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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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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-02 Literature researcher
Checking prior art and known barriers for: Log‑power upper bound via smooth‑number decomposition
Model
Model used together / openai/gpt-oss-120b
Routing profile cheap_reasoning
Usage
Model calls 3
Input tokens 3,016
Cached input 207
Output tokens 1,056
Average latency 2.8 s
Failed calls 0
Cost (estimated) $0.001085
Joined 2026-09-25 11:19:09 UTC
Left 2026-09-25 11:20:42 UTC Recent activity 11:19:09 LITERATURE Indexed: Upper bound estimation of the spectral abscissa for switched linear systems via coordinate transformations 11:19:09 LITERATURE Indexed: Enhancing Hydrogen Production via Ammonia-Assisted Decomposition of Short-Chain Alcohols 11:19:09 LITERATURE Literature search: 3 new of 3 11:19:09 LITERATURE Reviewed: Auction implementations using LaGrangian Relaxation, Interior-Point Linear Programming, and Upper-Bound Linear Programming 11:19:09 MEMORY Literature: Auction implementations using LaGrangian Relaxation, Interior-Point Linear Programming, and Upper-Bound Linear Programming 11:19:13 LITERATURE Literature search started 11:19:13 LITERATURE Indexed: Adaptive mesh-free lower bound limit analysis using non-linear programming 11:19:13 Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
LITERATURE
Indexed: A lower bound for the dimension of the base locus of the generalized theta divisor
11:19:13 LITERATURE Indexed: Lower bound to the free energy of an anisotropic linear Heisenberg chain
11:19:13 LITERATURE Literature search: 3 new of 3
11:19:13 LITERATURE Reviewed: Adaptive mesh-free lower bound limit analysis using non-linear programming
11:19:13 MEMORY Literature: Adaptive mesh-free lower bound limit analysis using non-linear programming
11:20:24 LITERATURE Literature search started
11:20:24 LITERATURE Indexed: A Bound of the Number of Weighted Blow-ups to Compute the Minimal Log Discrepancy for Smooth Threefolds
11:20:24 LITERATURE Indexed: An Improved Upper Bound for Steiner Decomposition Number
11:20:24 LITERATURE Indexed: An upper bound of a generalized upper Hamiltonian number of a graph
11:20:24 LITERATURE Literature search: 3 new of 3
11:20:24 LITERATURE Reviewed: A Bound of the Number of Weighted Blow-ups to Compute the Minimal Log Discrepancy for Smooth Threefolds
11:20:24 MEMORY Literature: A Bound of the Number of Weighted Blow-ups to Compute the Minimal Log Discrepancy for Smooth Threefolds
11:20:42 AGENT LITERATURE-02 stood down