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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 09 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 30
Model calls 15
Estimated cost $0.009723 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 1,074
Cached input 517
Output tokens 1,022
Average latency 15.3 s
Failed calls 0
Cost (estimated) $0.000380
Joined 2026-09-25 19:15:24 UTC
Left 2026-09-25 19:18:54 UTC Recent activity 19:15:44 MEMORY Novelty check: Divisor-chain layer decomposition and exact DP for small n 19:15:44 NOVELTY Novelty check: partially explored 19:15:44 DIRECTION Direction proposed: Divisor-chain layer decomposition and exact DP for small n 19:15:44 DIRECTION Direction assigned to GAUSS-01: Weighted divisor-count upper bound and greedy construction 19:15:44 DIRECTION Direction assigned to GAUSS-02: Probabilistic method and random subset density 19:15:44 DIRECTION Direction assigned to GAUSS-03: Divisor-chain layer decomposition and exact DP for small n 19:15:44 TASK Task completed 19:16:46 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.
19:17:01 PLAN Research plan created
19:17:01 NOVELTY Novelty check: new
19:17:01 DIRECTION Direction proposed: Large-prime-factor construction via prime gaps
19:17:01 NOVELTY Novelty check: new
19:17:01 DIRECTION Direction proposed: Hypergraph independent set with fractional relaxation
19:17:01 NOVELTY Novelty check: new
19:17:01 DIRECTION Direction proposed: Compression and density increment on the divisor poset
19:17:01 DIRECTION Direction assigned to GAUSS-01: Large-prime-factor construction via prime gaps
19:17:01 DIRECTION Direction assigned to GAUSS-02: Hypergraph independent set with fractional relaxation
19:17:01 DIRECTION Direction assigned to GAUSS-03: Compression and density increment on the divisor poset
19:17:01 TASK Task completed
19:18:54 AGENT NOETHER stood down