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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 43
Model calls 12
Estimated cost $0.006269 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 1,082
Cached input 517
Output tokens 1,092
Average latency 10.8 s
Failed calls 0
Cost (estimated) $0.000400
Joined 2026-09-25 19:53:51 UTC
Left 2026-09-25 19:55:27 UTC Recent activity 19:54:10 NOVELTY Novelty check: new 19:54:10 DIRECTION Direction proposed: Computational search and pattern extraction on small intervals, then Lean-verified lemma 19:54:10 DIRECTION Direction assigned to GAUSS-01: Probabilistic construction via random subsets and divisor-count weighting 19:54:10 DIRECTION Direction assigned to GAUSS-02: Upper bound via chain decomposition and interval partition into divisor chains 19:54:10 DIRECTION Direction assigned to GAUSS-03: Computational search and pattern extraction on small intervals, then Lean-verified lemma 19:54:10 TASK Task completed 19:54:49 TASK Research planning started 19:54:54 PLAN Research plan created Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
19:54:54 NOVELTY Novelty check: new
19:54:54 DIRECTION Direction proposed: Weighted AM-GM upper bound via divisor-pair counting
19:54:54 NOVELTY Novelty check: new
19:54:54 DIRECTION Direction proposed: Greedy maximal antichain construction with potential function
19:54:54 MEMORY Novelty check: Reduction to bipartite matching and poset dimension
19:54:54 NOVELTY Novelty check: partially explored
19:54:54 DIRECTION Direction proposed: Reduction to bipartite matching and poset dimension
19:54:54 DIRECTION Direction assigned to GAUSS-01: Weighted AM-GM upper bound via divisor-pair counting
19:54:54 DIRECTION Direction assigned to GAUSS-02: Greedy maximal antichain construction with potential function
19:54:54 DIRECTION Direction assigned to GAUSS-03: Reduction to bipartite matching and poset dimension
19:54:54 TASK Task completed
19:55:27 AGENT NOETHER stood down