Established in scope
Split joint carrier admits a parallel representative of the whole native C12 clock
In the question: Common clock sectors, quartic geometry and operational reconstruction
Conditional mathematical closure for a GIVEN split connection,not selected from P1. Original marked chat is not automatically parallel on unchanged A_E;conjugator must transport connection and all marks or preserve them. An extra nonabelian family connection needs its own commutator,potential and closed domain their own invariance. Vertical bundle action identifies no base transport,time,CAR,state or EM response. Twelve counts marked torus points before further quotients,not physical sources. The2+2 action supplies no dictionary to original SU3 flavor on H1.
Read the exact result, assumptions and evidence
Result
For every natural m and given block U3xU2 connection,sigma0 from b=(1,1,1,0,0,0,0,1)/3 acts on W_m exactly as LambdaEven(diag(omega I3,I2)) tensor diag(omega,omega2,omega2,omega). It centralizes every transition and the entire induced connection. With central glue quarter kappa,c0=kappa sigma0 gives global parallel automorphisms with c0^9=kappa,c0^4=sigma0 and the complete native C12 character. The old complete torus Weyl theorem gives full inner VOA conjugacy including the common clock tuple. Exactly12 of243 thirds in the fixed toral centralizer match:two color orientations times six A3 vector weights.
Required assumptions
- Existing natural joint lift with given split connection
Assume a GIVEN unitary E=E3+E2 and GIVEN block U3xU2 connection A_E. Use only the natural iota_m with sum m=-2 completely classified on22September and their derived connection A_Wm=rho_LambdaEven(A_E)+M_m tr A_E. This does not select A_E from P1;an independent nonabelian family connection is not silently assumed.
- Fixed glue quarter and toral thirds centralizing the carrier split
Fix the standard E8 Cartan,five plus three chart,three color and two weak indices and four family axes. Kappa=exp(2pi i v0),v0=(1/2^5,0^3). Study every sigma=exp(2pi i b/3),b in E8/3E8,centralizing the given U3xU2,and c=kappa sigma. This is a specified toral class of vertical bundle automorphisms,not an assumption about physical time or original base transport.
- Full unitary E8 field conjugacy with transported marks
Start with the existing unitary E8 lattice VOA, original cocycle and actual chat,Jhat,sigmahat. Full inner unitary E8 automorphisms are allowed for this conjugacy comparison. Cartan, Gaussian V4, Y, P5 and other marks are transported rather than frozen. This category is explicitly larger than original sign lifts and implies neither a G31 splitting nor a preferred microscopic conjugator.
- Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
Original evidence
- JOINT-LIFT-NATIVE-CLOCK-CONNECTION.txt lines 1–36
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/JOINT-LIFT-NATIVE-CLOCK-CONNECTION.txt
edd2cdaea4c4debd337b4850d48da95de68e9367d780b9e3f0a96755588a45c8
- JOINT-LIFT-NATIVE-CLOCK-CONNECTION.txt lines 88–175
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/JOINT-LIFT-NATIVE-CLOCK-CONNECTION.txt
edd2cdaea4c4debd337b4850d48da95de68e9367d780b9e3f0a96755588a45c8
- check_joint_lift_native_clock.py lines 103–191
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/check_joint_lift_native_clock.py
eea4b77219cd9d3192a64e257e4e69cd57f68137cc1573ef4908bd8c3dbce3e1
- joint-lift-native-clock-results.json lines 4421–4576
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/joint-lift-native-clock-results.json
8d86f0b905ae317362205fab66c49e0e240bd8fff8af30eaed2269f32a7c8de0
- NATIVE-CLOCK-CONJUGACY.txt lines 32–159
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/e-series-source-reconstruction-20261024/NATIVE-CLOCK-CONJUGACY.txt
5f208d8d32fdc77e774ec77b5a320f378cfc9e2c8793d4d3d439983aae583a45
- PROOF.md lines 30–64
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/source-boundary-lift-selection-20260922/PROOF.md
2429cb31655e4d0711ba895825d740fe18f6a4e39677a987b61a5cd97c21addd
finding:global-split-joint-carrier-admits-parallel-native-c12-clock