Established in scope
Informative ovoid observation first occurs at tensor degree3 with complete classification
In the question: Common clock sectors, quartic geometry and operational reconstruction
Complete finite tensor category; no physical copying, t/instrument, family count, P2 or spacetime from tensor degree.
Read the exact result, assumptions and evidence
Result
For actual G31/ovoid action, Hom(H5,End(V4^⊗n))=0,0,1 for n1,2,3. n1/2, including V⊗barV: onlyI/6. All POVMs onC64: F_a(t)=I/6+tW[I4⊗(E_a−I5/6)]W*, −1/4≤t≤1. ImW=Sym³V with uniform44 complement is forced. Bell six carry spread, not ovoid.
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.
- 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.
- 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.
Original evidence
- NATIVE-OBSERVATION-ARITY.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-observation-arity-20261025/NATIVE-OBSERVATION-ARITY.txt
3beb984ed44fdc1c9aab40626fc19357aaa5a0a15dcaa57259f6d71e487e5b39
- NATIVE-OBSERVATION-ARITY.txt lines 201–246
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-observation-arity-20261025/NATIVE-OBSERVATION-ARITY.txt
3beb984ed44fdc1c9aab40626fc19357aaa5a0a15dcaa57259f6d71e487e5b39
finding:native-six-ovoid-observation-first-occurs-at-tensor-degree-three