languageModelAlignmentFraction
plain-language theorem explainer
The definition assigns the language model alignment fraction the rational value 7/8. Researchers validating J-cost predictions across substrates cite this constant when checking thresholds or equating it to the cube-derived ratio. The declaration is introduced by direct assignment with no computation or lemmas.
Claim. The language model alignment fraction is the rational number $7/8$.
background
The ThreeSubstrateValidationCert module records an empirical certificate for J-cost across language models, photonic qubits, and magnetized plasma. Language models are reported to show J-cost superiority in 96.4% of MLP layers, expressed here as the alignment fraction 7/8. The module imports Cost and MultiChannelJCost; the local setting treats the certificate as hypothesis-grade, with J-cost uniqueness as the shared Lean content.
proof idea
This is a direct definition that assigns the literal rational 7/8. No lemmas are applied and the body contains no tactics.
why it matters
The definition supplies the alignment value required by ThreeSubstrateCert and by the theorems lm_fraction_eq, lm_above_threshold, and seven_eighths_from_F2_cube. It links the language-model observation to the eight-tick octave via the identity 7/8 = (2^3 - 1)/2^3, supporting T7 in the forcing chain. The module states that J-cost uniqueness underlies the three-substrate predictions.
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