Established within the stated premises
Original quartic, erasure and Hamming octic share the same marked ovoid response
finding:original-quartic-erasure-and-hamming-octic-share-marked-ovoid-response
Original decoder is (W*x³)_(a,i)=∂a phi_i/2. Actual marked R_A satisfy Igusa and p_A=||gradR_A||²/48, sum||x||⁶. All256 Hamming code pairs give I8=Σx⁸+14Σx_a⁴x_b⁴+168∏x²=96Σf_i²=(1/3)ΣR_A². Restoring allμ4 phases gives all14 marked code/root tetrads.
Scope: Given coherent inputs and constructors. Classical invariants; new comparison concerns marks/operator norm. Holomorphic ≠ Born squares.
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 - Native tensor actions and covariant six-outcome observation
Fix the original unitary G31 representation on V4, its ordinary complex tensor powers and the actual six-point action on E8/J ovoids. Consider all positive normalized operator families with this covariance. For the additional response identity x^tensor3 is a specified family of coherent probe inputs, not a physically derived or cloned preparation. Covariance does not select measurement contrast, an instrument, a physical time or a state.
premise:native-tensor-povm-and-coherent-source-category
- experiments/theory-contracts/native-observation-arity-20261025/COHERENT-QUARTIC-RESPONSE.txt, lines 1–134
Source SHA256: 012879c9ab78413ce229cb1dbc99eac4e2f4c229550d5853b74626385d389c83
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/native-observation-arity-20261025/NATIVE-SOURCE-INSERTION.txt, lines 1–65
Source SHA256: c13001c07bc49bca9054ddc64549e40fb15e78a454c3ac8365fee0ed9713efed
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/native-observation-arity-20261025/coherent_quartic_response.py, lines 62–198
Source SHA256: d50aca63a57f8dd9309b2906b951a05da1606bd3524b57202157af6efc22c62a
bounded-excerpt · current-at-snapshot