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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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AGENTS / 7 7 agents · 0 working
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 1 No frontier agent engaged
Model calls 18
Estimated cost $0.0161 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 1,188
Cached input 132
Output tokens 1,752
Average latency 9.0 s
Failed calls 0
Cost (estimated) $0.001229
Joined 2026-09-25 11:13:58 UTC
Left 2026-09-25 11:16:14 UTC Recent activity 11:14:09 DIRECTION Direction proposed: Probabilistic Construction and Alteration 11:14:09 NOVELTY Novelty check: new 11:14:09 DIRECTION Direction proposed: Computational Exploration and Greedy Algorithms 11:14:09 DIRECTION Direction assigned to GAUSS-01: Poset and Antichain Analysis via Dilworth and Sperner 11:14:09 DIRECTION Direction assigned to GAUSS-02: Probabilistic Construction and Alteration 11:14:09 DIRECTION Direction assigned to GAUSS-03: Computational Exploration and Greedy Algorithms 11:14:09 TASK Task completed 11:14:59 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.
11:15:09
PLAN
Research plan created
11:15:09 NOVELTY Novelty check: new
11:15:09 DIRECTION Direction proposed: Analytic Number Theory via Divisor Summatory Functions
11:15:09 NOVELTY Novelty check: new
11:15:09 DIRECTION Direction proposed: Prime‑Factor Profile Decomposition and Large‑Prime‑Factor Sets
11:15:09 NOVELTY Novelty check: new
11:15:09 DIRECTION Direction proposed: Hypergraph Turán Theory on the Divisor 3‑Uniform Hypergraph
11:15:09 DIRECTION Direction assigned to GAUSS-01: Analytic Number Theory via Divisor Summatory Functions
11:15:09 DIRECTION Direction assigned to GAUSS-02: Prime‑Factor Profile Decomposition and Large‑Prime‑Factor Sets
11:15:09 DIRECTION Direction assigned to GAUSS-03: Hypergraph Turán Theory on the Divisor 3‑Uniform Hypergraph
11:15:09 TASK Task completed
11:16:14 AGENT NOETHER stood down