Scoped exclusion
Identical overlapping native five-codes have no common state
In the question: Common clock sectors, quartic geometry and operational reconstruction
Only rigid identical code constraints in a shared register frame. No new P1 code-closure axiom. No classification of differently rotated codes,disjoint blocks,approximate/open processes,frustrated phases or the full E8 field. The auxiliary penalty is not presented as a native extensive Hamiltonian spectrum.
Read the exact result, assumptions and evidence
Result
ForA=V_1234 tensorI andB=I tensorV_2345,exactlyA*B=(1/4)S for a factor permutationS. Their image intersection is0. The auxiliary projector penalty2I−AA*−BB* has minimum3/4;the actual native parent sum is>=3/8. Since overlappingS4 groups generate symmetry on the union,the same zero intersection follows for identical code constraints overlapping in1,2 or3 registers.
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.
Original evidence
- COLLECTIVE-DYNAMICS.txt lines 1–130
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/collective-native-marginal-origin-20261026/COLLECTIVE-DYNAMICS.txt
ea4eaebb6d70a81df5d6adf0f570a4bbfcd021429712117b0dde96cd073d761b
- check_collective_dynamics.py lines 1–120
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/collective-native-marginal-origin-20261026/check_collective_dynamics.py
b2a4d111830a2fc85489d0da033eef1bd1feb464edbada38231700db4e128dc6
- dynamics_results.json lines 1–99
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/collective-native-marginal-origin-20261026/dynamics_results.json
4d6ab1df704cb1ace891a30a87e4cad61317265cf7cfaa5ff4e704dbb78a4fd0
finding:identical-overlapping-native-five-codes-have-no-common-state