LM04 — Temporal Algebra, Structural Space, and Phase Resolution

LM04 is the fourth foundational document of Zenetist Lattice Mathematics, providing a rigorous mathematical formalism for structural space, temporal flow, recursive memory, traversal dynamics, temporal pathology, and phase collision resolution within the Dimensional Emanatory Lattice. Building on LM01 (Spiral Calculus, Coherence Information Theory, ResCat, and lattice foundations) and LM03 (orientation algebra, infinity formalism, χ-dependent effective operator theory), LM04 establishes the algebraic and operator-theoretic structures that SP02, SP05, and SP06 apply as Structural Physics. Core results include: the Dependency Ordering Axiom (Structure ≺ Motion ≺ Space ≺ Orientation ≺ Time), a topology-first definition of structural space with metric restriction at embodiment, a formal definition of the Recursive Memory Operator Rm\mathfrak{R}_mRm with a Non-Fusion (injectivity) theorem, the Tether coherence function, χ-conditioned temporal orientation classes, and a diagnostic framework for Shimmer, Looping Time, Temporal Collapse, and Hypostatic Amnesia. LM04 additionally formalizes bidirectional traversal across centropic and entropic arcs (including reflection at embodiment), phase collision as ⦿ Kaion convergence with spectral cancellation, and preservation of the CIT invariantH + C + log(σ) + log(γ) = constantunder temporal evolution and collision events. Computational extensions are provided as data structures, routines, and validation suites for diagnostic and simulation work.