Existence and Embedding of a Recursive Field_ Fixed-Point Construction and CSP-Compatible Projection.pdf
Year: 2025
Type: article
Abstract: This paper establishes a rigorous bridge between recursive symbolic systems and classical mathematics. At its core is the Φ-field, a formally proven fixed-point attractor that emerges from logical closure, metric contractivity, and adjoint embedding–projection structure. Part One proves the existence, uniqueness, and inevitability of the Φ-field in any system satisfying these axioms, using constructive logic, Banach fixed-point theory, and categorical duality.Part Two constructs an explicit CSP-compatible projection that embeds recursive dynamics into Banach space operators, preserving convergence, symmetry, and analytic structure. This embedding allows recursive solutions, such as those arising in number theory and operator symmetries, to be represented in a fully verifiable classical mathematical framework. The result is a complete and general projection method for translating recursive fixed-point emergence into CSP-valid mathematics, closing the gap between symbolic recursion and formal analysis. https://doi.org/10.5281/zenodo.16623512 Other related work Riemann Hypothesis https://doi.org/10.5281/zenodo.16623916 Navier–Stokes Existence and Smoothness https://doi.org/10.5281/zenodo.16623943 P versus NP Problem https://doi.org/10.5281/zenodo.16623960 Yang–Mills Existence and Mass Gap h ttps://doi.org/10.5281/zenodo.16624071 Birch and Swinnerton-Dyer Conjecture https://doi.org/10.5281/zenodo.16624087 Hodge Conjecture: Algebraic Cycles as Recursive Cohomological Emergence https://doi.org/10.5281/zenodo.16624254 The Φ-Field: A Unified Theory of Recursive Information Structure https://doi.org/10.5281/zenodo.16342661
Source: Figshare
Author: Rodgers, Jeremy
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6902405379
FWCI:
Cites:
Cited by:
Related to: