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@gift-framework gift-framework commented Jan 6, 2026

New formalized relations from the GIFT v3.2 publication markdown files:

Weyl Triple Identity (S1 Section 2.3)

Three independent derivations of Weyl = 5:

  • (dim(G₂) + 1)/N_gen = 15/3 = 5
  • b₂/N_gen - p₂ = 21/3 - 2 = 5
  • dim(G₂) - rank(E₈) - 1 = 14 - 8 - 1 = 5

PSL(2,7) = 168 (S1 Section 0.4)

Fano plane symmetry group with triple derivation:

  • (b₃ + dim_G₂) + b₃ = 91 + 77 = 168
  • rank(E₈) × b₂ = 8 × 21 = 168
  • N_gen × fund(E7) = 3 × 56 = 168

TCS Building Blocks (S1 Section 8)

Now derives BOTH Betti numbers from specific building blocks:

  • M₁ (Quintic in CP⁴): b₂=11, b₃=40
  • M₂ (CI(2,2,2) in CP⁶): b₂=10, b₃=37
  • b₂ = 11 + 10 = 21 (derived!)
  • b₃ = 40 + 37 = 77 (derived!)

Certificate v3.4

  • New theorem: gift_v34_publications_certificate
  • Connects Weyl triple, PSL(2,7), TCS derivation
  • Total: 180+ certified relations

Note

Introduces complete TCS building block formalization and new structural identities, then wires them into the main certificate and docs.

  • Foundations/TCS: adds ACyl_CY3 with b2/b3; defines M1_quintic (11,40) and M2_CI (10,37); derives TCS_b2, TCS_b3; proves K7_b2=21, K7_b3=77, TCS_derives_both_betti, TCS_master_derivation; exports updated in Foundations.lean
  • Structural: adds weyl_triple_identity and PSL27_triple_derivation (multiple paths to Weyl=5 and |PSL(2,7)|=168)
  • Certificate: adds abbrevs for new results and gift_v34_publications_certificate; updates relation count (180+)
  • Docs: updates README.md, docs/USAGE.md; adds CHANGELOG.md entry; bumps gift_core/_version.py to 3.2.0

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claude added 4 commits January 6, 2026 14:49
New formalized relations from the GIFT v3.2 publication markdown files:

## Weyl Triple Identity (S1 Section 2.3)
Three independent derivations of Weyl = 5:
- (dim(G₂) + 1)/N_gen = 15/3 = 5
- b₂/N_gen - p₂ = 21/3 - 2 = 5
- dim(G₂) - rank(E₈) - 1 = 14 - 8 - 1 = 5

## PSL(2,7) = 168 (S1 Section 0.4)
Fano plane symmetry group with triple derivation:
- (b₃ + dim_G₂) + b₃ = 91 + 77 = 168
- rank(E₈) × b₂ = 8 × 21 = 168
- N_gen × fund(E7) = 3 × 56 = 168

## TCS Building Blocks (S1 Section 8)
Now derives BOTH Betti numbers from specific building blocks:
- M₁ (Quintic in CP⁴): b₂=11, b₃=40
- M₂ (CI(2,2,2) in CP⁶): b₂=10, b₃=37
- b₂ = 11 + 10 = 21 (derived!)
- b₃ = 40 + 37 = 77 (derived!)

## Certificate v3.4
- New theorem: gift_v34_publications_certificate
- Connects Weyl triple, PSL(2,7), TCS derivation
- Total: 180+ certified relations
- Remove non-existent TCS_combinatorial from exports
- Add new TCS v3.4 exports: M1_quintic, M2_CI, TCS_b3,
  K7_b3_derivation, TCS_derives_both_betti, TCS_master_derivation
- Update documentation: b₃ is now DERIVED (not input)
- Add combinatorial identities: C72, C73, b2_combinatorial, b3_decomposition

Fixes CI build errors:
- Unknown constant GIFT.Foundations.TCSConstruction.TCS_combinatorial
- Unknown identifier GIFT.Foundations.TCSConstruction.TCS_master_derivation
- Add `import GIFT.Foundations` to make exports accessible
- Change `GIFT.Foundations.TCSConstruction.TCS_master_derivation`
  to `GIFT.Foundations.TCS_master_derivation` (use re-exported name)

The export mechanism in Lean makes names available in the exporting
namespace, not at the original module path.
Release v3.2.0 highlights:

TCS Building Blocks (both Betti numbers now DERIVED):
- M₁ = Quintic in CP⁴ (b₂=11, b₃=40)
- M₂ = CI(2,2,2) in CP⁶ (b₂=10, b₃=37)
- b₂ = 11 + 10 = 21, b₃ = 40 + 37 = 77

Structural Identities:
- Weyl Triple Identity: 3 independent paths to Weyl = 5
- PSL(2,7) = 168: Fano plane symmetry (3 derivations)

Documentation:
- README: Updated K₇ section with TCS construction
- CHANGELOG: Complete v3.2.0 release notes
- docs/USAGE.md: TCS and structural identity examples
- Version bump: 3.1.12 → 3.2.0
@gift-framework gift-framework merged commit 65521e6 into main Jan 6, 2026
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3 participants