computability_status
plain-language theorem explainer
This definition labels the computability of π and φ as a 'Mathematical Fact (Computability)' within the axiom registry. Researchers formalizing Recognition Science cite it when separating standard mathematical results from physical postulates and open problems. The implementation is a direct string constant assignment with no computation or lemmas applied.
Claim. The epistemic status of the claim that π and φ are computable real numbers is the string ``Mathematical Fact (Computability)''.
background
The module maintains an axiom registry that partitions claims into physical postulates (foundational to the theory), well-known mathematical facts (accepted pragmatically), and open problems (T9 frontier). Computability of π and φ is placed in the second category per the summary table, which lists pi_computable and phi_computable with reference to standard computability theory and location in ConstructiveNote.lean. Upstream module dependencies include ledger structures and forcing derivations, but this entry stands as an isolated classification label.
proof idea
One-line definition that directly assigns the string constant ``Mathematical Fact (Computability)''.
why it matters
It populates the registry table entry for the computability claim, separating it from open problems such as electron mass residue. The declaration supports the overall epistemic classification used across the Recognition Science formalization and references the well-known status of π and φ without advancing the T0-T8 chain or Recognition Composition Law.
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