TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/joint-native-algebra-selection-20261016/FULL-SOURCE-HULL-AND-QUARTIC-OPE.txt
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Inclusive original lines: 267-296
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000267 | 9. Complete invariant current returns and the recovered canonical stress
000268 | 
000269 | In the dual original root basis, E_alpha(-1)E_-alpha vacuum multiplied
000270 | by epsilon(alpha,-alpha)^(-1) is
000271 |  (1/2)alpha(-1)²+(1/2)alpha(-2).
000272 | The complete240-root sum cancels the linear terms. Its root moment is
000273 |  sum_alpha alpha tensor alpha=60I8, so h_dual=30.
000274 | The resulting fixed Sugawara field is
000275 |  T_Sug=(1/62)sum_(A=1)^248:J^A J_A:
000276 |       =(31/62)sum_(a=1)^8:h_a²:
000277 |       =(1/2)sum_a:h_a²:=T_E8, c=248/31=8.
000278 | It is the SAME field obtained from r3 in the quartic OPE, without
000279 | assuming an independent geometric field. The grade2 singlet is unique;
000280 | requiring the source current Ward law fixes its coefficient.
000281 | 
000282 | Define T_n=sum_A J^A(-n)J_A(n) in a real Hermitian orthonormal basis.
000283 | The full actual source calculations on C5, including every charged
000284 | intermediate and the entire neutral final vector, give
000285 |  n:                       0       1        2       3
000286 |  P T_n P:               134I    103/2 I    5I     1/2 I
000287 |  (Q T_n P)*(Q T_n P):   100I    225/4 I    9I     1/4 I.
000288 | Modes n>=4 annihilate C5; negative-mode endpoint factors obey
000289 | kappa_-m=kappa_m+248m by the exact current CCR.
000290 | Most importantly, the full source vectors satisfy
000291 |  (T0/2+T1+T2+T3) f_i=124 f_i.
000292 | Their exterior terms cancel in this invariant Ward combination; this
000293 | is NOT inferred from compression alone. It equals31 L0 at weight4.
000294 | Individual returns retain exterior feedback even though their endpoint
000295 | Grams are scalar. This supplies an explicit complete symmetric reference
000296 | process, not a new physical event law or arbitrary root reweighting.