languageModelAlignmentFraction
Defines the language model alignment fraction as the rational number 7/8. Researchers auditing the three-substrate validation certificate cite this value when checking J-cost performance against cross-entropy baselines. The definition is a direct constant assignment that requires no lemmas or computation steps.
claimThe language model alignment fraction is the rational number $7/8$.
background
Recognition Science tests J-cost uniqueness across three substrates in the validation certificate: language models, photonic qubits, and magnetized plasma. All three share the fixed point at argument 1 where J-cost vanishes, descent along the gradient, and symmetry under inversion. The language-model substrate contributes the reported 7/8 alignment fraction for MLP-layer comparisons.
proof idea
Direct definition that assigns the constant 7/8 with no lemmas or tactics applied.
why it matters in Recognition Science
Supplies the numerical constant required by the ThreeSubstrateCert structure and its dependent theorems lm_above_threshold, lm_fraction_eq, and seven_eighths_from_F2_cube. The value matches the eight-tick octave relation (2^3 - 1)/2^3 from the forcing chain. The surrounding certificate remains at hypothesis grade.
scope and limits
- Does not derive the fraction from the J-cost functional equation.
- Does not prove the empirical 96.4% layer-alignment claim.
- Does not address photonic or plasma substrate results.
- Does not establish uniqueness of the 7/8 value across all possible models.
Lean usage
theorem lm_fraction_eq : languageModelAlignmentFraction = 7/8 := rflformal statement (Lean)
45def languageModelAlignmentFraction : ℚ := 7/8