AllConstantsDerived
plain-language theorem explainer
AllConstantsDerived defines the proposition that there exists a real number equal to the golden ratio phi. Researchers building zero-parameter derivations in Recognition Science cite it as the capstone linking mass-to-light results to constant unification. The definition is a direct existential statement with no reduction steps or lemmas applied.
Claim. There exists a real number $c$ such that $c = φ$, where $φ$ is the golden ratio.
background
The MassToLight module derives the stellar mass-to-light ratio via three strategies: recognition cost minimization in stellar assembly yielding M/L = φ^n, nuclear densities and photon fluxes on discrete φ-tiers from NucleosynthesisTiers.of, and geometric observability limits forcing M/L onto the φ-ladder. All strategies converge on M/L = φ ≈ 1.618 in solar units, with valid range {1, 1.618, 2.618, 4.236}. This module setting supports the claim of true zero-parameter status once M/L is internalized, as stated in the module doc: 'With M/L derived, Recognition Science achieves TRUE ZERO-PARAMETER STATUS' for c, ℏ, G, and α⁻¹.
proof idea
The declaration is a direct definition of an existential proposition. It functions as a one-line wrapper asserting equality to phi with no lemmas, tactics, or reductions from upstream results.
why it matters
It is referenced by H_RSZeroParameterStatus to close the zero-parameter status hypothesis after the M/L derivation. The module doc positions it as completing the chain where all constants derive from the meta-principle with no external inputs. It touches the open scaffolding task of a master certificate importing constant derivations across modules, aligning with framework goals of deriving physics from the single functional equation without free parameters.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.