TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/seam-collar-multifield-20261016/P1-INSERTION-TANGENT.txt
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Inclusive original lines: 134-187
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000134 | 5. Actual E8 insertion action: use the existing reader, no chosen Yukawa tensor
000135 | 
000136 | In the retained positive E8_1 lattice dictionary, use root charges p of internal
000137 | quarter grade1, target charges s of grade3, and grade2 roots r. There are64,
000138 | 64 and60 respectively. The grade2 roots are exactly +/-e_i +/-e_j with
000139 | i in the first five coordinates and j in the last three, the (10,6) module.
000140 | All are bosonic weight-one currents, including the spinor-labeled currents.
000141 | 
000142 | The already fixed cocycle and OPE give the actual zero-mode action on root
000143 | current states, when r+p is a root:
000144 |   J_r,0 |p> = epsilon(r,p) |r+p>.
000145 | The condition is r.p=-1. For these grades there are no r=-p Cartan exceptions.
000146 | Verify it through the original current_response, at positions(3,2,1):
000147 |   2 <V_r(3)V_p(2)V_-(r+p)(1)> / <V_(r+p)(2)V_-(r+p)(1)>
000148 |     = epsilon(r,p).
000149 | 
000150 | All3840 pairs were inspected:960 nonzero root actions,15 per incoming current,
000151 | and rank16 for each of the60 root actions. The exact raw-cocycle three-point
000152 | values are +1/2 for480 actions and -1/2 for480. They are basis-convention
000153 | amplitudes at these positions, NOT coupling constants or physical masses.
000154 | 
000155 | The last three coordinates of a grade1 current give one of four A3 fundamental
000156 | weights w_i. A target grade3 weight is compared with its conjugate -w_j. A
000157 | grade2 root changes one of the last three coordinates; it never sends w_i to
000158 | -w_i. The960 actions occupy12 ordered distinct-family channels,80 each.
000159 | The1024 same-family pairs of incoming grade1 spinor currents have no grade2
000160 | root that can neutralize their charge. This follows analytically since
000161 | 2w_i has three nonzero integer coordinates while the mediator family weight
000162 | has just one. It was checked for every pair against the root set, with direct
000163 | current-reader zero probes as regression. This is the antisymmetric A3 module
000164 | Lambda^2(4)=6; it does NOT by itself assert an antisymmetric physical Yukawa.
000165 | 
000166 | Thus this supplied current model has an explicit nontrivial sector action.
000167 | A linear insertion supported on these60 currents has60 complex root-basis
000168 | components before reality constraints; opposite-root adjoint relations reduce
000169 | this to60 real degrees of freedom for selfadjoint insertions. It has the above
000170 | actual action; P1 has not selected those coefficient functions
000171 | or equated this current action with a physical fermion/Higgs vertex. Composite,
000172 | twisted or dressed fields and changed states are not excluded by this result.
000173 | Known dressed-fermion constructions are retained with their own premises.
000174 | 
000175 | 6. Decisive conclusion and remaining task
000176 | 
000177 | The original displayed seed does not determine a Phi -> (D_+,B_Sigma,Q,C_Sigma)
000178 | family. The valid collar and modular constructions explicitly propagate its
000179 | first variation if it is supplied. Their invertibility cannot select it.
000180 | The full current reader supplies exact targets for a proposed charged map,
000181 | including sector transitions, but supplies no original choice of that map.
000182 | 
000183 | The next required source data are the ACTUAL charged physical field/readout
000184 | and the source-derived first variation dot C_Sigma with its embedding motion,
000185 | or equivalently the actual dot B/Phi insertion in a proven common chart.
000186 | Testing only uninserted spectra, normalized vacuum numbers or another KMS
000187 | inverse cannot answer this question. One must demonstrate the original