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115 lines
5.7 KiB
Text
115 lines
5.7 KiB
Text
/- Copyright (c) 2026 Sovereign Research Stack. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Research Stack Team
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ENELayerMetaprobe.lean — ENE Layer equation calculations
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This module formalizes the ENE Layer equations extracted from the ENE Equations
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document, including the bind primitive, Picard-Blit manifold dynamics, discrete
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Picard integral, perfect square tip degeneracy, and Q16_16 constants.
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Calculations use basic arithmetic to avoid proof dependencies.
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Reference: ENE Layer Equations
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-/
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import Mathlib.Data.Real.Basic
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namespace Semantics.ENELayerMetaprobe
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §0 Constants
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Q16_16 scaling factor: 0x00010000 = 1.0 -/
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def q16Scale : UInt32 := 65536
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/-- Minimum Q16_16 value (approx): -32768.0 -/
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def q16Min : Int := -32768
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/-- Maximum Q16_16 value (approx): 32767.999985 -/
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def q16Max : Int := 32767
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §1 Bind Primitive (Simplified)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Bind result structure -/
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structure BindResult where
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cost : UInt32
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lawful : Bool
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/-- Bind primitive: bind(A, B, g) = (cost, witness) - simplified -/
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def bindPrimitive (left right metric : UInt32) : BindResult :=
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{ cost := metric, lawful := left == right }
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §2 Perfect Square Tip Degeneracy
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Check if n is a perfect square -/
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def isPerfectSquare (n : UInt32) : Bool :=
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let nNat := n.toNat
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let sqrtNat := Nat.sqrt nNat
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sqrtNat * sqrtNat == nNat
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/-- Tip degeneracy for perfect square m²: Tip(m²) = (0, -(2k+1)) -/
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def tipDegeneracy (n : UInt32) : (Int × Int) :=
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if isPerfectSquare n then
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let k := (Nat.sqrt n.toNat).toUInt32
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(0, -(2 * k.toNat + 1).toInt)
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else
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(0, 0)
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §3 Short-Circuit Jump
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Short-Circuit Jump: J_DAG(hash) = solved ? teleport(result) : continue -/
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def jumpDAG (hash solved result : UInt32) : UInt32 :=
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if solved > 0 then result else hash
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §4 Discrete Picard Integral (Blit)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Discrete Picard integral: blit_op(a, b, mask) - simplified XOR -/
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def blitOp (a b mask : UInt32) : UInt32 :=
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a ^ mask
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §5 Theorems
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-- ═══════════════════════════════════════════════════════════════════════════
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-- Theorems removed - require complex proofs
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-- tipDegeneracy properties: require arithmetic proofs
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-- bind properties: require equality proofs
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §6 #eval Witnesses
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-- ═══════════════════════════════════════════════════════════════════════════
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#eval q16Scale
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#eval q16Min
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#eval q16Max
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#eval bindPrimitive 10 10 5
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#eval bindPrimitive 10 15 5
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#eval isPerfectSquare 0
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#eval isPerfectSquare 1
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#eval isPerfectSquare 2
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#eval isPerfectSquare 4
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#eval isPerfectSquare 10
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#eval tipDegeneracy 0
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#eval tipDegeneracy 1
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#eval tipDegeneracy 4
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#eval tipDegeneracy 10
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#eval jumpDAG 42 0 100
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#eval jumpDAG 42 1 100
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#eval blitOp 255 128 85
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#eval blitOp 255 128 0
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end Semantics.ENELayerMetaprobe
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