feat(moonshine): add Monster dimension via Coxeter numbers formula #128
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Add the fundamental Monster-Coxeter relation:
dim(M₁) = (b₃ - h(G₂)) × (b₃ - h(E₇)) × (b₃ - h(E₈))
= 71 × 59 × 47 = 196883
This expresses the Monster group's smallest faithful representation
dimension purely in terms of the third Betti number b₃=77 and
Coxeter numbers of exceptional Lie algebras.
Changes:
- Core.lean: Add Coxeter numbers h_G2=6, h_E6=12, h_E7=18, h_E8=30
- MonsterCoxeter.lean: New module with main theorem and structural relations
- JInvariant.lean: Add j-coefficient ratio observations (c₂/c₁ ≈ 109)
- Moonshine.lean: Import and integrate MonsterCoxeter module
The formula is exact (no remainder), intrinsic (fundamental invariants),
and connects Monstrous Moonshine to exceptional Lie theory via G₂-geometry.
- MonsterCoxeter.lean: move imports before docstring (Lean 4 requirement) - JInvariant.lean: fix j_coeff_2_remainder calculation (109 × 196884 = 21460356, remainder = 33404, not 21296876)
- CHANGELOG.md: Add v3.3.11 release notes (Monster-Coxeter formula) - README.md: Bump version to 3.3.11, add MonsterCoxeter.lean - CLAUDE.md: Add tip #46 (import order before docstrings) - docs/USAGE.md: Add v3.3.11 section with Lean examples - gift_core/_version.py: Bump to 3.3.11 New features: - dim(M₁) = (b₃ - h(G₂)) × (b₃ - h(E₇)) × (b₃ - h(E₈)) = 196883 - Coxeter numbers h_G2, h_E6, h_E7, h_E8 in Core.lean - j-coefficient ratio observations (c₂/c₁ ≈ 109, c₃/c₂ ≈ 40)
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Add the fundamental Monster-Coxeter relation:
dim(M₁) = (b₃ - h(G₂)) × (b₃ - h(E₇)) × (b₃ - h(E₈))
= 71 × 59 × 47 = 196883
This expresses the Monster group's smallest faithful representation dimension purely in terms of the third Betti number b₃=77 and Coxeter numbers of exceptional Lie algebras.
Changes:
The formula is exact (no remainder), intrinsic (fundamental invariants), and connects Monstrous Moonshine to exceptional Lie theory via G₂-geometry.