MetaRRF
plain-language theorem explainer
MetaRRF assembles a self-referential structure in which the recognition field is described by its own Lean code, with successful type-checking serving as the validity witness. Researchers studying formal self-reference in physical theories cite this as the closure point of the Recognition Science formalization. The definition is a direct structure construction from three sibling definitions with no additional lemmas or tactics.
Claim. A structure consisting of a subject description of the recognition field, a Lean code object holding source and module strings, and a type-check result witnessing successful compilation.
background
The module sets the local theoretical setting for self-reference as the deepest closure level of the framework. RRF is the local non-sealed recognition field interface given by the abbreviation (Fin 4 → ℝ) → ℝ. RRFDescription is the structure recording a core witness via the golden ratio φ, a theorem count, a nonempty model witness (ℝ → ℝ), and an explicit hypothesis count. LeanCode is the structure carrying the source string and module name, while TypeCheckResult is the inductive type with constructors success and failure(error). The module states that this Lean code is a recognition event, its compilation a proof, and its type-checking a measurement, making the formalization itself an octave of the RRF.
proof idea
The declaration is a structure definition that directly assembles three fields: subject drawn from RRFDescription, description drawn from LeanCode, and description_compiles drawn from TypeCheckResult. No lemmas are invoked and no tactics are used; the construction is a pure data-structure declaration.
why it matters
This definition supplies the Meta-RRF component required by SelfReferenceComplete, which further demands a DescriptiveFixedPoint and internal consistency. It realizes the module claim that the RRF formalization is itself an octave of the RRF, closing the self-reference loop at the eight-tick octave level. The construction touches the Gödel-like limit noted in the module by establishing internal consistency without claiming external consistency.
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