TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/PAULI-VERSUS-CODE-SOURCE-TARGET.txt
Original file SHA-256: 618a48566f2a1ad1be9b7f09aa1b2892f43b52644d9d8883db94fd6a75be699d
Inclusive original lines: 181-265
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.

000181 | centralizer are included, these nine frame representatives become one
000182 | conjugacy orbit.  Treating that orbit as gauge requires a separate assertion
000183 | about allowed equivalences.  Additional q versus p, P1, P2, anchor, state, or
000184 | readout markings were not imposed in the orbit statement.
000185 | 
000186 | 
000187 | 4. CENTRAL PHASE AND CURRENT SCOPE
000188 | 
000189 | The source selected even spin line supplies the projective lift alpha of Q,
000190 | with
000191 | 
000192 |     alpha^2=beta,       beta^2=-I,
000193 | 
000194 | and the marked local phase beta=+i.  On Jac(C)[2], beta is invisible because
000195 | it is central.  This is the same mathematical slot in which the native mu4
000196 | center is invisible on Pauli16.  The separate exact central lift census in
000197 | PAULI-SPIN-CENTRAL-LIFT.txt proves that a compatible realization beta maps to
000198 | native J=iI exists, and that alpha then lies in the nontrivial zeta8 G31 coset
000199 | rather than in G31.  Imposing the exact lifted relation
000200 | alpha sigma alpha^(-1)=sigma^(-1) selects a unique lift modulo alpha maps to
000201 | -alpha for every one of the nine Q actions.  The source spin result fixes +i
000202 | on the marked beta fiber, but does not yet prove the global scalar identity
000203 | beta=iI or the cubic spin linearization on a four dimensional theta module.
000204 | Nor does the local phase alone determine its image under
000205 | S0 -> Theta -> H0(2Theta): because the determinant of cohomology has Euler
000206 | characteristic zero, the central phase may cancel there.  The actual functor
000207 | must decide whether beta reaches J on H0(2Theta).
000208 | 
000209 | This closes the earlier central square obstruction as an existence question,
000210 | gives the index two coset a precise conditional source interpretation, and
000211 | constructs an order 24 common subgroup candidate generated by the cubic and
000212 | quarter lifts.  It still does not construct
000213 | the complete source theta Heisenberg extension and its four dimensional
000214 | Schrodinger module as the native N64 module.  The nine representatives form
000215 | one native centralizer conjugacy class, while the physical gauge status of
000216 | that conjugacy still depends on the other markings.  Those are the precise
000217 | remaining extension and marking steps.  No identification with V_code is
000218 | required or allowed.
000219 | 
000220 | 
000221 | 5. EXACT CHECK
000222 | 
000223 | Run
000224 | 
000225 |     python3 research-20261026-real-boundary/check_pauli_source_target.py
000226 |     python3 -OO research-20261026-real-boundary/check_pauli_source_target.py
000227 | 
000228 | Both runs pass.  The checker recomputes (3) through (13), enumerates all
000229 | thirty five two planes and all 720 elements of Sp(4,2), and returns the exact
000230 | counts 18, 9, and 2 above.
000231 | 
000232 | 
000233 | SOURCE ANCHORS
000234 | 
000235 | Atlas audit frame: revision 966491c8570e1f00b7db8adf, read only.
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