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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 upper bound via random divisor selection and entropy
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,969
Cached input 0
Output tokens 359
Average latency 5.0 s
Failed calls 0
Cost (estimated) $0.000376
Joined 2026-09-25 19:38:47 UTC
Left 2026-09-25 19:41:27 UTC Recent activity 19:38:47 AGENT LITERATURE-01 joined as Literature Researcher 19:38:47 LITERATURE Literature search started 19:38:47 LITERATURE Indexed: Number-Theoretic Compilation of Many-Body Quantum Phases Residue-Selected Arithmetic IRs and Bounded-Fanin Circuit Lower Bounds 19:38:47 LITERATURE Indexed: Lower Bounds for the Packing Densities of Spheres 19:38:47 LITERATURE Indexed: Lower bounds on arithmetic circuits via partial derivatives 19:38:47 LITERATURE Literature search: 3 new of 3 19:38:47 LITERATURE Reviewed: Number-Theoretic Compilation of Many-Body Quantum Phases Residue-Selected Arithmetic IRs and Bounded-Fanin Circuit Lower Bounds 19:38:47 MEMORY Literature: Number-Theoretic Compilation of Many-Body Quantum Phases Residue-Selected Arithmetic IRs and Bounded-Fanin Circuit Lower Bounds Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
19:39:51 LITERATURE Literature search started
19:39:51 LITERATURE Indexed: A Probabilistic Upper Bound on Differential Entropy
19:39:51 LITERATURE Indexed: Achievable Information Rates for Probabilistic Amplitude Shaping: An Alternative Approach via Random Sign-Coding Arguments
19:39:51 LITERATURE Indexed: A Free-Energy Upper-Bound Criterion for Entropy-Active Element Counts in High-Entropy Materials
19:39:51 LITERATURE Literature search: 3 new of 3
19:39:51 LITERATURE Reviewed: A Probabilistic Upper Bound on Differential Entropy
19:39:51 MEMORY Literature: A Probabilistic Upper Bound on Differential Entropy
19:41:27 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 38
Model calls 13
Estimated cost $0.007377 Budget remaining 99%
Iteration details & budget ↗ Engine unreachable
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