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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: Probabilistic density bound via dependent rounding on divisor chains
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,871
Cached input 0
Output tokens 431
Average latency 5.8 s
Failed calls 0
Cost (estimated) $0.000382
Joined 2026-09-25 19:24:35 UTC
Left 2026-09-25 19:27:00 UTC Recent activity 19:24:35 AGENT LITERATURE-01 joined as Literature Researcher 19:24:35 LITERATURE Literature search started 19:24:35 LITERATURE Indexed: Modular Arithmetic: Calculating with Residue Classes 19:24:35 LITERATURE Indexed: Modular Arithmetic: Calculating with Residue Classes 19:24:35 LITERATURE Indexed: Modular Arithmetic: Calculating with Residue Classes 19:24:35 LITERATURE Literature search: 3 new of 3 19:24:35 LITERATURE Reviewed: Modular Arithmetic: Calculating with Residue Classes 19:24:35 MEMORY Literature: Modular Arithmetic: Calculating with Residue Classes Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
19:26:10
LITERATURE
Literature search started
19:26:10 LITERATURE Indexed: Probabilistic Inverse Design of Nanoporous FabryPerot Color Filters via Mixture Density Networks
19:26:10 LITERATURE Indexed: Divisor density
19:26:10 LITERATURE Indexed: Dependent Randomized Rounding via Exchange Properties of Combinatorial Structures
19:26:10 LITERATURE Literature search: 3 new of 3
19:26:10 LITERATURE Reviewed: Probabilistic Inverse Design of Nanoporous FabryPerot Color Filters via Mixture Density Networks
19:26:10 MEMORY Literature: Probabilistic Inverse Design of Nanoporous FabryPerot Color Filters via Mixture Density Networks
19:27:00 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 33
Model calls 12
Estimated cost $0.006367 Budget remaining 99%
Iteration details & budget ↗ Engine unreachable
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