TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/OFFDIAGONAL-K-E8-PRODUCT-TEST.txt
Original file SHA-256: ae3e8ef16097fae858cd07c395af8e04d3741276f6ba149287e441199d563f13
Inclusive original lines: 201-251
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
Conversation metadata and personal execution details are omitted where indicated.

000201 | bracket still wedges two distinct family vectors.
000202 | 
000203 | Finally, the family calculation alone does not supply the D5 vector 10.
000204 | An actual realization of the remaining half of (10,6) needs both an
000205 | original O-valued field insertion and the source-specified symmetric
000206 | Spin(10) bilinear into 10, with the transported marking and domain. The
000207 | existence of the full local O bundle does not by itself provide that
000208 | operator or a nonzero global spin zero mode.
000209 | 
000210 | 
000211 | 6. PRECISE SCOPE AND NEXT ORIGINAL QUESTION
000212 | 
000213 | Established:
000214 | 
000215 |   * the p-to-q comparison is fixed by the old Kummer and spin lifts;
000216 |   * OffDiag End(F) and Lambda^2(O+F) are explicitly, isometrically and
000217 |     A4-equivariantly isomorphic in the two-torsion chart;
000218 |   * the old six off-diagonal arrows therefore carry the same restricted
000219 |     A4 bundle type as the family six.
000220 | 
000221 | Excluded for the present source inputs:
000222 | 
000223 |   * derivation of the full family six by bracketing the two triplet fields;
000224 |   * full SU4 covariance of (5), and even covariance under the tested
000225 |     original quarter generator on the symmetric triplet;
000226 |   * identification of the coefficient six alone with the physical
000227 |     E8 (10,6) Higgs/current field.
000228 | 
000229 | The smallest remaining positive source question is now sharply typed:
000230 | does an already original full-field insertion provide one S0 tensor O
000231 | leg together with a (16,4) carrier field and the actual Sym^2(16)->10
000232 | bracket? If such an insertion exists, its bracket with the known triplet
000233 | can populate O wedge F. It is not supplied by the closed zero-mode sector
000234 | and is not introduced here.
000235 | 
000236 | 
000237 | SOURCES READ
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