Honest scope
Research status
Axiom is an implementation project informed by the Chuzhoy–Khanna–Song paper. This page separates shipped behavior from work still being validated.
Product boundary, updated October 4, 2026: Axiom supports only paper-derived basic and multilevel matching; basic is the default. Both flow through the same SQLite-backed Durable/Service path. Compact Packed storage is not a matching method. The latest hosted resource gate fails both modes: Multilevel during startup and Basic during disk-pressure recovery. Historical measurements from the removed native matcher do not qualify these modes. See the 17-item roadmap.
Implemented today
- Matcher and durable Service expose canonical
basicandmultilevelmodes. - Deterministic updates with explicit invariant checks.
- Bounded atomic durable batches and version-coherent query groups are implemented.
- Recursive hierarchy state and level-schedule validation are implemented; constrained scale qualification is failing and remains open.
Still under validation
- Complete paper-faithful recursive coloring behavior.
- End-to-end ABB+26 asymptotic guarantee.
- Full stress evidence across every multilevel transition.
Paper-to-code map
| Paper area | Current implementation | Boundary |
|---|---|---|
| Single-level z-system | Implemented | Validated partitions, saturation, adjacency indexes, and maximality. |
| Recursive levels | Implemented and checked | Child levels inherit the previous structure and validate A_i, N_i, R_i, and I3. |
| Dynamic transitions | Implemented locally | Insertion, deletion, rematching, deferred edges, and phase rebuilds are covered by runtime checks; proof-level equivalence remains open. |
| Deterministic coloring | Paper-oriented construction | Fan operations and explicit failure diagnostics are present; the complete ABB+26 construction and bound are not claimed. |
| Asymptotic theorem | Not claimed | Python hash-set adjacency and incomplete ABB+26 validation differ from the theorem's model. |
How to use this page
Use Modes to choose a confidence level, API reference to integrate it, and Architecture to inspect state ownership and update boundaries. If your result depends on the paper's asymptotic guarantee, record it as a research experiment rather than a production benchmark.
Read the paper for the research result. Read this site for the current implementation boundary.