Established in scope
Existing C12 lift induces coherent E8 field action between two lattice objects
In the question: Common clock sectors, quartic geometry and operational reconstruction
Two-object mathematical field closure preserves every given c0 linearization. Executable strict witness does not replace original J marking. No full G31 extension splitting,256 physical theories,single common local VOA or P1 source/time identification. Test deliberately uses T² different from1 and [T,beta0] different from1.
Read the exact result, assumptions and evidence
Result
For every given geometric faithful c0 and every unitary isometry lift T:V0->V1 set beta1=T beta0 T^-1,sigma1=T sigma0^-1 T^-1,alpha01=T,alpha10=beta0 T^-1. Then alpha²=diag(beta0,beta1),alpha^8=1 and alpha sigma alpha^-1=sigma^-1 hold on all lattice charges and finite-energy vertex fields. Both objects carry faithful C12 clocks. Standard cocycle depends only on Lambda/2Lambda; all256 classes and65536 pairs exhaust cocycle checks,while matrix relations separately hold exactly over Z. Character-gauge changes of T give equivalent groupoids. Optional strict C4×S3 census yields256 raw sign sections,but none with the zero-character J lift.
Required assumptions
- 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.
- Completed theta frame with explicit primitive Gaussian integral normalization
Start with completed Wq=H0(Jac(C),O(2Theta)) tensor Nq^-1, beta=i, fixed Schrodinger frame e_x for x in F2², a unit norm-line trivialization and actual alpha=zeta8 V. The same-spin representative also retains odd B_O^-1 and its alpha sign. For affine d planes A and stabilizer phases phi in mu4 explicitly choose r(A,phi)=(1+i)^(2-d) sum(phi(x)e_x)/sqrt2. Gaussian integer numerators,norm squared2 and the central i orbit are the arithmetic construction. This is not deduced from complex dimensions and does not assert P1 selection,physical length normalization or uniqueness among all Heisenberg-stable lattices.
- Two theta lattice VOAs with a given faithful geometric C12 lift
Lattices Lambda0 and Lambda1=zeta8 Lambda0 come from the explicitly normalized theta construction. Use their unitary lattice VOAs with standard cocycle. On object0 the existing faithful C12 lift c0 with geometric action i sigma is given; beta0=c0^9 lifts i and sigma0=c0^4 lifts sigma. T is any standard-cocycle VOA isomorphism lifting actual lattice isometry alpha01=zeta8 V. Branch-one marks are transported. No T²=1,[T,beta0]=1,full G31 splitting,common local VOA or physical P1 identification is assumed.
Original evidence
- TWO-BRANCH-VERTEX-GROUPOID.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/theta_lattice_closure_20261027/fields/TWO-BRANCH-VERTEX-GROUPOID.txt
fe9459880a659895813853671b5959855d32826cc52c244ca167ff2453b6f8dc
- TWO-BRANCH-VERTEX-GROUPOID.txt lines 201–297
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/theta_lattice_closure_20261027/fields/TWO-BRANCH-VERTEX-GROUPOID.txt
fe9459880a659895813853671b5959855d32826cc52c244ca167ff2453b6f8dc
- check_small_vertex_lifts.py lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/theta_lattice_closure_20261027/fields/check_small_vertex_lifts.py
5493a6b479c554897eac88a5eea987f1f31f9c462c143f8d4607ef999da0ac42
- check_small_vertex_lifts.py lines 201–294
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/theta_lattice_closure_20261027/fields/check_small_vertex_lifts.py
5493a6b479c554897eac88a5eea987f1f31f9c462c143f8d4607ef999da0ac42
- vertex-lifts.json lines 1–64
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/theta_lattice_closure_20261027/fields/vertex-lifts.json
51a243b5a2674dc08e67edd279e2b2c262482d536a97d4112b8f4a997348dc31
- COHERENT-TWO-LATTICE-FIELD-REVIEW.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/theta_lattice_closure_20261027/review/COHERENT-TWO-LATTICE-FIELD-REVIEW.txt
46c897da691c6f1730cc71a8d243788289328fbeccd61812247919a8acf9c2b6
- COHERENT-TWO-LATTICE-FIELD-REVIEW.txt lines 201–216
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/theta_lattice_closure_20261027/review/COHERENT-TWO-LATTICE-FIELD-REVIEW.txt
46c897da691c6f1730cc71a8d243788289328fbeccd61812247919a8acf9c2b6
finding:existing-c12-lift-induces-coherent-two-object-e8-vertex-groupoid