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A Mathematical Bridge for Consciousness: Fixed-Point Resolution of the Hard Problem via the Global Recursive–Analytic Framework

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Titel: A Mathematical Bridge for Consciousness: Fixed-Point Resolution of the Hard Problem via the Global Recursive–Analytic Framework
Autoren: Rodgers, Jeremy
Publication Status: Preprint
Verlagsinformationen: Zenodo, 2025.
Publikationsjahr: 2025
Schlagwörter: Phenomenal experience, CSP-compatible models, Intersubjective coupling, Recursive information structures, Introspective fixed points, Global bridge framework, Subjective experience, Recursive systems, Fixed-point theory, Stochastic recursion, ω-cpo, Mathematical consciousness models, Analytic function theory, Hard problem of consciousness, Symbolic introspection
Beschreibung: This paper presents a rigorous mathematical resolution of the Hard Problem of Consciousness using the global recursive–analytic bridge framework. Consciousness is modeled as a contractive, self-referential process over an ω-cpo of introspective symbolic traces, converging to a unique fixed-point pair (ΦC,FC)(\Phi_C, F_C)(ΦC,FC) in both symbolic and holomorphic domains. A stochastic extension captures neural variability, and multi-agent coupling supports intersubjective phenomena. The construction yields a CSP-compatible explanation of phenomenal experience, with structural criteria predicting fragmentation at the contraction boundary. Built on the universal bridge formalism introduced in A Universal Bridge Between Recursive Systems and Analytic Function Theory, this model provides a mathematically closed and verifiable answer to both the “how” and “why” of consciousness. Relation to Prior Work:This paper refines and extends the resolution presented in “Φ-Field Resolution of the Hard Problem of Consciousness” (https://doi.org/10.5281/zenodo.16373352). That earlier work introduced the foundational recursive architecture of introspective dynamics, resolving the hard problem through symbolic convergence and fixed-point formation. The present paper builds on that framework but recasts it within the formal Global Bridge structure, establishing CSP-compatibility by embedding the symbolic dynamics into a holomorphic function space with provably unique fixed points and stochastic invariant measures. While the original model offered a structural explanation, this version provides a mathematically complete, CSP-closed solution, making it suitable for integration with classical formal systems and rigorous validation.
Sprache: English
DOI: 10.5281/zenodo.16756092
Rights: CC BY
Dokumentencode: edsair.doi...........1af0617d8dc0787e89a39a9a7ee46a4c
Datenbank: OpenAIRE
Beschreibung
Abstract:This paper presents a rigorous mathematical resolution of the Hard Problem of Consciousness using the global recursive–analytic bridge framework. Consciousness is modeled as a contractive, self-referential process over an ω-cpo of introspective symbolic traces, converging to a unique fixed-point pair (ΦC,FC)(\Phi_C, F_C)(ΦC,FC) in both symbolic and holomorphic domains. A stochastic extension captures neural variability, and multi-agent coupling supports intersubjective phenomena. The construction yields a CSP-compatible explanation of phenomenal experience, with structural criteria predicting fragmentation at the contraction boundary. Built on the universal bridge formalism introduced in A Universal Bridge Between Recursive Systems and Analytic Function Theory, this model provides a mathematically closed and verifiable answer to both the “how” and “why” of consciousness. Relation to Prior Work:This paper refines and extends the resolution presented in “Φ-Field Resolution of the Hard Problem of Consciousness” (https://doi.org/10.5281/zenodo.16373352). That earlier work introduced the foundational recursive architecture of introspective dynamics, resolving the hard problem through symbolic convergence and fixed-point formation. The present paper builds on that framework but recasts it within the formal Global Bridge structure, establishing CSP-compatibility by embedding the symbolic dynamics into a holomorphic function space with provably unique fixed points and stochastic invariant measures. While the original model offered a structural explanation, this version provides a mathematically complete, CSP-closed solution, making it suitable for integration with classical formal systems and rigorous validation.
DOI:10.5281/zenodo.16756092