TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/joint-native-algebra-selection-20261016/CURRENT-RESPONSE-AND-DICTIONARY.md
Original file SHA-256: db9163de1017810818e104f651e531247378a4c8295580c8936cb19e594b4b73
Inclusive original lines: 79-109
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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000079 | The checker compares ALL 60 original event charts with the actual
000080 | quartic code action using Gaussian-integer compression. The comparison
000081 | uses the original oriented determinant-path lift h=lambda r,
000082 | lambda=exp(-i pi/4). Its source five-action is
000083 | 
000084 |     A5=lambda^4 rho5(r)=-rho5(r).
000085 | 
000086 | The opposite currents F then transform as
000087 | 
000088 |     A5 tensor bar(h)=lambda^3 rho5(r) tensor bar(r).
000089 | 
000090 | This is exactly the actual W20 intertwiner action of h^tensor3. Its
000091 | central square is +i. It is a statement about the coupled finite cover
000092 | <G31,zeta8 I> intersect SU4, not the unchanged order-two word r in G31.
000093 | All phases and both representations must be transported together.
000094 | 
000095 | This finite match is not a current-algebra tensor dictionary. If the
000096 | four charged source currents C_a are identified with the unchanged native
000097 | four-register, every source clock branch has C^tensor3=-I20. On F20 its
000098 | action is R5 tensor I4, which is nonscalar. With the actual isometry W,
000099 | 
000100 |     || -W-W(R5 tensor I4) ||_HS^2=48.
000101 | 
000102 | Already infinitesimally, every traceless Q(H) acts trivially on C_a and
000103 | ALL their products/OPEs, but as H tensor I4 on F. Thus this literal
000104 | charged-current dictionary fails. This does not identify the original
000105 | native Cartan four-space with C4; that different realization is tested next.
000106 | 
000107 | ## 4. Test the actual J-positive Cartan quartic realization
000108 | 
000109 | Use original Construction-A roots r of raw norm squared four and the