English Abstract This paper, strictly based on the 3+1-dimensional topological cognitive model and the V3.0 unified paradigm of primordial manifestation topology, takes the K₀ zero-state primordial field as the sole ultimate physical substrate and follows the 12-character core axiomatic system of "the unity of substance and function, triple-nature recursion, and topological conservation" to construct a complete taxonomy, dynamics and cosmogony framework of K-phase evolution. Taking the full cycle of primordial manifestation "excitation-topological locking-deconstruction-return" as the main line, this paper systematically defines the strict boundaries, mathematical representations and cosmic shaping functions of five topological phases: Pure-K (K₀ ground state), Excited-K, Old-K, Filling-K and Free-K. For the first time, it fully maps the five-phase evolution to the four-dimensional cognitive framework of "substantial characteristic X + functional metric Y + structural isomorphism Z + time T", completing the bidirectional logical closed loop from "the end of deconstruction from the manifest to the hidden" to "the starting point of creation from the hidden to the manifest". The core innovations of this paper include: (1) Proving the hierarchical necessity of "stability first, flexibility expansion, and economy constraint", and defining it as the intrinsic tension of the unity of substance and function of the K₀ field and the core screening mechanism of the Y-dimensional functional metric; (2) Proposing the geometric mechanism of spatial manifestation driven by the topological degree gradient of Old-K, establishing a natural connection with general relativity; (3) Constructing the memory closed loop of "storage-resonance reading-accelerated evolution" of returning Free-K, and clarifying the "learning" nature of the universe and the physical connotation of the T dimension; (4) Optimizing the terminology system to enhance the academic tension and physical connotation of the theory; (5) Proposing three types of falsifiable observational predictions to provide a clear path for theoretical verification. This paper lays an unshakable evolutionary theoretical foundation for subsequent research on particle physics mapping, cosmology deepening and higher-order emergence of consciousness in the K Theory system. English Keywords K Theory; K₀ zero-state primordial field; elementary dynamic phase; five-phase evolution; topology of primordial manifestation; 3+1-dimensional topological cognitive model; topological compactification; spacetime manifestation; cosmic memory; triple-nature recursion; multi-path convergence; learning universe
Jian Wen (Sat,) studied this question.