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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
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Research record
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Frontier availability 08 Research director Not started On the roster; the workflow has not woken it in this iteration. 09 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration. Mission
Runtime 6 h 14 min
Iteration 10 of 10
Directions 54
Hypotheses 8
Experiments 21
Rejected paths 39 Current direction No direction is open.
Verified 0 Lean-verified intermediate lemmas A verified lemma covers exactly the declaration the kernel accepted. The problem stays open until it is settled either way. Literature
Indexed 26
Highly relevant 0 Iteration 3 No frontier agent engaged
Model calls 19
Estimated cost $0.0158 Budget remaining 99%
Iteration details & budget ↗
NOETHER Strategist
Plan iteration 2
Model
Model used together / openai/gpt-oss-120b
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,340
Cached input 136
Output tokens 1,763
Average latency 8.2 s
Failed calls 0
Cost (estimated) $0.001259
Joined 2026-09-25 11:18:29 UTC
Left 2026-09-25 11:20:42 UTC Recent activity 11:18:41 DIRECTION Direction proposed: Probabilistic Construction via Lovász Local Lemma 11:18:41 NOVELTY Novelty check: new 11:18:41 DIRECTION Direction proposed: Arithmetic Construction Using Large Prime Factors and Sieve Estimates 11:18:41 DIRECTION Direction assigned to GAUSS-01: Poset‑Chain Decomposition and Dilworth‑type Upper Bounds 11:18:41 DIRECTION Direction assigned to GAUSS-02: Probabilistic Construction via Lovász Local Lemma 11:18:41 DIRECTION Direction assigned to GAUSS-03: Arithmetic Construction Using Large Prime Factors and Sieve Estimates 11:18:41 TASK Task completed 11:19:44 TASK Research planning started Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
11:19:51 PLAN Research plan created
11:19:51 NOVELTY Novelty check: new
11:19:51 DIRECTION Direction proposed: Smooth‑Number Lattice Decomposition
11:19:51 NOVELTY Novelty check: new
11:19:51 DIRECTION Direction proposed: 3‑Uniform Hypergraph Turán Method
11:19:51 NOVELTY Novelty check: new
11:19:51 DIRECTION Direction proposed: Exact Computation and Pattern Extraction
11:19:51 DIRECTION Direction assigned to GAUSS-01: Smooth‑Number Lattice Decomposition
11:19:51 DIRECTION Direction assigned to GAUSS-02: 3‑Uniform Hypergraph Turán Method
11:19:51 DIRECTION Direction assigned to GAUSS-03: Exact Computation and Pattern Extraction
11:19:51 TASK Task completed
11:20:42 AGENT NOETHER stood down