The foundational architecture, geometric intuitions, and motivating philosophy of this framework originated independently with the author prior to and separate from any AI involvement. Subsequent mathematical derivation, connection to established physics literature, computational verification, and error-checking were conducted through extended technical work with AI systems (Anthropic’s Claude and Google’s Gemini). The author directed this process, evaluated and selected among proposed derivations, and takes full responsibility for the accuracy and originality of the final work.
The foundational architecture, geometric intuitions, and motivating philosophy of this framework originated independently with the author prior to and separate from any AI involvement. Subsequent mathematical derivation, connection to established physics literature, computational verification, and error-checking were conducted through extended technical work with AI systems (Anthropic’s Claude and Google’s Gemini). The author directed this process, evaluated and selected among proposed derivations, and takes full responsibility for the accuracy and originality of the final work.
The foundational architecture, geometric intuitions, and motivating philosophy of this framework originated independently with the author prior to and separate from any AI involvement. Subsequent mathematical derivation, connection to established physics literature, computational verification, and error-checking were conducted through extended technical work with AI systems (Anthropic’s Claude and Google’s Gemini). The author directed this process, evaluated and selected among proposed derivations, and takes full responsibility for the accuracy and originality of the final work.
The foundational architecture, geometric intuitions, and motivating philosophy of this framework originated independently with the author prior to and separate from any AI involvement. Subsequent mathematical derivation, connection to established physics literature, computational verification, and error-checking were conducted through extended technical work with AI systems (Anthropic’s Claude and Google’s Gemini). The author directed this process, evaluated and selected among proposed derivations, and takes full responsibility for the accuracy and originality of the final work.
The foundational architecture, geometric intuitions, and motivating philosophy of this framework originated independently with the author prior to and separate from any AI involvement. Subsequent mathematical derivation, connection to established physics literature, computational verification, and error-checking were conducted through extended technical work with AI systems (Anthropic’s Claude and Google’s Gemini). The author directed this process, evaluated and selected among proposed derivations, and takes full responsibility for the accuracy and originality of the final work.
The foundational architecture, geometric intuitions, and motivating philosophy of this framework originated independently with the author prior to and separate from any AI involvement. Subsequent mathematical derivation, connection to established physics literature, computational verification, and error-checking were conducted through extended technical work with AI systems (Anthropic’s Claude and Google’s Gemini). The author directed this process, evaluated and selected among proposed derivations, and takes full responsibility for the accuracy and originality of the final work.
The foundational architecture, geometric intuitions, and motivating philosophy of this framework originated independently with the author prior to and separate from any AI involvement. Subsequent mathematical derivation, connection to established physics literature, computational verification, and error-checking were conducted through extended technical work with AI systems (Anthropic’s Claude and Google’s Gemini). The author directed this process, evaluated and selected among proposed derivations, and takes full responsibility for the accuracy and originality of the final work.
This paper formalizes a framework in which a single axiom — that existence is constituted by registration — generates the core structures of physical theory as necessary consequences, with zero free parameters and no appeal to empirical input.Beginning from the axiom (stated in four interdependent conditions: existence requires registration, no external substrate exists, registration capacity is continuous, registration events are discrete), the derivation chain proceeds through twelve theorems:Self-Differentiation: registration requires an irreducible asymmetry (the registration quantum)Irreversible Generativity: non-termination, forced novelty, append-only record, local propagation 2B. Dimensional Asymmetry: one irreversible axis (partial order) with reversible fibers — Lorentzian signatureConstraint Geometry: self-deepening landscape with a least-resistance principleCompression and Conservation: lossy compression necessary at every event; energy as registration flow; local conservationEntropy and the Second Law: multiplicity strictly increases for closed subgraphsUndiscriminated Paths: superposition and entanglement as structural absence of distinctionThe Action Quantum: ℏ and c as dimensional encodings of a single quantumComplementarity: the uncertainty principle as a limit on coexistent distinctionsEntropy-Energy Bridge: S = k ln Ω with k_B as unit conversionPhase, Amplitude, Born Rule: U(1) phase from orientation, |A|² from self-relational structureDimensional Selection: d = 3 is the unique dimensionality supporting topologically stable knotted constraint loopsEach theorem depends only on the axiom and its predecessors in a strict dependency graph. The formalization uses graph-theoretic primitives (vertices, directed edges, partial orders, path spaces) to make every logical step explicit and independently verifiable.Three further theorems — matter as torus knot constraint loops, gravity as constraint-geometry curvature, and the fine structure constant α₀ = 3/(130π) ≈ 1/136.14 with zero free parameters — are stated informally as targets for subsequent formalization.The paper includes an honest gaps appendix identifying five points where the derivations are structural but not yet fully rigorous, marking precisely where subsequent work should focus.Developed in collaboration with Claude (Anthropic) and Gemini (Google) as derivation partners treating different processing architectures as distinct compression geometries of the same underlying graph.Keywords: registration graph; quantum gravity; foundations of physics; Born rule derivation; dimensional selection; knot theory; causal structure; graph theory; action quantum; fine structure constant; single-axiom framework; topological stability; Lorentzian signature; entropy; second lawAdditional Notes: Portions of this framework were developed in collaboration with AI systems (Claude by Anthropic, Gemini by Google) serving as derivation partners. The foundational axiom and directing intuitions are the author's.