TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/seam-joint-ward-state-20261014/PROOF.txt
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Inclusive original lines: 602-675
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000602 | 14. Intrinsic primitive source direction in the mixed (10,6) channel
000603 | 
000604 | The full Ls source lattice class yields more than projection norms alone.
000605 | Originally q=(1)^8 and lambda=q/2=(1/2)^8 belongs to Ls with norm2.
000606 | After ANY genuine E8 lattice isometry lambda remains a root. In a
000607 | clock-compatible canonical D5/D3 frame the inherited source projections
000608 | (4,4) become (1,1) for lambda. E8 half-spinor roots have projections
000609 | (5/4,3/4); pure D5 or D3 roots have(2,0) or(0,2). Consequently lambda
000610 | must be one of the60 mixed integer roots
000611 | 
000612 |   lambda=+/-e_a +/-e_b, 1<=a<=5, 6<=b<=8.
000613 | 
000614 | Their complete weight set is the D5 vector10 times A3 antisymmetric6.
000615 | Thus the original source class and common clock force
000616 | 
000617 |   q=2 lambda, lambda in (10,6),
000618 |   ||lambda_C||^2=||lambda_F||^2=1.
000619 | 
000620 | Neither the factor2 nor this primitive unit carrier direction is now
000621 | an additional q=k lambda_m or norm-minimization assumption. Other
000622 | integer q_C patterns of norm4 and trace2, apparently allowed by those
000623 | numbers alone, would give mixed half/integer coordinates for q/2 and
000624 | fail membership in E8. This restriction concerns the carrier component
000625 | of this SAME transported q, not an arbitrary independent U5 connection.
000626 | It also does not select a physical weak/color axis, a Chern-clutch
000627 | operator, a particular signed root, or the raw P1/P2 source.
000628 | 
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000631 | [OMITTED: non-scientific conversation or execution metadata]
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000633 | [OMITTED: non-scientific conversation or execution metadata]
000634 | 
000635 | This is a dictionary of WEIGHT LABELS in the three-dimensional Cartan
000636 | space, not an identification of six independent native mode amplitudes.
000637 | The matrix with columns h(B_ij) has rank3 and sends opposite weights to
000638 | opposite vectors. It therefore cannot be a complex-linear, CCR-preserving
000639 | isometry from the full native SU4 six-boson module into a three-component
000640 | field. For a chosen fundamental3 submodule, epsilon identifies Lambda2(3)
000641 | with its dual3, but those field coefficients are distinct objects from
000642 | the Cartan label vectors. Claiming that a native b_A carries the h-vertex
000643 | requires an actual source-selected 6-to-3 projector or intertwiner and
000644 | its compatibility with the operator algebra; none is supplied here.
000645 | 
000646 | Operator types and normalizations remain essential. In the stipulated
000647 | even E8 current net E_lambda is a BOSONIC conformal-weight1 current,
000648 | with source Cartan charge q.lambda=4 and inherited C clock grade2.
000649 | It is neither the neutral memory root p* nor the odd-clock-grade
000650 | (16,4) spinor-current selector. For the retained quarter time law,
000651 | 
000652 |   K(lambda)=3/4+alpha/2=7/8 or9/8,  H_source=8K=7 or9.
000653 | 
000654 | Conformal weight is not this time energy. A numerical scale match
000655 | does not supply an operator map or a native Delta value.
000656 | 
000657 | The separately given native model has CAR fermions in (16,4), bosons
000658 | in (10,6), the pair tensor W and conserved particle count N_f+2N_b.
000659 | The matching weights do not prove E_lambda=b_A, identify that count
000660 | with H_q, derive g or Delta, or establish locality/statistics. In
000661 | particular H_q gives E_lambda charge4; its normalization must not be
000662 | silently replaced by a boson-count charge2. Also the finite CAR pair
000663 | is in Lambda2(16 tensor4); a local4D same-chirality Yukawa scalar needs
000664 | the corresponding Lorentz-spin and internal exchange dictionary,
000665 | whose symmetric internal channels were separately audited in the
000666 | existing native-clock-flavor contract. A one-leg clock insertion does
000667 | not by itself derive this field identification.
000668 | 
000669 | Finally WW^dagger=8I60 is scalar: every endomorphism of that output
000670 | space commutes with it. A proposed source operator 'not commuting
000671 | with WW^dagger' cannot exist there. A meaningful test instead specifies
000672 | its actual input/output space, action on W or W^dagger W, and the
000673 | state/time response. The primitive charge-channel result supplies a
000674 | concrete common geometric weight and existing candidate interaction
000675 | slot. It does not deliver the requested full physical source/event law.