Skip to main content

Read the result in its research context.

Follow the published construction into its registered claims, then explore reviewed research questions, attempts and the connections that remain open.

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