UniversalStructure
plain-language theorem explainer
A single structure type serves as the common carrier for physics theories, logic systems, and qualia spaces under a shared recognition relation and non-negative strain functional. Foundational physicists and logicians working on unified theories would cite it as the concrete realization of the one thing in the Reality Recognition Framework. The declaration is a direct structure definition encoding the five required fields with no additional proof obligations.
Claim. A universal structure consists of a state space $S$, a recognition predicate $R:S×S→Prop$, a witness that self-recognition exists, a strain map $σ:S→ℝ$, and the axiom that $σ$ is non-negative everywhere.
background
The module establishes that physics, logic, and experience are isomorphic structures inside the Reality Recognition Framework. The state space is fixed to the reals for simplicity; the recognition relation and strain functional stay abstract. Upstream results supply the discrete Galerkin state from fluid models, the active edge count per fundamental tick, and self-reference certificates from forcing chains. The local setting requires that one such structure admits embeddings of any physics theory, logic system, and qualia space while the strain remains non-negative.
proof idea
The declaration is a plain structure definition that introduces the five fields directly. No lemmas or tactics are applied; the type itself becomes the input to downstream completeness theorems.
why it matters
It supplies the carrier for the completeness theorems reality_recognition_framework_complete and reality_is_recognition, which close the RRF by showing every structure embeds into it. This realizes the final step of the forcing chain where a universal J-cost and phi-ladder scaling emerge from ledger closure. It leaves open the concrete identification of the strain functional with the Recognition Composition Law.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.