computability_status
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.
claimThe 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 in Recognition Science
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.
scope and limits
- Does not derive or prove computability of π or φ inside Lean.
- Does not supply any algorithm or constructive witness.
- Does not link to J-cost, phi-ladder, or spatial dimension forcing.
formal statement (Lean)
159def computability_status : String := "Mathematical Fact (Computability)"
proof body
Definition body.
160
161/-! ## Category 3: Open Problems
162
163These axioms represent claims that are conjectured but not yet derived.
164They mark the research frontier of Recognition Science.
165-/
166
167/-- **Electron Mass Residue**: The electron mass follows the Z-structure
168with a shift that is not yet derived.
169
170**Status**: Open problem (T9 frontier).
171**Location**: IndisputableMonolith/Physics/ElectronMass.lean
172-/