TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/graded_boundary_functor/old_source_embedding/REVIEW-CLAUDE-P2.txt
Original file SHA-256: 274bb0ff37dfd8362568de0d6851a1807449f2c2870efe0f0739922a51b4e9d5
Inclusive original lines: 49-73
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000049 |   U(u)=pi(u) J_F pi(u) J_F^-1,
000050 | with u=(lambda,q,m), |lambda|=1, q in SU(2), m in U(3).
000051 | This formula specifies the gauge action being compared. v252 supplies pi
000052 | and J but does not itself contain a separately implemented gauge_lift or Y
000053 | function; its numerical axiom checks alone are not this identification.
000054 | The following is a direct calculation with those supplied matrices.
000055 | 
000056 | For one generation det(pi(u))=(lambda det(m))^4; for three it is the twelfth
000057 | power. Thus the connected unimodular branch is lambda det(m)=1. No charge
000058 | fit is used: normalize its U(1) using the original P2 Y above and put
000059 |   lambda=exp(i t/2), m=exp(-i t/6) conjugate(U3), q in SU(2).
000060 | The physical color matrix U3 is the conjugate of the raw determinant-one
000061 | part of m because the particle color action comes from J_F pi(u) J_F^-1.
000062 | 
000063 | Multiplying the actual blocks gives
000064 |   particle Q_L: exp(+i t/6) (U3 tensor q),
000065 |   particle L_L: exp(-i t/2) q,
000066 |   antiparticle u_R^c: exp(-2i t/3) conjugate(U3),
000067 |   antiparticle d_R^c: exp(+i t/3) conjugate(U3),
000068 |   antiparticle e_R^c: exp(+i t),
000069 |   antiparticle nu_R^c: 1.
000070 | These are exactly the gamma_F=+1 slots. The dimensions are 6,2,3,3,1,1,
000071 | and the complete hypercharge multiset is
000072 |   (1/6)^6, (-1/2)^2, (-2/3)^3, (1/3)^3, (1)^1, (0)^1.
000073 | This verifies SU(3), SU(2) and hypercharge together, not just the multiset.