math-gambling · working draftResult pending
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 combines measured curve yield and execution cost with an explicit geometric prior while preserving exploration. The selected domains are finite and do not constitute an exhaustive height search. No solution is claimed in this draft.
1. 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.
2. Search construction
For S = x + y and V = x − y, the defining identity is
3SV² = 4(114 − z³) − S³. (1)
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
N(a + bα + cα²) = a³ + 114b³ + 12996c³ − 342abc. (2)
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.
3. Volunteer execution and verification
Opt-in browser clients use a Rust WebAssembly kernel with a BigInt fallback; the local runner offers Rust computation with exact wider final checks. 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. Eligible negative banks are randomly sampled after submission. Unreplayed claims earn no verified credit, certify no coverage and supply no learning observations.
4. Adaptive allocation
Every 64 newly verified tasks freezes a policy. Existing epochs retain their original method. The current policy combines aggregate curve yield and CPU, including empty-task costs, with an uncalibrated geometric band/shell prior. New epochs reserve forty percent of predicted CPU equally across contexts; actual device costs vary. The shared-feature predictor stays in shadow, and the earlier discovery experiment failed its acceptance test. Neither is a validated estimate of discovery probability.
5. Validation and limitations
The preceding native campaign recovered all 662 known-positive fixtures in its regression corpus and included arithmetic-boundary, differential and crash-recovery checks. Those results apply to the archived native release; the portable public client has its own independent cross-language tests. Neither set is a formal proof of the complete software stack. Public receipts only certify the finite task actually replayed. Unknown global coverage and unknown success probability remain central limitations.
6. Result (intentionally unfilled)
- Verified solution (x, y, z)
- ________________________________________
- Finder / verified contributor
- ________________________________________
- Discovery date and receipt
- ________________________________________
- Independent reproduction
- ________________________________________
No counters, near misses or local credit preview fill this section. It requires an actual independently verified identity.
7. Reproducibility and attribution
Code, fixed task definitions, verification tests, strategy revisions, research notes and their failed hypotheses are maintained at github.com/Kuberwastaken/math-gambling. Final authorship and discovery attribution require evidence and agreement; participation alone does not confer authorship.
References
- A. R. Booker and A. V. Sutherland. On a question of Mordell. PNAS 118 (2021). arXiv:2007.01209.
- J. Grantham and P. G. Walsh. Representing integers as a sum of three cubes. (2022). arXiv:2211.12149.
- S. G. Huisman. Newer sums of three cubes. (2016). arXiv:1604.07746.
- math-gambling. Implementation, campaign evidence and research verdict (2026). Versioned project repository.