# L17: EXCEPTIONAL JORDAN ALGEBRA — DIMENSION COUNTING

**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING

## Prompt

EXCEPTIONAL JORDAN ALGEBRA — DIMENSION COUNTING
Verify J3(Os) has dim=27: 3 diagonal reals + 3 off-diagonal octonions * 8 components * 2 (Re+Im split) -> 3+24=27. Confirm. Then show lambda_H = 8/63: 8 = off-diagonal dim contribution, 63 = dim(E6)-dim(F4)? Or 63 = 27*(7/3)? Derive the exact ratio from the algebra. This is the Higgs coupling derivation core. #SuperGrokTOE #J3dimension #HiggsCoupling