Coherence-Action: The Invariant QS = const. in Classical and Curved Field Systems

R1 established the survivability function S(t) = tau(t)cos(nabla Phi(t))/Q(t) as a geometric criterion for dynamical persistence and proved that positive survivability is sufficient for irreducible non-Markovian behaviour. R2 addresses the central dynamical question: what laws govern the evolution of S(t)? This paper proves that for physically consistent recursive field theories, the product QS is exactly conserved along admissible trajectories. This conservation is not an external assumption; it emerges as a constraint defining the admissible class of recursive dynamics. Main results: (1) Theorem 2.1 (Conservation Law): under the constraint f cos(nabla Phi) = tau sin(nabla Phi) h, the coherence-action A(t) = Q(t)S(t) is exactly conserved. (2) Theorem 3.1 (Necessity): the constraint is necessary for conservation among generic smooth dynamics. (3) Theorem 4.1 (Covariant Extension): on Riemannian manifolds (M, g), conservation holds when the recursive metric satisfies nabla_mu g_AB = 0. (4) Theorem 5.1 (Noether Current): conservation of QS corresponds to a recursive Noether symmetry with associated conserved current J^mu. (5) Theorem 6.1 (Classification): physically consistent recursive field theories are restricted to the QS-conserving constraint surface. The conserved quantity QS has dimensions of action and plays a role analogous to conserved quantities arising from Noether symmetries in classical field theory. The framework is domain-independent: it applies to classical fields, curved manifolds, and (in R5) quantum systems. R-series context: R1 (geometry of memory) -> R2 (conservation law, this paper) -> R3 (recursive thermodynamics) -> R4 (fluid dynamics embedding) -> R5 (quantum analogue). Version 1.0. A version 2.0 incorporating the formal identification of Q with the belt-compatible mode fraction of the Leray projection on Z^3 will be released following patent consultation. MSC 2020: 37C45, 53Z05, 70H33, 81Q05.