A shaped degree-eight source has a two-step degree-eight composition chain

Identifier: F:gf2-degree-eight-octuple-two-step-chain
Proof route: cas-certificate
External status: unknown
Axiom footprint: gf2-polynomial-semantics-v1, rabin-irreducibility-criterion

Recorded description

There exist a shaped irreducible binary polynomial f of degree 8 and nonmonomial shaped binary polynomials sigma_1 and sigma_2 of degree 8 such that f(sigma_1) and f(sigma_1)(sigma_2) are irreducible.

Formal statement

{"exists":"shaped irreducible f degree 8 and shaped nonmonomial sigma_1,sigma_2 degree 8 with f(sigma_1),f(sigma_1)(sigma_2) irreducible","field_order":2,"format":"axeyum-gf2-degree-eight-octuple-two-step-chain","version":1}

Dependencies

The graph shows direct ledger edges. Follow a node to open its artifact page.

1 direct dependencies 0 direct dependents

Evidence

gf2-degree-eight-octuple-two-step-exhaustion

Kind: exhaustive-enumeration
Status: checked

Supports: Complete enumeration of the two shaped irreducible degree-eight sources and all 31 nonmonomial shaped degree-eight substitutions at both stages; four certified first-stage outputs and zero certified continuations.

Checker command

cargo test -p axeyum-cas --all-features no_degree_eight_source_has_a_two_step_octuple_composition_chain

Evidence notes

This refutes only the stated repeated degree-eight chain. It does not refute isolated degree-64-to-512 compositions or chains using a different substitution degree.

Provenance

{
  "date": "2026-08-20",
  "established_by": "Axeyum gf2-lemire lane",
  "source": "bounded exhaustive native search with replayed Rabin certificates"
}