14 Summary and Status
14.1 Proof Status Overview
|
Module |
Theorems |
Status |
|
E8 Lattice |
15 |
|
|
G2 Cross Product |
10 |
B5, B6 pending |
|
Betti Numbers |
8 |
|
|
SO(16) Decomposition |
11 |
|
|
Fibonacci/Lucas |
20 |
|
|
Prime Atlas |
20 |
|
|
Heegner Numbers |
10 |
|
|
Monster Group |
15 |
|
|
McKay Correspondence |
12 |
|
|
Joyce Theorem |
10 |
|
|
Physical Relations |
50+ |
|
|
Total |
180+ |
– |
14.2 Key Results
The GIFT framework achieves:
0.087% mean deviation across 18 dimensionless predictions
180+ formally verified relations in Lean 4
Complete Fibonacci/Lucas embeddings (\(F_3\)–\(F_{12}\), \(L_0\)–\(L_9\))
100% prime coverage \({\lt} 200\) via three generators
All 9 Heegner numbers GIFT-expressible
Monster dimension \(196883 = 47 \times 59 \times 71\) from \(b_3\)
Joyce existence theorem for torsion-free \(G_2\) on \(K_7\)