ERDOS-OPEN programme triage
Protected source intake: grandchallenge/MATHFORGE@ec80b855c988e8dc7ddff40cb892b67263d5c86e, ERDOS-OPEN-001.
This is an operational readiness triage, not a ranking of mathematical importance, difficulty, or probability of solution. Prize values are retained as metadata only.
Portfolio disposition
| Class | Count | Programme meaning |
|---|---|---|
| Existing active campaign | 1 | Problem 3 continues as GCL-ERDOS3; no duplicate campaign. |
| Status reconciliation hold | 4 | Registry says open while a formal Lean solution is reported. Reconcile first. |
| First reconnaissance tranche | 8 | Protected statement plus a visible bounded entry point. |
| Cross-campaign synergy only | 1 | Problem 142 is routed into GCL-ERDOS3 because both use the r_k(N) extremal interface. |
| Defer until new mechanism | 6 | Protected, prominent headline targets with no bounded new entry point identified by this triage. |
| Protected ready backlog | 280 | Source-ready but requires statement-level manual prioritization. |
| Formal source refresh required | 58 | Registry reports a statement formalization that is not in the protected FC snapshot. |
| Statement capture required | 235 | No protected or registry-reported statement formalization. |
First reconnaissance tranche
The order below is not a claim of mathematical easiness. It is the order in which GCL can most cleanly create falsifiable, bounded work packages.
- Erdős 593 — characterize obligatory finite 3-uniform hypergraphs. The protected formalization already splits the conjecture into necessary and sufficient directions. Start with two independent proof/obstruction lanes plus a finite testbed.
- Erdős 595 — infinite (K_4)-free graph not countably coverable by triangle-free graphs. The protected file records finite analogues, giving a concrete finite-to-infinite compactness/limit target.
- Erdős 241 — Sidon-type extremal function (f(N)\sim N^{1/3}). The protected file records both lower and upper comparison results, exposing an explicit constant-gap programme.
- Erdős 470 — odd weird numbers / infinitely many primitive weird numbers. Exact integer search and structural obstruction can proceed in parallel.
- Erdős 1052 — finiteness of unitary perfect numbers. The protected file contains exact small examples and a formalized evenness result, which gives a clean successor boundary.
- Erdős 99 — diameter-minimizing planar point sets and forced equilateral triangles. Finite extremal search can identify candidate mechanisms without confusing numerics with proof.
- Erdős 101 — (o(n^2)) four-point-line incidence under no-five-collinear. Pair source-bound incidence inequalities with finite extremal construction search.
- Erdős 138 — growth of van der Waerden numbers. Build a source-grade bound ledger and small-(k) exact computational layer before attempting an asymptotic bridge.
Cross-campaign route
Erdős 142 should not become a fresh campaign. Its (r_k(N)) interface directly overlaps the active GCL-ERDOS3 extremal-series programme. The next action is to map its variants and bound ledger onto the current E3-Q4-SERIES frontier and admit only genuinely new reusable lemmas.
Explicit mechanism holds
The following protected problems are not rejected. They are parked against generic attack until GCL has a new mechanism or a substantially smaller native target:
- 20 — sunflower exponential threshold.
- 28 — Erdős–Turán additive basis conjecture.
- 52 — near-quadratic sum-product.
- 89 — optimal-order planar distinct distances.
- 564 — double-exponential lower bound for 3-uniform hypergraph Ramsey numbers.
- 1135 — Collatz conjecture.
This prevents available agent capacity from being consumed by undifferentiated attacks on mature headline problems.
Source debt
The remaining intake is split mechanically:
- 280 protected-source-ready problems await statement-level manual prioritization.
- 58 require protected Formal Conjectures refresh/source-lock because the registry reports a newer formalization than the admitted FC snapshot.
- 235 require statement capture before campaign design.
Authority boundary
No row in this triage authorizes MATHSOLVE execution. A first-tranche label authorizes only campaign design and bounded reconnaissance-package preparation. A later Programme transaction must bind the exact statement, work-package scope, source evidence, adversarial lane, and stopping rule before launch.