Established in scope
The actual clock doily reconstructs the original quartic five
In the question: Common clock sectors, quartic geometry and operational reconstruction
Given Construction A and J; no P2/D5 or physical measurement identification from dimensions.
Read the exact result, assumptions and evidence
Result
The actual ovoid module ker(B^T) of E8/(1−J)E8 is marked-isomorphic to original quartic H5: detT=−96 and N_rT=16TD_r for all60 reflections. Spread and both twists have Hom0. Form diag(1,3,3,3,6), P5 and six rank1 effects follow.
Required assumptions
- Existing even E8 lattice, Gaussian J and sign lifts
Given existing even unimodular E8 with actual J(x0,x1,...)=(-x1,x0,...) and J²=-I, and the original ordered sign lattice cocycle. Sign automorphisms have kernel Hom(L,F2). Retain original integral ordered basis and generator phases; no enlargement to U1 characters except explicitly defined scalar pushouts.
- 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
- DOILY-QUARTIC.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/atlas-defect-synthesis-20261024/DOILY-QUARTIC.txt
666355194ef46ca3e8768dcb05a6c4158c7f3f9d2a5f64aa10e5eaa94dc6c853
- DOILY-QUARTIC.txt lines 201–212
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/atlas-defect-synthesis-20261024/DOILY-QUARTIC.txt
666355194ef46ca3e8768dcb05a6c4158c7f3f9d2a5f64aa10e5eaa94dc6c853
- doily_quartic_bridge.py lines 438–510
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/atlas-defect-synthesis-20261024/doily_quartic_bridge.py
b99af5f633f10e779454a3f8957b126b0aebf36e07ea24dcba1205bcf1ac8584
finding:actual-clock-doily-ovoid-kernel-is-native-quartic-five