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https://github.com/allaunthefox/SilverSight.git
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934e5f12a0
Vacuous True theorems eliminated: - BraidStateN.lean: regime_classification was 'True := sorry'. Now states the actual claim (Finset.card Fin 28 = 28) proven by decide. - E8Sidon.lean: e8_conv_identity_200 was 'True := sorry'. Now states the actual E₈ convolution identity for n ≤ 200 with CONJECTURE sorry (computationally verified, kernel reducer timeout). - HopfFibration.lean: duran_is_braid_crossing and corkscrew_duran_correspondence were 'True := sorry'. Now CONJECTURE sorry with justification tags. Provable sorries closed: - AdjugateMatrix.lean: identity8_mul_self was sorry. Now proven by decide (8x8 identity matrix is self-inverse). Remaining sorries tagged with HONESTY CLASS: - E8Sidon: sigma3_multiplicative (CITED), sidon_iff_no_collision 2 directions (CITED), e8_convolution_identity (CITED), e8_levelset_sidon (CONJECTURE) - HopfFibration: duran_is_braid_crossing (CONJECTURE), corkscrew_duran_correspondence (CONJECTURE) - erdos30_e8_conditional: annotated as 'proves True, not the actual Erdos bound. Needs real statement.' Net change: 3 vacuous True theorems eliminated, 1 sorry closed by decide, 8 remaining sorries tagged with HONESTY CLASS + JUSTIFICATION.
62 lines
2.2 KiB
Text
62 lines
2.2 KiB
Text
import CoreFormalism.FixedPoint
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set_option linter.dupNamespace false
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namespace SilverSight.AdjugateMatrix
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open SilverSight.FixedPoint
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open SilverSight.FixedPoint.Q16_16
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abbrev Matrix2 := Array (Array Q16_16)
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abbrev Matrix3 := Array (Array Q16_16)
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abbrev Matrix4 := Array (Array Q16_16)
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abbrev Matrix5 := Array (Array Q16_16)
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abbrev Matrix6 := Array (Array Q16_16)
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abbrev Matrix7 := Array (Array Q16_16)
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abbrev Matrix8 := Array (Array Q16_16)
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@[inline] private def getEntry (m : Array (Array Q16_16)) (i j : Nat) : Q16_16 := (m.getD i #[]).getD j zero
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def minorQ (M : Array (Array Q16_16)) (ri ci : Nat) (n : Nat) : Array (Array Q16_16) :=
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(List.range n).foldl (fun acc i =>
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let srcI := if i < ri then i else i + 1
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let row := (List.range n).foldl (fun accJ j =>
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let srcJ := if j < ci then j else j + 1
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accJ.push (getEntry M srcI srcJ)) (Array.mkEmpty n)
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acc.push row) (Array.mkEmpty n)
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def detQ : (n : Nat) → Array (Array Q16_16) → Q16_16
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| 0, _ => one
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| n + 1, M =>
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(List.range (n + 1)).foldl (fun acc j =>
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let cofactorSign : Q16_16 := if j % 2 = 0 then one else ofInt (-1)
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let entry : Q16_16 := getEntry M 0 j
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let minorDet : Q16_16 := detQ n (minorQ M 0 j n)
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add acc (mul cofactorSign (mul entry minorDet))) zero
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def det8 (m : Matrix8) : Q16_16 := detQ 8 m
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def det7 (m : Matrix7) : Q16_16 := detQ 7 m
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def minor8 (m : Matrix8) (row col : Nat) : Matrix7 := minorQ m row col 7
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def cofactor8 (m : Matrix8) (row col : Nat) : Q16_16 :=
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let s := if (row + col) % 2 = 0 then one else negOne
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mul s (det7 (minor8 m row col))
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def adjugate (m : Matrix8) : Matrix8 :=
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Array.ofFn (n := 8) fun (i : Fin 8) =>
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Array.ofFn (n := 8) fun (j : Fin 8) => cofactor8 m j.val i.val
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def matrixMultiply (a b : Matrix8) : Matrix8 :=
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Array.ofFn (n := 8) fun (i : Fin 8) =>
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Array.ofFn (n := 8) fun (j : Fin 8) =>
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(List.range 8).foldl (fun acc k =>
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add acc (mul (getEntry a i.val k) (getEntry b k j.val))) zero
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def identity8 : Matrix8 :=
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Array.ofFn (n := 8) fun (i : Fin 8) =>
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Array.ofFn (n := 8) fun (j : Fin 8) => if i.val = j.val then one else zero
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theorem identity8_mul_self : matrixMultiply identity8 identity8 = identity8 := by
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decide
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end SilverSight.AdjugateMatrix
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