TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/FULL-MARKED-G-FRAME-AND-ORIGINAL-OPEN-WORD.txt
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000001 | FULL ORIGINAL MARKED FAMILY FRAME AND THE ACTUAL HARDY OPEN WORD
000002 | 30 October2026. Exact continuation of the already reviewed G metric bridge.
000003 | No Atlas, original or pinned source changes.
000004 | 
000005 | 1. The common marked frame is fixed by the ORIGINAL Gbase
000006 | 
000007 | Reuse ORIGINAL-FUCHS-ALGEBRAIC-FRAME.txt, section4 and section5, and
000008 | FUCHS-FRAME-INDEPENDENT-TRACE-REVIEW.txt. With the ALREADY calibrated
000009 | rho principal, tau=i omega², t=2omega+1=i sqrt3, b=sqrt5/3,
000010 | 
000011 |  Gbase=[[0,0,-3tau t/sqrt10],
000012 |         [-3rho/(2b),t/(3b rho tau),0],
000013 |         [-3rho t/2,1/(rho tau),0]],
000014 |  H0=diag(10/27,5/(9sqrt3),1/(3sqrt3)).
000015 | 
000016 | The original principal branch is
000017 |  rho=(sqrt2/3^(3/4)) exp(-5pi i/12).
000018 | Direct substitution into these ACTUAL old expressions gives
000019 | 
000020 |  B0=H0^(1/2) Gbase=exp(7pi i/12) Bstar,
000021 |  Bstar=(1/sqrt2)[[0,0,-1+i],[1,i,0],[i,1,0]].              (1)
000022 | 
000023 | The global phase in(1) is retained from the old half-form/root frame.
000024 | It cancels in every operator identity below. Bstar is not fitted to a
000025 | spectral target, and does not select a new first axis.
000026 | 
000027 | 2. All marked generators, not only one matrix, are intertwined
000028 | 
000029 | Use the ACTUAL +1 based loop from the completed original P/Q calculation,
000030 | 
000031 |  Cs=[[0,0,1],[-1,0,0],[0,-1,0]],
000032 |  KQ=[[0,1,0],[-1,0,0],[0,0,1]].
000033 | 
000034 | The original row quarter is U=diag(1,i,-i). The explicit v117/v118
000035 | unitary monodromy is
000036 | 
000037 |  M0=[[0,-(1+i)/2,(1-i)/2],
000038 |      [-(1+i)/2,-i/2,-1/2],[(1-i)/2,-1/2,i/2]].
000039 | 
000040 | Exact rational-complex calculation proves SIX identities:
000041 | 
000042 |  Bstar Bstar*=I,
000043 |  Bstar Cs Bstar*=M0,
000044 |  Bstar KQ^-1 Bstar*=U,
000045 |  Bstar E02 Bstar*=M0 P0,
000046 |  Bstar E22 Bstar*=P0,
000047 |  Bstar(KQ^-k Cs KQ^k)Bstar*=U^k M0 U^-k, k=0,1,2,3,       (2)
000048 | 
000049 | where P0=diag(1,0,0). The four based meridians multiply to I and each has
000050 | order3. Thus(1)-(2) carry the ENTIRE actual four-puncture monodromy tuple,
000051 | its marked quarter and the fixed endpoint basis in one frame.
000052 | The inverse on KQ follows from G(Qy)=U G(y)KQ and the fixed original
000053 | point above z=0; it is not an arbitrary inversion of a clock.
000054 | 
000055 | The previous cyclic-frame F=(e0,M0 e0,M0²e0) intertwiner did correctly
000056 | intertwine Cs and M0. By itself it did not imply the simultaneous KQ/U
000057 | identity. Formula(1) is the stronger source-derived joint identification.
000058 | The earlier halfpath result is preserved, now with its full marked frame.
000059 | 
000060 | 3. The certified Hardy contribution is an ORIGINAL open word channel
000061 | 
000062 | HARDY-BMU-FIRST-NONZERO-ENTRY.txt gives kappa E02 P_gamma,+, kappa!=0,
000063 | in this actual G-column/induced-Hardy frame. Equations(1)-(2) yield
000064 | 
000065 |  Bstar(kappa E02)Bstar*=kappa M0 P0.                      (3)
000066 | 
000067 | Thus its incoming q2 defect line maps to the original distinguished axis
000068 | P0, and its outgoing q0 line maps to M0 P0 M0*. This is an actual
000069 | monodromy-word endpoint dictionary, not a resemblance of ranks or spectra.
000070 | For example, its two nonzero neutral family coefficients in the canonical
000071 | v117 frame are kappa[-(1+i)/2] at(1,0) and
000072 | kappa[(1-i)/2] at(2,0), using zero-based indices.
000073 | The original primitive exterior contraction therefore still reads +kappa,
000074 | with the already fixed KO convention -kappa, when ALL its endpoint and
000075 | carrier maps are transported. No free matrix-element reader was added.
000076 | 
000077 | P0 here is an identified marked FAMILY endpoint. It is not P_str, a
000078 | selected physical scalar channel, or a claim that P1 chose a new rank1
000079 | source. Nor is kappa P0 asserted equal to the positive whole K_str:
000080 | kappa is complex and this is one contribution, with other source terms
000081 | and the adjoint completion retained. Equation(3) is not by itself a
000082 | Z_adm variation or an evaluated entire branch Yukawa tensor.
