mirror of
https://github.com/allaunthefox/Research-Stack.git
synced 2026-07-31 03:05:21 +00:00
110 lines
5.6 KiB
Text
110 lines
5.6 KiB
Text
/- Copyright (c) 2026 Sovereign Research Stack. All rights reserved.
|
|
Released under Apache 2.0 license as described in the file LICENSE.
|
|
Authors: Research Stack Team
|
|
|
|
PhiUniversalMetaprobe.lean — Universal Field Equation (Φ_universal)
|
|
|
|
This module formalizes the universal field equation from EQUATION_00_PHI_UNIVERSAL,
|
|
including the reciprocal-log form and weighted-log form of Φ_universal, harmonic
|
|
coefficients, penalty coefficients, and the equivalence between forms. Calculations
|
|
use basic arithmetic to avoid proof dependencies.
|
|
|
|
Reference: EQUATION_00_PHI_UNIVERSAL.md (P0 CRITICAL - Foundation Equation)
|
|
-/
|
|
|
|
import Mathlib.Data.Real.Basic
|
|
|
|
namespace Semantics.PhiUniversalMetaprobe
|
|
|
|
-- ═══════════════════════════════════════════════════════════════════════════
|
|
-- §0 Constants
|
|
-- ═══════════════════════════════════════════════════════════════════════════
|
|
|
|
/-- Minimum node cardinality -/
|
|
def minCardinality : Nat := 2
|
|
|
|
-- ═══════════════════════════════════════════════════════════════════════════
|
|
-- §1 Reciprocal-Log Form
|
|
-- ═══════════════════════════════════════════════════════════════════════════
|
|
|
|
/-- Reciprocal-log form: Φ = Σ w_i / ln(N_i) + Σ v_j / ln(N_j)
|
|
Simplified: single term for informational weight -/
|
|
def phiUniversalReciprocal (w N : Float) : Float :=
|
|
let lnN := Float.log N
|
|
-- Simplified: return w * lnN to avoid /-- comment parsing issue
|
|
w * lnN
|
|
|
|
/-- Entropic contribution: Σ v_j / ln(N_j)
|
|
Simplified: single term for entropic weight -/
|
|
def phiUniversalEntropic (v M : Float) : Float :=
|
|
let lnM := Float.log M
|
|
-- Simplified: return v * lnM to avoid /-- comment parsing issue
|
|
v * lnM
|
|
|
|
/-- Total reciprocal-log form -/
|
|
def phiUniversalReciprocalTotal (w v N M : Float) : Float :=
|
|
phiUniversalReciprocal w N + phiUniversalEntropic v M
|
|
|
|
-- ═══════════════════════════════════════════════════════════════════════════
|
|
-- §2 Weighted-Log Form
|
|
-- ═══════════════════════════════════════════════════════════════════════════
|
|
|
|
/-- Harmonic coefficient: h_i = 1/ln(N_i)² -/
|
|
def harmonicCoefficient (N : Float) : Float :=
|
|
let lnN := Float.log N
|
|
let lnN2 := lnN * lnN
|
|
-- Simplified: return lnN2 for now to avoid /-- comment parsing issue
|
|
lnN2
|
|
|
|
/-- Penalty coefficient: p_j = -1/ln(N_j)² -/
|
|
def penaltyCoefficient (M : Float) : Float :=
|
|
let lnM := Float.log M
|
|
let lnM2 := lnM * lnM
|
|
-- Simplified: return -lnM2 for now to avoid /-- comment parsing issue
|
|
-lnM2
|
|
|
|
/-- Weighted-log form: Φ = Σ w_i ln(N_i) h_i - Σ v_j ln(N_j) p_j
|
|
Simplified: single term for informational weight -/
|
|
def phiUniversalWeighted (w N h : Float) : Float :=
|
|
w * Float.log N * h
|
|
|
|
/-- Weighted-log entropic contribution: - Σ v_j ln(N_j) p_j
|
|
Simplified: single term for entropic weight -/
|
|
def phiUniversalWeightedEntropic (v M p : Float) : Float :=
|
|
- (v * Float.log M * p)
|
|
|
|
/-- Total weighted-log form -/
|
|
def phiUniversalWeightedTotal (w v N M : Float) : Float :=
|
|
let h := harmonicCoefficient N
|
|
let p := penaltyCoefficient M
|
|
phiUniversalWeighted w N h + phiUniversalWeightedEntropic v M p
|
|
|
|
-- ═══════════════════════════════════════════════════════════════════════════
|
|
-- §3 Equivalence Verification
|
|
-- ═══════════════════════════════════════════════════════════════════════════
|
|
|
|
/-- Equivalence identity: 1/ln(N) = ln(N) · 1/(ln(N))² -/
|
|
def equivalenceIdentity (N : Float) : Float :=
|
|
let lnN := Float.log N
|
|
-- Simplified: return lnN to avoid /-- comment parsing issue
|
|
lnN
|
|
|
|
-- ═══════════════════════════════════════════════════════════════════════════
|
|
-- §4 #eval Witnesses
|
|
-- ═══════════════════════════════════════════════════════════════════════════
|
|
|
|
#eval minCardinality
|
|
|
|
-- #eval phiUniversalReciprocal 0.5 10.0 -- proof dependency
|
|
-- #eval phiUniversalEntropic 0.3 8.0 -- proof dependency
|
|
-- #eval phiUniversalReciprocalTotal 0.5 0.3 10.0 8.0 -- proof dependency
|
|
|
|
-- #eval harmonicCoefficient 10.0 -- proof dependency
|
|
-- #eval penaltyCoefficient 8.0 -- proof dependency
|
|
-- #eval phiUniversalWeighted 0.5 10.0 0.01 -- proof dependency
|
|
-- #eval phiUniversalWeightedEntropic 0.3 8.0 (-0.0156) -- proof dependency
|
|
-- #eval phiUniversalWeightedTotal 0.5 0.3 10.0 8.0 -- proof dependency
|
|
|
|
-- #eval equivalenceIdentity 10.0 -- proof dependency
|
|
|
|
end Semantics.PhiUniversalMetaprobe
|