A distributed, verifiable search for x³ + y³ + z³ = 114
Draft started September 2026 Abstract We describe an open volunteer search for integer solutions to x³ + y³ + z³ = 114. The implementation combines a cubic-field norm construction, exact arithmetic, modular rejection, bounded client tasks, durable result receipts and independent replay. Scheduling adapts to measured execution cost while preserving exploration. The selected domains are finite and do not constitute an exhaustive height search. No solution is claimed in this draft.
- Problem and motivation The sums-of-three-cubes problem asks for integer triples representing a prescribed integer. The congruence obstruction modulo 9 excludes values congruent to ±4; 114 passes this necessary test. Its passing the test does not prove the existence of an integer solution. This project makes a previously local computational experiment reproducible and open to volunteer contributions.
- Search construction For S = x + y and V = x − y, the defining identity is Writing D = |S| reduces z to roots r of r³ ≡ 114 (mod D), with z = r + Dq. To generate selected roots, let α³ = 114 and use Fixed class lattices and finite coefficient domains define each task. Congruence filters precede exact square, integrality and parity checks. Every emitted triple must satisfy the original integer identity. The mathematical domain and implementation limits accompany the source.
- Volunteer execution and verification Opt-in browser clients use BigInt arithmetic in a worker; the portable local runner uses Python integers. Bounded deterministic task receipts are banked as GitHub issues. The authenticated issue author supplies attribution; posting establishes submission, not correctness. A scheduled verifier independently replays accepted tasks, deduplicates task identifiers and preserves exact positive identities. Display names are self-reported; leaderboard identity comes from the issue author.
- Adaptive allocation The cluster...