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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 48
Model calls 13
Estimated cost $0.006627 Budget remaining 99%
Iteration details & budget ↗
LITERATURE-01 Literature researcher
Reading the landscape around: Multiplicative Dilates and Interval Partition into Chains
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,889
Cached input 0
Output tokens 481
Average latency 3.2 s
Failed calls 0
Cost (estimated) $0.000399
Joined 2026-09-25 20:03:50 UTC
Left 2026-09-25 20:05:18 UTC Recent activity 20:03:50 AGENT LITERATURE-01 joined as Literature Researcher 20:03:50 LITERATURE Literature search started 20:03:50 LITERATURE Indexed: Ordered Ranked Posets, Representations of Integers and Inequalities from Extremal Poset Problems 20:03:50 LITERATURE Literature search: 3 new of 3 20:03:50 LITERATURE Reviewed: Ordered Ranked Posets, Representations of Integers and Inequalities from Extremal Poset Problems 20:03:50 MEMORY Literature: Ordered Ranked Posets, Representations of Integers and Inequalities from Extremal Poset Problems 20:04:41 LITERATURE Literature search started 20:04:41 LITERATURE Indexed: Generalized multiplicative interval type-2 fuzzy partition C-means clustering Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
20:04:41 LITERATURE Indexed: Multiplicative partition of true diversity yields independent alpha and beta components; additive partition does not
20:04:41 LITERATURE Literature search: 3 new of 3
20:04:41 LITERATURE Reviewed: Interval Type-2 Multiplicative Fuzzy Partition C-Means Clustering
20:04:41 MEMORY Literature: Interval Type-2 Multiplicative Fuzzy Partition C-Means Clustering
20:05:18 AGENT LITERATURE-01 stood down