TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-HIGGS-FIBER-PROOF.txt
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000001 | ORIGINAL HIGGS FIBER: WHOLE96 ORBIT, DETERMINANT JET AND RESIDUE MATCH
000002 | 31 October2026. Results R028/R029. Established scoped algebra; source-match
000003 | failure of specific printed formulas. No physical completion or ledger change.
000004 | 
000005 | 1. Question and original data
000006 | Continue F1.M6 at its actual source consumer. Keep the original four supplied
000007 | 3x3 matrices Yu,Yd,Ye,Ynu and symmetric MR, weak quaternion q(H), whole96
000008 | particle/antiparticle and chirality slots, and the original source/state maps.
000009 | Do not optimize Yukawas, change primitive profile, add Gamma_H to a master,
000010 | or identify a bare Hessian with the full connected H covariance.
000011 | Original v252 full_D and rep supply the actual coefficients. R026's288 images
000012 | already identify the complete real Higgs one-form. That result is reused.
000013 | The new question is whether all constant H directions require a search, and
000014 | whether the displayed geometric producer actually matches the displayed H
000015 | potential before it is used as the joint H integration weight.
000016 | 
000017 | 2. Entire constant H orbit on the actual original coefficient
000018 | Use real coordinates H=(x1+i x2,x3+i x4), u=sum x_a^2 and r=sqrt(u).
000019 | There is no1/sqrt2 factor in these coordinates. The original quaternion is
000020 |  q(H)=[[bar h2,h1],[-bar h1,h2]].
000021 | It obeys q* q=u I2 and det q=u. For r>0, U=q/r lies in SU2.
000022 | Let V(U) act by U on EACH original weak LEFT doublet, identity on all
000023 | right singlets, and complex-conjugate actions on the antiparticle slots.
000024 | Then, with DY=full_D(Yu,Yd,Ye,Ynu,0), DM=full_D(0,0,0,0,MR),
000025 |  Phi(H)=V(U) [r DY+DM] V(U)*.                          (1)
000026 | Proof is the actual LR block multiplication U(r diag(Yup,Ydown)) and its
000027 | adjoint. No commutation with Yup or Ydown is used. DM is between right
000028 | neutrino singlets and remains unchanged. V commutes with original grading
000029 | and JF. At H=0, Phi=DM, so no singular polar coordinate is needed.
000030 | All72 real Y coefficient directions and12 real symmetric MR directions
000031 | are checked against the unmodified original builder at an integral q with
000032 | r=5 using W=rV: W*W=25I and W Phi_rad W*=25 Phi(H), exact integer arithmetic.
000033 | The generic q identities and block proof establish ALL H and ALL matrices;
000034 | one quaternion replay is a constructor check, not the generic proof.
000035 | This is a weak LEFT gauge rotation, not a custodial right symmetry. Unequal
000036 | Yu,Yd or Ynu,Ye do not destroy (1). A contrary Gemini proposal was rejected.
000037 | 
000038 | 3. Full determinant reduction, with Majorana and all multiplicities
000039 | For z>0 put P(z,u)=det96(zI+Phi(H)^2). In the original neutrino chiral
000040 | ordering plus=(nuL,antiNuR),minus=(nuR,antiNuL), the whole12 block is
000041 |  N=[[0,B],[B*,0]], B=[[r Ynu,0],[MR*,r Ynu^T]], B a6x6 matrix.              (2)
000042 | Here * is adjoint; bar is entrywise conjugation. Consequently
000043 |  P=det3(z+u Yu*Yu)^12 det3(z+u Yd*Yd)^12