TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/joint-native-algebra-selection-20261016/ORIGINAL-ORDERED-CURRENT-KERNEL-AND-SEAM-GRADING.txt
Original file SHA-256: 62a9eeb4519b59d4514445f9d4dd5d2059e29179956a4c97ec94b7bae9ae3094
Inclusive original lines: 166-180
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000166 | CAR phases are [-1,i,1,-i]^2, or u_r=-i^(-r). Therefore EXACTLY
000167 |  t_v J_m t_v^-1=i^m J_m,
000168 |  t_v Lcal_m^alpha t_v^-1=i^m Lcal_m^alpha.
000169 | Products carry the total Fourier degree, with all OPE/contact terms;
000170 | the central terms have total degree0, so the character respects them.
000171 | 
000172 | The known global identity is retained on EVERY charge sector:
000173 |  t_v=exp(-4pi iK_alpha) exp(i pi(1+alpha/2)Q)=(-1)^Q W_alpha^-1,
000174 |  W_alpha=exp(4pi iK_alpha)exp(-i pi alpha Q/2).
000175 | Indeed, with original residue charges p and oscillator level N,
000176 |  t.p-[-2K_alpha+(1/2+alpha/4)Q]
000177 |    =2N+sum_k p_k^2-Q+sum_(k=4..7)p_k is integer.
000178 | Odd CAR parity must NOT be deleted on the full CAR; it disappears only on
000179 | the even source. The internal order4 character is still not the original
000180 | charged quarter holonomy. Its time/charge relation does not physically