Established in scope
Four E6 projectors connect48,4/3 and5/4 in the same representation
In the question: Active mathematical program: marked seam monodromies and lattice lifts
Canonical unordered S4 projector family on the original root-current block. Exact representation interpretation of the existing seed ratio, without an additional readout law or selection of a tetrahedral vertex.
Read the exact result, assumptions and evidence
Result
In the original half-root block B=(16,4), the four D5-containing E6 cuts yield literal rank16 projectors P_t, with P_t P_u=delta_tu P_t and sum P_t=I64. Q_t=I-P_t has rank48 and carries exactly(16,3), with checked D5 and A2 root action. Every cut gives Tr(I64)/Tr(Q_t)=64/48=4/3=phi_base/c3. Every weight of the same block has squared D5 projection5/4 and A3 projection3/4. The same48 lies in(27,3)=(16,3)_1+(10,3)_-2+(1,3)_4, hence81=48+30+3. The E7 missing48 instead carries(12,2,2), whose actual Y character rejects identification with three D5 spinors.
Required assumptions
- Original D5+A3 compiler split and established seed
Retain the established P1/P2 compiler with cyclic C4 glue to E8, D5 on the first5 and A3=D3 on the last3 standard coordinates, c3=1/(8pi) and phi_base=(4/3)c3=1/(6pi). No replacement by an optional E7 readout. Cut equivalence is the actual W(D5)xW(A3) action in the fixed chart, without conjugating J.
- 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.
Original evidence
- CUTS.txt lines 219–324
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/e-series-compiler-closure-20261023/CUTS.txt
e4eb9b53f944d411e887deb1783ff2d12e6a949e7550f9e6ebdd0cf77cd1ef21
- THEOREMS.txt lines 99–127
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/e-series-compiler-closure-20261023/THEOREMS.txt
361450df688c5dc8fa3b8c69ff6a8d0f35156772bee5ec0acab494eb32d3587f
finding:native-four-cut-projectors-unify48-fourthirds-fivequarters