TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/seam-joint-conjugation-20261015/PROOF.txt
Original file SHA-256: bbea15f5ebb1dff698f1ecdfd8a18e724089c8fe9880dea684a5f9fd45cb1c8a
Inclusive original lines: 189-216
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
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000189 | 6. DO NOT REPLACE THE SOURCE BY A SPINOR-COEFFICIENT CAR MODEL
000190 | 
000191 | In the free-fermion realization of D5_1, the one-particle coefficient space is
000192 | the 10-real-dimensional vector representation (five complex fermions). The
000193 | 32-dimensional Ramond zero-mode space is Lambda C^5; its two chiral sectors
000194 | are S+ and S-, dimension 16 COMPLEX each. This is a space of occupation states
000195 | or spin-field sectors, not 16 elementary fermion species.
000196 | 
000197 | Making S+ the ordinary one-particle coefficient of L2 would instead give 16
000198 | complex chiral fermions, c=16, and Spin(10) current level 4. One Cartan H1 has
000199 | tr_(S+) H1^2=16/4=4; for the ten-real vector it has tr_V H1^2=2, and the real
000200 | fermion current coefficient includes 1/2, so level one is 1. The proposed
000201 | complex-spinor source coefficient is therefore four times that normalization.
000202 | The self-dual doubling S+ direct-sum S- does not halve this back to c=8: it has
000203 | 32 real fermionic degrees of freedom.
000204 | 
000205 | The documented c=8 source has 16 real fermions, organized as 10+6 under the
000206 | specified Spin(10)xSpin(6) embedding. The spin-field weights are 5/8 and 3/8;
000207 | their product has weight 1 and yields (16,4) and its conjugate among the 128
000208 | E8 spin currents. The other currents are 120 NS bilinears. This is the existing
000209 | v462 construction, not a new proof of its physical realization.
000210 | 
000211 | Likewise the Spin(10) center generator has eigenvalues +i,-i on S+,S-, but
000212 | acts as -I on the real vector 10. Substituting i times spinor chirality as the
000213 | one-particle holonomy changes the field representation. Original quarter domains
000214 | have no Dirac zero mode. Ramond ground-state Clifford generators cannot simply
000215 | be inserted as quarter-mode zero operators. Sector-changing spin fields need
000216 | their actual twist-module and cocycle action, not a dimension-based dictionary.