TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/puncture-metric-joint-completion-20261102/TOPOLOGY-METRIC-AND-MIXED-CURRENT-REVIEW.txt
Original file SHA-256: de71d13fdbcdcbc50ce6eac6d9ebd73d85e9573ca513935aad72f3b3c69d9be7
Inclusive original lines: 88-172
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
Conversation metadata and personal execution details are omitted where indicated.

000088 | 
000089 | The concrete source test imports the EXISTING
000090 |  tfpt_explorer.current_block_geometry._actual_current_source()
000091 | and uses its actual original Chevalley table, ordered cocycle and Affine.act
000092 | from verification/v498_celestial_wp5b_singular_vector.py. It imports the
000093 | original v983 OMEGA_F, permutes its four meridians, and transports them by
000094 | O3 into the source's actual doubled standard R8 coordinates. Every input
000095 | is literally present in the existing240-root source; there is no nearest
000096 | root search, fitted rotation, individual phase adjustment or new source.
000097 | 
000098 | The original compact convention is E_r^dagger=-E_-r, kappa_root=-1.
000099 | For every spinor and every ordered i!=j, the ACTUAL mode path
000100 | 
000101 |  E_vsi(0) E_vsj^dagger(-1)|Omega>
000102 | 
000103 | has exactly one term,
000104 | 
000105 |  c_sij E_(0,ei-ej)(-1)|Omega>,
000106 |  c_sij=-epsilon_original(v_si,-v_sj) in {+1,-1}.
000107 | 
000108 | All192=16*12 mixed cases pass. The real original sign distribution is
000109 | 96 plus and96 minus, not an asserted all-positive convention. Their target
000110 | set is literally the same12 family roots obtained from the original
000111 | source's w20[0,a]-w20[0,b]. There are no other current or oscillator terms.
000112 | 
000113 | All64=16*4 diagonal cases have mode-one/double-pole coefficient exactly+1;
000114 | the mode-zero/simple-pole term is the original Cartan current H(v_si).
000115 | Mixed mode-one/double poles vanish.
000116 | 
000117 | Hence the concise picture is source-correct within the given E8_1 type:
000118 | cancel a common carrier spinor and the surviving transition is precisely
000119 | the family root. It is an operator/OPE consequence of one joint source,
000120 | not a numerical coincidence between ranks or sector dimensions.
000121 | 
000122 | The mixed OPE was not an input to the metric uniqueness calculation. It is
000123 | a concrete held-out consequence at the source level, not an independent
000124 | empirical observation. It is also not claimed to be a previously unknown
000125 | general E8 branching theorem.
000126 | 
000127 | 5. ORIGINAL STATE, TWIST AND CLOCK ARE NOT DISCARDED
000128 | 
000129 | The existing ordered full-source formula explicitly gives
000130 |  Y_d(E_v,z)=z^(d.v)Y(E_v,z), with the original cocycle and charged carry.
000131 | For i!=j the leading simple-pole factor transforms as
000132 | 
000133 |  z^(d.v_i) w^(-d.v_j) E_(vi-vj)(w)/(z-w)
000134 |   = Y_d(E_(vi-vj),w)/(z-w) + regular terms.
000135 | 
000136 | Thus the tested leading root coefficient is unchanged in that supplied
000137 | twisted module. For i=j, the expansion of (z/w)^(d.vi) contributes
000138 | (d.vi)/w to the simple pole, precisely the transported Cartan shift;
000139 | the double-pole coefficient remains+1. No unshifted-state equivalence is
000140 | silently asserted. Original H_exc=8[L0+d.h0] and charged carry remain the
000141 | time/clock data of that source; C4 has not been identified with physical
000142 | time, the Coxeter30 clock or the native quartic J.
000143 | 
000144 | C4 permutation is trivial on the discriminant because all m_i have one
000145 | class. Translation by that class cycles the four sectors as an affine
000146 | shift/fusion rule. Translation is not a root-preserving linear isometry
000147 | and does not by itself supply a physical clock operator.
000148 | 
000149 | 6. ORIGINAL SOURCE AUDIT AND NOVELTY BOUNDARY
000150 | 
000151 | documents/tfpt_1_architecture_e8/sections/011-source.tex:32-45 already
000152 | calls puncture-DIFFERENCE cycles gamma_i-gamma_j the A3 roots. Thus that
000153 | distinction must not be advertised as wholly absent from TFPT.
000154 | 
000155 | The same passage writes Res(omega_i,gamma_j)=delta_ij and then infers I4.
000156 | For four classes with sum gamma_j=0 this is not literally a pairing on the
000157 | quotient: summing delta_ij over j gives1. Correct forms/residue vectors have
000158 | zero total residue, and the projected four-label Gram is I-J/4. The new
000159 | integral quotient and joint metric proof make that distinction exact without
000160 | depending on the old positive-metric inference.
000161 | 
000162 | verification/v983_simple_current_generator.py:9-44 already explicitly has
000163 | the same s,m0, their norms, order4 and52/64/60/64 sector census. These are
000164 | not new here. Newer value is the integral H1/H^1 identification and the
000165 | joint integrality/unimodularity proof that fixes all invariant metric scales,
000166 | followed by the literal current implementation test instead of an assertion
000167 | that abstract norms guarantee the physical source dictionary.
000168 | 
000169 | 7. FULL Z_adm: WHAT THIS CAN AND CANNOT MAKE CONCRETE NOW
000170 | 
000171 | The original full parent already exists formally:
000172 |  exp(W_k[J])=integral Dvarphi exp(-S_adm[varphi]-1/2 varphi R_k varphi+J.varphi).