Established within the stated premises
The new observable reaches the original erasure output
finding:native-six-effect-readout-on-existing-erasure-output
Original W:C4⊗H5→C64 is reconstructed exactly. E20_a=I4⊗E5_a has rank4, sumI20; W E20_a W* sums to rank20 projector. All25 rho entries,60 intertwiners and360 covariances agree. Stabilizer average gives P_a=(6/5)E_a.
Scope: Additional logical readout; original loss has effectsI5/4. No identification, Hilbert extension or preparation.
Required premises and original source excerpts
- 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.
premise:native-even-e8-gaussian-clock-and-sign-extension - 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.
premise:native-clock-complex-reflection-and-quartic-subspace - Symmetric quartic and actual erasure intertwiner
Use Sym^4 of the native four-representation, the actual five codeword sums, and the existing one-register erasure intertwiner. The symmetric tensor rule and its physical selection are not silently inferred from the full tensor product.
premise:native-symmetric-quartic-and-erasure-constructors
- experiments/theory-contracts/atlas-defect-synthesis-20261024/NATIVE-ERASURE-READOUT.txt, lines 1–200
Source SHA256: 5be50c2142b498e91350c011c904a13ce823d7a0eef1ff490d89469187e72357
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/atlas-defect-synthesis-20261024/NATIVE-ERASURE-READOUT.txt, lines 201–204
Source SHA256: 5be50c2142b498e91350c011c904a13ce823d7a0eef1ff490d89469187e72357
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/atlas-defect-synthesis-20261024/PROVENANCE-AND-ORIGIN.txt, lines 15–108
Source SHA256: 53fe5a1345544d0d864c339115f8be7e12fc49e741300fa4559fdf1d05a300a2
bounded-excerpt · current-at-snapshot