PFUSRC-146 Prime-Node Rigid Morphing Topological Space ——The Third Topological Configuration of Observable Cosmic Spacetime Subtitle: From Octopus/Amoeba Structures to PFUSRC Hierarchical Spatial Cosmology Standard Abbreviation: Rigid-Node Morphing Space Acronym: PNRMTS

Abstract

Modern physics has long established two ideal spatial substrate models: Newtonian globally absolute rigid space and the globally steady-state fluid vacuum framework. Both models carry irreparable inherent flaws and are restricted by the three-dimensional reductionist paradigm, failing to coherently explain cosmic large-scale filamentary structures, spacetime curvature deformation, quantum nonlocal correlation and dark matter equivalent gravitational fields. This paper proposes a third complete topological spatial framework: Prime-Node Rigid Morphing Topological Space (PNRMTS). This spacetime takes discrete prime-number topological anchor points as permanent rigid skeletons, while interstitial regions between anchor points possess full capacity for stretching, twisting, bending and adaptive deformation, with structural logic analogous to octopus and amoeba natural topological morphologies. This paper rigorously derives PNRMTS’s full topological postulates, number-theoretic constraints and dynamical laws, clearly distinguishes its properties from globally rigid and globally fluid space, and proves its natural nesting and compatibility with the PFUSRC 11-dimensional triple coaxial 45° double-cone steady-state system. PNRMTS provides spatial substrate support for PFUSRC-147 damped imprint cosmic skeleton and systematically resolves multiple core observational contradictions within the ΛCDM cosmological paradigm. This paper clarifies that PNRMTS is not an independent third type of space, but the inevitable discretization and morphing projection of L4 parent-universe 45° double-cone rigid ontology at the L5 observable projection layer; rigid prime-node networks originate from discretized L4 continuous skeletons, while deformable interstitial zones embody the double-cone topological breathing rhythm projected into three dimensions. The three-layer topological architecture of PNRMTS (rigid node layer, morphing interstitial zone, transition state region) corresponds to frontier results across discrete mathematics, continuum mechanics, cosmology and non-equilibrium thermodynamics, including Riemann ζ-function, finite simple group classification, prime knot theory, Connes noncommutative geometry, Navier-Stokes equations, Ricci flow, bulk viscous cosmology, Wilson renormalization group and BKT topological phase transitions. PNRMTS unifies these scattered disciplinary discoveries into a consistent cosmic spatial topological spectrum for the first time. This paper emphasizes that all PFUSRC conceptual constructs (double-cone, prime anchor nodes, interstitial morphing zones) serve merely as cognitive tools like “fingers pointing to the moon”, rather than ultimate cosmic ontology. Linear fixed modeling holds valid application scope at lower receiving layers (L5-L7) for engineering and classical physics, yet cannot be misapplied as ontological truth of higher dispatching layers. PNRMTS offers a falsifiable, parameter-free spatial cosmology nested within PFUSRC seven-layer ontology, laying foundational topological premises for the subsequent PFUSRC-148 Spatial Hierarchical Nesting Dynamics monograph.