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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 54.
Research chronicle 93 RECORDS
All Research Review Verification System
↑ 87 earlier records 20:21:19 §88
GAUSS-01 GAUSS-01 stood down
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GAUSS-02 GAUSS-02 stood down
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GAUSS-03 GAUSS-03 stood down
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LITERATURE-01 LITERATURE-01 stood down
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SYSTEM Research run finished
20:21:19 §93
SYSTEM Iteration 54 completed
Research graph / proof lineage 7 objects · 0 links · 9 in complete graph
DIRECTION
DIRECTION Density/entropy upper bound via random sampling and divisor graph COMPLETED DIRECTION Constructive lower bound via multiples of a large prime or near-n intervals COMPLETED DIRECTION Exact computation and pattern detection for small n COMPLETED DIRECTION Poset chain-decomposition and LP dual upper bounds COMPLETED DIRECTION Residue-class and dyadic block decomposition COMPLETED DIRECTION Second-moment and divisor-sum analytic bounds COMPLETED PROOF
PROOF Exact f(N) for N=1..40 v1 MARKDOWN Explore complete graph / 16 objects → Research record
Agent record Close ×
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 54
Model calls 13
Estimated cost $0.006917 Budget remaining 99%
Iteration details & budget ↗
LITERATURE-01 Literature researcher
Reading the landscape around: Poset chain-decomposition and LP dual upper bounds
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 2,172
Cached input 0
Output tokens 353
Average latency 6.6 s
Failed calls 0
Cost (estimated) $0.000403
Joined 2026-09-25 20:19:25 UTC
Left 2026-09-25 20:21:19 UTC Recent activity 20:19:25 AGENT LITERATURE-01 joined as Literature Researcher 20:19:25 LITERATURE Literature search started 20:19:25 LITERATURE Indexed: Targeted random walk sampling 20:19:25 LITERATURE Literature search: 2 new of 2 20:19:25 LITERATURE Reviewed: A Fast Algorithm for Estimating Two-Dimensional Sample Entropy Based on an Upper Confidence Bound and Monte Carlo Sampling 20:19:25 MEMORY Literature: A Fast Algorithm for Estimating Two-Dimensional Sample Entropy Based on an Upper Confidence Bound and Monte Carlo Sampling 20:20:32 LITERATURE Literature search started 20:20:32 LITERATURE Indexed: Upper bounds for generalized Lp-discrepancy of random points Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
07 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration.
20:20:32 LITERATURE Literature search: 3 new of 3
20:20:32 LITERATURE Reviewed: The Numbers of Shared Upper Bounds Determine a Poset
20:20:32 MEMORY Literature: The Numbers of Shared Upper Bounds Determine a Poset
20:21:19 AGENT LITERATURE-01 stood down