Established in scope
Relative clock-Hom transport forces exactly the existing C12
In the question: Active mathematical program: marked seam monodromies and lattice lifts
Comparison of native and explicitly cover-induced Burau local systems. No independently geometric Gauss-Manin H1 family, forced carrier equality or extra line twist erasing carry. The earlier clock dictionary remains valid but is not a parallel peripheral dictionary.
Read the exact result, assumptions and evidence
Result
On the actual common Phi12 lattices, Hom_clock=Q[A12] has dimension4 and integral Hom=Z[zeta12], with integral isomorphisms a unit torsor. Native periphery is A12^9; the Burau periphery induced from the existing mu3 cover deck module is A12^4. Relative Hom transport is therefore H->A12^7 H, with exactly0 parallel clock intertwiners. Every nonzero relative orbit has order12. Exponent vector(7,7,7,7,8) has exactly the original winding kernel modulo12, so the existing C12 is the minimal trivialization.
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.
- Joint category of original compiler flags and cover actions
Retain original E8 lattice VOA products, J/sigma/c/Y, D5+A3 root factors and quartic/erasure diagram. Transitions transport all marks through actual lifts in the original sign extension; they are not fixed-J stabilizers. The Burau peripheral comparison uses the associated local system induced from the existing marked C3 cover and its retained deck module. No independent geometric Gauss-Manin identification, added line correction or selected E6 vertex.
Original evidence
- RELATIVE-TRANSPORT.txt lines 1–118
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/e-series-joint-source-20261023/RELATIVE-TRANSPORT.txt
cfe6ed1c5d80ceba8cb84ea73c162b9664cc134b9a8f08b2f5741be24e6606ed
finding:relative-native-burau-clock-hom-faithful12-transport