000083 | 
000084 | 4. What the three existing source programs ALREADY do
000085 | 
000086 | Code graph first, then actual source read. These are not merely records
000087 | of one puncture eigenvalue list.
000088 | 
000089 | source_mass_transport.py:35-127,210-286 derives from the ENTIRE original
000090 | A(z) the native spin-triplet connection
000091 |  B=(tr A)/2 I-J^T A^T J,
000092 | its six-channel symmetric-pair connection L:X->BX+XB^T, and an exact
000093 | inverse recovering every entry of A from L. The finite functor is
000094 |  det(g)^(-1) Sym²(P^T wedge²(g)P). It is defined for arbitrary genuine
000095 | original path transports g, including compositions. Its numerical
000096 | integrate_pair_loop:132-207 uses one actual puncture loop to replay this
000097 | GENERAL connection identity. It explicitly does not select the initial
000098 | mass tensor, Higgs coefficient or physical 4D action.
000099 | 
000100 | source_flavor_correlator.py:67-128 supplies charged polygonal parallel
000101 | transport for the full original four-residue A, while its actual RHP
000102 | fermion kernel has the DIFFERENT order [Psi(w)^-1 Psi(z)]^T/(z-w).
000103 | Its connected neutral RR answer uses all four residues and is exactly
000104 | rational: the whole neutral field cancels its two monodromy legs.
000105 | No chosen path survives in that neutral answer. Its mark port is a
000106 | separately named v484/v485 regulated contact construction, not a direct
000107 | R insertion at a singular Fuchs puncture. Source:191-309 and the existing
000108 | function docstrings. The full common field response is retained.
000109 | 
000110 | source_neutrino_dictionary.py:48-119 gives exact native pair Gram,
000111 | complex-amplitude tomography, and the common original M0/U family frame.
000112 | The actual heavy tensor is supplied from the named existing YAML/CI
000113 | source and then encoded/read in that source; state and covariant mass
000114 | forms have explicitly different variance. The program contains both
000115 | marked generators and the genuine heavy source-mode block, but does not
000116 | derive the heavy coefficients by choosing a D4 spine. It cannot be
000117 | relabelled as a missing whole Y producer, nor its already solved OPE
000118 | and common marked transport forgotten.
000119 | 
000120 | 5. Original spine and source consumer, precise remaining comparison
000121 | 
000122 | Original EM3:329-352 FIXES a distinguished cycle basis and its canonical
000123 | family representation. EM4:180-197 names the D4-invariant geodesic spine
000124 | and Gamma_ij^min and defines Y_ij=<ei,Hol_G Kstr ej>. Its proof219-244
000125 | invokes their intrinsic/canonical status. The three examined programs
000126 | supply full A, actual path integration, its associated field/pair kernels
000127 | and the joint marked frame. They do not list the nine Gamma_ij^min
000128 | endpoint paths, execute the full prescribed Pstr, or pass the concrete
000129 | Hardy coefficient to that original Y/Zadm consumer.
000130 | 
000131 | This is the scoped result of these actual calls and original passages,
000132 | not a universal claim that no older sewing rule can do so. The stronger
000133 | positive reduction is now explicit: all source/frame/word ingredients of
000134 | (3) already lie in the ORIGINAL common marked family representation.
000135 | The remaining original comparison is the actual coefficient insertion
000136 | (or another original branch producer) at this identified open word, with
000137 | its fixed carrier and endpoint contraction. No new C6 matrix search,
000138 | polar metric, free first leg, state, time or Hardy=wholeY requirement
000139 | is needed to continue that original consumer calculation.
000140 | 
000141 | 6. Whole source and KO typing of the common frame change
000142 | 
000143 | Bstar is nonreal. Its neutral family equation(3) must not be promoted to
000144 | a whole96 map by freezing every old matrix after changing only Y. For
000145 | the actual chosen whole lift R, transport the SAME data together:
000146 |  D->R D R^-1, gamma->R gamma R^-1,
000147 |  J_F->R J_F R^-1 (antiunitary conjugation),
000148 |  X_H->R X_H R^-1 and likewise C_faces,G,states/reflection/time.
000149 | A charge-conjugate frame Bstar on particle slots and bar(Bstar) on
000150 | antiparticle slots retains canonical J_F; the already chosen chiral P2
000151 | dictionary instead puts its corresponding conjugate frame on the opposite
000152 | grading sector. These are typed conventions to be followed, not silently
000153 | interchanged. Neutral block(3) is on the specified gamma+ input; the
000154 | primitive Cliffordcreator and its other leg must follow the same lift.
000155 | Thus(1)-(3) preserve the established whole-source diagram by its existing
000156 | functor, without asserting a new physical P1 field/quarter assignment.
000157 | 
000158 | Durable six exact zero-difference checks:
000159 | workspace outputs/multi-model-source-search-20261029/
000160 | FULL-MARKED-G-FRAME-OPEN-WORD-CHECK.json. No original suite rerun.