TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/e-series-compiler-closure-20261023/CUTS.txt
Original file SHA-256: e4eb9b53f944d411e887deb1783ff2d12e6a949e7550f9e6ebdd0cf77cd1ef21
Inclusive original lines: 250-276
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000250 | Choose one of the two chiral half-root blocks in (5.1), and write its literal
000251 | weight basis as
000252 | 
000253 |   B = {(s,t): s is one of the16 D5 half-spin weights,
000254 |               t is one of the four even-parity family sign triples}.
000255 | 
000256 | Thus B is the existing (16,4) root-current block and dim B=64. Let
000257 | 
000258 |   T={(1,1,1),(1,-1,-1),(-1,1,-1),(-1,-1,1)}.
000259 | 
000260 | The four D5-compatible E6 cuts are naturally indexed by t in T. On the root
000261 | current basis define
000262 | 
000263 |   P_t E_(s,u) = delta_(t,u) E_(s,u),       Q_t=I_B-P_t.          (8.1)
000264 | 
000265 | These are explicit coordinate projectors, not fitted embeddings. They satisfy
000266 | 
000267 |   rank P_t=16,       rank Q_t=48,
000268 |   P_t P_u=delta_(t,u)P_t,       sum_(t in T) P_t=I_B.           (8.2)
000269 | 
000270 | For the cut indexed by t, the E6 adjoint contains exactly P_t B. The
000271 | complement is
000272 | 
000273 |   Q_t B = 16 tensor 3,                                           (8.3)
000274 | 
000275 | where the A2 is the normal root subsystem of that same cut. W(D3)=S4
000276 | conjugates these projectors by