Abstract

Synthetics proposes a fixed-point metaphysical framework exploring how relational geometry (R), distinguishability structure (D), and universal lawful constraints (U) might co-emerge rather than forming a linear foundation. Drawing on the Knaster–Tarski theorem, the framework investigates these aspects as mutually dependent primitives stabilizing through fixed-point operators over complete lattice structures. The resulting picture aims for compatibility with general relativity, quantum field theory, renormalization group theory, dynamical systems, information theory, and active inference. Existence is provisionally identified with global coherence in a space of admissible configurations. Subsystems are characterized through coupled fixed-point construction as renormalization-stable, decoherence-robust, Markov-blanket-bounded regions co-emerging with identity attractors. Minds are modeled as predictive identity attractors minimizing free-energy-like functionals. Teleology is explored as identity-conditioned constraint minimization, while consciousness is characterized as high-measure identity–teleology fixed points exhibiting integration, counterfactual depth, and representational richness. Teleology is always identity-conditioned constraint satisfaction, never “ends causing beginnings”. The framework engages five persistent conceptual tensions: irreducibility of distinguishability structure, non-uniqueness of fixed points, reconciliation of block-universe eternalism with attractor dynamics, limits of functional consciousness criteria, and interpretation-dependence in quantum measurement. While full resolution remains open, the fixed-point approach offers novel perspectives on each. Several technical components are developed schematically rather than rigorously. The framework demonstrates conceptual coherence and suggests pathways toward structural continuity, though significant mathematical development remains. This working paper presents the conceptual architecture; rigorous formalization constitutes a program for future collaborative work. A short appendix addresses model-theoretic limits, including the Löwenheim–Skolem theorem and Skolem’s Paradox, to show why distinguishability must be treated as an internal structural feature rather than an externally fixed magnitude. This reinforces the central claim: reality is determined by internal coherence, not by absolute syntactic description or external set-theoretic facts. This analogy is conceptual and not a claim that physical theories are first-order complete.