PFUSRC-121B: System Anchoring and Rheological Cognition Methodology Supplement — Positioning Statement of PFUSRC-121 in the PFUSRC-035 Holographic Topology Map and the Cognitive Framework of Living Mathematics

PFUSRC-121 has completed the optimal configuration of discrete anchors, the complete constraint system of Topological Self-Reduction of Dimensions (TSRD), and the endogenous derivation of the black hole nested sub-universe topological hypothesis, establishing the full physical mechanism for the evolution from high-dimensional topology to low-dimensional spacetime. However, during the drafting of PFUSRC-121, the hierarchical anchoring of its core modules within the PFUSRC-035 holographic topology map—including the TSRD operator, the TER hot-cold dual energy reservoir cavities, the dispersion-aggregation topological rheology, the 6:5 regional weighting markers, and the recursive black hole nesting structure—had not been formally defined. This paper systematically extracts the rheological proof methodology implicit in PFUSRC-121, distinguishing between two distinct logical paradigms: boundary-constrained judgmental derivation and full-chain steady-state structural proof. It clarifies the legitimate rules of proof for dynamic topological evolution systems. Furthermore, it provides a unified PFUSRC topological interpretation of classical mathematical achievements including Gödel’s incompleteness theorems, Riemannian differential geometry, and classical Cauchy calculus, demonstrating that these results all touched upon the boundary essence of topological rheology but did not achieve ontological mechanism tracing. This paper establishes the core conclusion: PFUSRC-121 is not an isolated independent paper within the system, but rather the mechanism-concretizing document of the transition channel from Level 4 to Level 5 and the internal recursive nesting structure within Level 4 of the PFUSRC-035 holographic topology architecture. The boundary-anchored rheological proof method it proposes is the fundamental cognitive foundation for upgrading PFUSRC theory from a static axiomatic logical skeleton to an implementable dynamic topological engineering system.