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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 07 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration. Mission
Runtime 9 h 14 min
Iteration 57 of 57
Directions 331
Hypotheses 17
Experiments 266
Rejected paths 64 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 109
Highly relevant 1 Iteration 50
Model calls 12
Estimated cost $0.006004 Budget remaining 99%
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 1,072
Cached input 517
Output tokens 1,058
Average latency 13.0 s
Failed calls 0
Cost (estimated) $0.000390
Joined 2026-09-25 20:09:20 UTC
Left 2026-09-25 20:11:58 UTC Recent activity 20:09:36 DIRECTION Direction proposed: Upper bound via divisor-chain decomposition and interval partition 20:09:36 NOVELTY Novelty check: new 20:09:36 DIRECTION Direction proposed: Computational search and pattern discovery for small N 20:09:36 DIRECTION Direction assigned to GAUSS-01: Modular residue class constructions for large divisor-free subsets 20:09:36 DIRECTION Direction assigned to GAUSS-02: Upper bound via divisor-chain decomposition and interval partition 20:09:36 DIRECTION Direction assigned to GAUSS-03: Computational search and pattern discovery for small N 20:09:36 TASK Task completed 20:10:47 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.
20:10:59 PLAN Research plan created
20:10:59 NOVELTY Novelty check: new
20:10:59 DIRECTION Direction proposed: Random greedy construction with divisor-count potential
20:10:59 NOVELTY Novelty check: new
20:10:59 DIRECTION Direction proposed: Linear programming upper bound via disjoint divisor chains
20:10:59 NOVELTY Novelty check: new
20:10:59 DIRECTION Direction proposed: Rank-based Sperner-type bound on the divisibility poset
20:10:59 DIRECTION Direction assigned to GAUSS-01: Random greedy construction with divisor-count potential
20:10:59 DIRECTION Direction assigned to GAUSS-02: Linear programming upper bound via disjoint divisor chains
20:10:59 DIRECTION Direction assigned to GAUSS-03: Rank-based Sperner-type bound on the divisibility poset
20:10:59 TASK Task completed
20:11:58 AGENT NOETHER stood down