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OPENMATH-2026 — Post-event research agenda

The competition event window closed on 2 October 2026 with 0 official submissions and 0 official acceptances. This document now records the surviving mathematical backlog. OPENMATH itself does not issue new replay-successor work.

Research reset rule

New mathematics first. Operational evidence processing and research scheduling are separate. A return may be fully captured and adjudicated without creating a successor. A successor requires a protected frontier disposition naming the unresolved mathematical node it advances.

Surviving frontiers

  1. H1 — Kobon triangles: remaining q≥6 and source-scoped premise closure.
  2. H2 — Busy Beaver 6 certificates: expand the machine-search neighbourhood substantially or stop; do not replay the closed 324-mutant audit again.
  3. H3 — clique-cluster Ramsey multiplicity: move to m≥4.
  4. H4 — Collatz modular descent: SOURCE_BLOCKED until exact canonical nonempty serialization and contraction-margin/tie semantics are supplied.
  5. H5 — Grothendieck witnesses: repair exact small-size classification; then investigate genuinely non-circulant 5×5–8×8 cases if useful.
  6. H6 — 3×3 matrix multiplication tensor: move outside the exhausted elementary-transvection neighbourhood toward broader rank-23 transformations or rank-22 obstruction.
  7. H7 — Erdős Problem 3: promoted into standalone GCL-ERDOS3.

GCL-ERDOS3

GCL-ERDOS3 is the first campaign using the frontier-advancement gate as the scheduler. Its imported conclusion-side D3/D4 lemmas are formalized; the D5 hypothesis-side file is not yet proof-receipted. The active frontier is D5 formal closure plus a scale-local reciprocal-mass-to-AP bridge.

The independent-agent interface is retained. What changes is successor selection: one independent replay is the default bounded verification budget, and repeated replay requires a named reason.