{"slug":"formal-coherence-score-bounds","identifier":"formal-coherence-score-bounds","title":"Coherence Score Bounds","author":"Maclain Hunter","sourceSha256":"a2a5c4da4b0602feec70eb02bea120499d45d7c68b837311032d8274213b8349","sourceKind":"formal-theorem","recordedAt":null,"recordedAtMeaning":"Database registration time, not a claim of original handwritten authorship.","originalAuthoredAt":null,"formalizedAt":"2026-10-03T10:37:05.082Z","checkedAt":"2026-10-03T10:37:46.866Z","status":"partial","axiomFree":false,"axioms":["Classical.choice","propext","Quot.sound"],"theoremNames":["HunterAuthored.finite_fixed_point_clamp_bounds"],"units":[{"id":"finite_fixed_point_clamp_bounds","sourceStatement":"Formal statement: ∀array ∈ MCBExponent[]: exponentCoherence(array) ∈ [0, 1]","sourceOffset":0,"scope":"The source's clamp stage on every finite fixed-point/rational representation with a positive denominator: numerator lies between 0 and the denominator, hence the normalized score lies in [0,1]. Variance computation, nonfinite floating values and the current host binding are not certified by this clamp theorem.","status":"candidate","variables":[],"premises":[],"conclusion":"See the exact typed Lean theorem","leanStatement":"def clampNumerator (raw scale : Int) : Int := max 0 (min scale raw)\ntheorem finite_fixed_point_clamp_bounds (raw scale : Int) (positive : 0 < scale) :\n    0 ≤ clampNumerator raw scale ∧ clampNumerator raw scale ≤ scale :=\n  ⟨Int.le_max_left 0 (min scale raw),\n   Int.max_le.mpr ⟨Int.le_of_lt positive, Int.min_le_left scale raw⟩⟩\n#print axioms finite_fixed_point_clamp_bounds\n","kernelStatus":"verified","axioms":["Classical.choice","propext","Quot.sound"],"axiomFree":false,"reportedTheorem":"HunterAuthored.finite_fixed_point_clamp_bounds"}],"files":{"source.json":{"sha256":"33da00df0404d1f3ae4202e3acbd0b6dc21d607686a62838d3360dd2051cbdda","bytes":776},"Proof.lean":{"sha256":"0b962035624058aec72ee0213481a64a4856264a06e66a589632bf3a1ceff7ac","bytes":664},"lean-check.txt":{"sha256":"37e284552556b9fff807f4aef6d328447e527155d47b7ef3823c24c4c44a367e","bytes":164}},"boundary":"Lean establishes the listed formal statements and dependencies. 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