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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 08 Research director Not started On the roster; the workflow has not woken it in this iteration. 09 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration. Mission
Runtime 6 h 14 min
Iteration 10 of 10
Directions 54
Hypotheses 8
Experiments 21
Rejected paths 39 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 26
Highly relevant 0 Iteration 3 No frontier agent engaged
Model calls 19
Estimated cost $0.0158 Budget remaining 99%
Iteration details & budget ↗
LITERATURE-01 Literature researcher
Reading the landscape around: Smooth‑Number Lattice Decomposition
Model
Model used together / openai/gpt-oss-120b
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 2,039
Cached input 138
Output tokens 1,169
Average latency 6.2 s
Failed calls 0
Cost (estimated) $0.001008
Joined 2026-09-25 11:18:41 UTC
Left 2026-09-25 11:20:42 UTC Recent activity 11:18:41 AGENT LITERATURE-01 joined as Literature Researcher 11:18:41 LITERATURE Literature search started 11:18:41 LITERATURE Indexed: Decomposition Theory for Lattices without Chain Conditions 11:18:41 LITERATURE Indexed: Effective Versions of the Chain Decomposition Theorem 11:18:41 LITERATURE Indexed: The Numbers of Shared Upper Bounds Determine a Poset 11:18:41 LITERATURE Literature search: 3 new of 3 11:18:41 LITERATURE Reviewed: Decomposition Theory for Lattices without Chain Conditions 11:18:41 MEMORY Literature: Decomposition Theory for Lattices without Chain Conditions Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
11:19:51
LITERATURE
Literature search started
11:19:51 LITERATURE Indexed: Nuclide Number Density Prediction in the Lattice Physics Calculation Based on Dynamic Mode Decomposition
11:19:51 LITERATURE Indexed: On the number field sieve: polynomial selection and smooth elements in number fields
11:19:51 LITERATURE Indexed: Self-Attractive Hartree Decomposition: Partitioning Electron Density into Smooth Localized Fragments
11:19:51 LITERATURE Literature search: 3 new of 3
11:19:51 LITERATURE Reviewed: Nuclide Number Density Prediction in the Lattice Physics Calculation Based on Dynamic Mode Decomposition
11:19:51 MEMORY Literature: Nuclide Number Density Prediction in the Lattice Physics Calculation Based on Dynamic Mode Decomposition
11:20:42 AGENT LITERATURE-01 stood down