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gift-framework merged 1 commit into from
Dec 25, 2025
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Connect fano_lines cluster to main dependency graph #87

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37 changes: 37 additions & 0 deletions Lean/GIFT/Certificate.lean
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Expand Up @@ -733,6 +733,43 @@ abbrev v32_harmonic := GIFT.Foundations.Analysis.HarmonicForms.harmonic_forms_ce
/-- V3.2 G2 tensor form relations -/
abbrev v32_G2_tensor := GIFT.Foundations.Analysis.G2TensorForm.G2_certified

-- =============================================================================
-- G₂ CROSS PRODUCT CONNECTIONS (v3.1.11)
-- Connects fano_lines cluster to main dependency graph
-- =============================================================================

/-- Fano plane lines count (7 lines = 7 imaginaries of octonions) -/
abbrev fano_lines_count := GIFT.Foundations.G2CrossProduct.fano_lines_count

/-- Epsilon structure constants antisymmetry -/
abbrev epsilon_antisymm := GIFT.Foundations.G2CrossProduct.epsilon_antisymm

/-- G2 cross product bilinearity (proven) -/
abbrev G2_cross_bilinear := GIFT.Foundations.G2CrossProduct.G2_cross_bilinear

/-- G2 cross product antisymmetry (proven) -/
abbrev G2_cross_antisymm := GIFT.Foundations.G2CrossProduct.G2_cross_antisymm

/-- Lagrange identity for 7D cross product (proven) -/
abbrev G2_cross_norm := GIFT.Foundations.G2CrossProduct.G2_cross_norm

/-- Cross product structure matches octonion multiplication (proven) -/
abbrev cross_is_octonion_structure := GIFT.Foundations.G2CrossProduct.cross_is_octonion_structure

/-- G2 dimension from stabilizer: dim(GL7) - orbit = 49 - 35 = 14 -/
abbrev G2_dim_from_stabilizer := GIFT.Foundations.G2CrossProduct.G2_dim_from_stabilizer

/-- GIFT v3.1.11 G2 Cross Product Certificate
Connects Fano plane structure to main dependency graph -/
theorem gift_G2_cross_product_certificate :
-- Fano plane has 7 lines
(GIFT.Foundations.G2CrossProduct.fano_lines.length = 7) ∧
-- G2 dimension from stabilizer: 49 - 35 = 14
(49 - GIFT.Foundations.G2CrossProduct.orbit_phi0_dim = 14) ∧
-- G2 dimension from roots: 12 + 2 = 14
(12 + 2 = 14) := by
repeat (first | constructor | rfl)

/-- V3.2 Joyce analytic relations -/
abbrev v32_joyce_analytic := GIFT.Foundations.Analysis.JoyceAnalytic.joyce_analytic_certified

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