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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
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.
LITERATURE-01 Literature researcher
Reading the landscape around: Unblock and run exact small-N computation, then compare with (N/3,N]
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,868
Cached input 0
Output tokens 484
Average latency 9.6 s
Failed calls 0
Cost (estimated) $0.000397
Joined 2026-09-25 18:29:56 UTC
Left 2026-09-25 18:35:41 UTC Recent activity 18:29:56 AGENT LITERATURE-01 joined as Literature Researcher 18:29:56 LITERATURE Literature search started 18:29:56 LITERATURE Indexed: 6. Infinite divisibility, generalities 18:29:56 LITERATURE Indexed: 7. Infinite divisibility, special cases 18:29:56 LITERATURE Indexed: A Stability and infinite divisibility 18:29:56 LITERATURE Literature search: 3 new of 3 18:29:56 LITERATURE Reviewed: 6. Infinite divisibility, generalities 18:29:56 MEMORY Literature: 6. Infinite divisibility, generalities Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
18:32:14
LITERATURE
Literature search started
18:32:14 LITERATURE Indexed: Run length, average run length and false alarm rate of shewhart x-bar chart: exact derivations by conditioning
18:32:14 LITERATURE Indexed: unblock
18:32:14 LITERATURE Indexed: The Exact Run Length Distribution and Design of the Shewhart Chart with Estimated Parameters Based on Median Run Length
18:32:14 LITERATURE Literature search: 3 new of 3
18:32:14 LITERATURE Reviewed: Run length, average run length and false alarm rate of shewhart x-bar chart: exact derivations by conditioning
18:32:14 MEMORY Literature: Run length, average run length and false alarm rate of shewhart x-bar chart: exact derivations by conditioning
18:35:41 AGENT LITERATURE-01 stood down 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 18
Model calls 15
Estimated cost $0.0449 Budget remaining 98%
Iteration details & budget ↗ Engine unreachable
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