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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 / 6 6 agents · 0 working
Frontier availability 07 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration. Mission
Runtime 8 h 4 min
Iteration 31 of 31
Directions 175
Hypotheses 15
Experiments 125
Rejected paths 57 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 66
Highly relevant 1 Iteration 9
Model calls 12
Estimated cost $0.0485 Budget remaining 98%
Iteration details & budget ↗
NOETHER Strategist
Plan iteration 2
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,480
Cached input 0
Output tokens 1,092
Average latency 15.6 s
Failed calls 0
Cost (estimated) $0.000513
Joined 2026-09-25 17:00:50 UTC
Left 2026-09-25 17:26:06 UTC Recent activity 17:01:09 DIRECTION Direction proposed: Density increment / Fourier-analytic approach on divisor graph 17:01:09 NOVELTY Novelty check: new 17:01:09 DIRECTION Direction proposed: Probabilistic construction and lower bound via random subsets 17:01:09 DIRECTION Direction assigned to GAUSS-01: Extremal hypergraph via 3-uniform divisibility hypergraph 17:01:09 DIRECTION Direction assigned to GAUSS-02: Density increment / Fourier-analytic approach on divisor graph 17:01:09 DIRECTION Direction assigned to GAUSS-03: Probabilistic construction and lower bound via random subsets 17:01:09 TASK Task completed 17:24:57 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.
17:25:12 PLAN Research plan created
17:25:12 NOVELTY Novelty check: new
17:25:12 DIRECTION Direction proposed: Chain-decomposition upper bound via 2- and 3-smooth chains
17:25:12 NOVELTY Novelty check: new
17:25:12 DIRECTION Direction proposed: Explicit layered construction: (N/3, N] plus controlled small elements
17:25:12 NOVELTY Novelty check: new
17:25:12 DIRECTION Direction proposed: Targeted literature search for this Erdős-type problem
17:25:12 DIRECTION Direction assigned to GAUSS-01: Chain-decomposition upper bound via 2- and 3-smooth chains
17:25:12 DIRECTION Direction assigned to GAUSS-02: Explicit layered construction: (N/3, N] plus controlled small elements
17:25:12 DIRECTION Direction assigned to GAUSS-03: Targeted literature search for this Erdős-type problem
17:25:12 TASK Task completed
17:26:06 AGENT NOETHER stood down