Established in scope
Common covers and maximal actual integral clock intertwiner
In the question: Active mathematical program: marked seam monodromies and lattice lifts
Fixed deck orientation, actual matrices and saturated integral Phi12 sublattices. The displayed intertwiner is an explicit certificate, not a uniquely selected identification. Trace form and basis belong to the retained Burau lattice model, without an independent geometric cycle identification. Quartic5, exterior6, erasure20 and permutation characters remain distinct and are completely compared.
Read the exact result, assumptions and evidence
Result
C6 and C12 are the minimal marked common covers of C2/C3 and C4/C3, of genera7 and15. J<->Q, sigma<->deck and c=J sigma<->R=Q deck preserve c⁹=J and c⁴=sigma. The unique lift with this full marking is Qn Delta_n^4. Actual real8 has character Phi4² Phi12; the retained rational Burau rank6 model has Phi6 Phi12. Their canonical Phi12 kernels admit an explicit integral Z[C12] intertwiner also transporting J and sigma. Different complementary spectra obstruct full equality; retained alternating forms of types(1,3) and(1,2) obstruct any form-preserving unimodular intertwiner. Peripheral J is deck on C4 while compiler J=c⁹ rotates the base; no phase choice merges these roles.
Required assumptions
- Existing marked cyclic covers and Burau lattice model
On B=P1 minus(mu4 union infinity), Cn:un^n=x^4-1 for n=2,3,4 are the existing marked covers with positive finite exponent1. Fix the mu3 deck orientation omega. Use the original J and sigma with c=J sigma, actual reduced Burau matrices at omega and their retained Z[omega]^3 basis and invariant Hermitian form. Do not identify this integral model and trace form with independently constructed geometric cycles or their intersection form.
- Actual clock/complex-reflection subgroup and native quartic space
R=diag(-1,1,1,1) on Gaussian C4 is the complex reflection of root line(1+i)e0; G0=<J,R>=C4×C2. P5 is the existing five-dimensional symmetric quartic subspace in Sym4(V4), W6=exterior²V4. R is not a real codim1 E8 Weyl reflection; P5 is not the full fourth tensor power.
Original evidence
- COVERS.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/e-series-compiler-closure-20261023/COVERS.txt
cdd04f5f38819b60ddd8488eb1c3c316c6849829387205e78ec5e4bf767f80bf
- COVERS.txt lines 201–400
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/e-series-compiler-closure-20261023/COVERS.txt
cdd04f5f38819b60ddd8488eb1c3c316c6849829387205e78ec5e4bf767f80bf
- COVERS.txt lines 401–432
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/e-series-compiler-closure-20261023/COVERS.txt
cdd04f5f38819b60ddd8488eb1c3c316c6849829387205e78ec5e4bf767f80bf
finding:common-cover-clock-and-maximal-integral-phi12-intertwiner