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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 41.
Research chronicle 94 RECORDS
All Research Review Verification System
↑ 88 earlier records 19:50:36 §89
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
19:50:36 §94
SYSTEM Iteration 41 completed
Research graph / proof lineage 7 objects · 0 links · 12 in complete graph
DIRECTION
DIRECTION Probabilistic construction with multiplicative weights COMPLETED DIRECTION Poset decomposition and chain upper bounds COMPLETED DIRECTION Exact computation on small intervals and Lean formalization COMPLETED DIRECTION Weighted chain-counting upper bound via entropy COMPLETED DIRECTION Residue-class construction for lower bounds COMPLETED DIRECTION Layered graph reduction and greedy maximum independent set COMPLETED PROOF
PROOF Weighted chain-counting bound analysis v1 MARKDOWN Explore complete graph / 19 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 41
Model calls 12
Estimated cost $0.006209 Budget remaining 99%
Iteration details & budget ↗
LITERATURE-01 Literature researcher
Reading the landscape around: Weighted chain-counting upper bound via entropy
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 2,238
Cached input 0
Output tokens 583
Average latency 7.8 s
Failed calls 0
Cost (estimated) $0.000477
Joined 2026-09-25 19:48:46 UTC
Left 2026-09-25 19:50:36 UTC Recent activity 19:48:46 AGENT LITERATURE-01 joined as Literature Researcher 19:48:46 LITERATURE Literature search started 19:48:46 LITERATURE Indexed: The Reasonable Effectiveness of the Multiplicative Weights Update Algorithm 19:48:46 LITERATURE Indexed: The Reasonable Effectiveness of the Multiplicative Weights Update Algorithm 19:48:46 LITERATURE Indexed: Figure 2—figure supplement 4. Weight normalization is not crucial for the emergence of grid cells. 19:48:46 LITERATURE Literature search: 3 new of 3 19:48:46 LITERATURE Reviewed: The Reasonable Effectiveness of the Multiplicative Weights Update Algorithm 19:48:46 MEMORY Literature: The Reasonable Effectiveness of the Multiplicative Weights Update Algorithm 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.
19:49:37 LITERATURE Literature search started
19:49:37 LITERATURE Indexed: Distribution-Dependent Weighted Union Bound
19:49:37 LITERATURE Indexed: A Free-Energy Upper-Bound Criterion for Entropy-Active Element Counts in High-Entropy Materials
19:49:37 LITERATURE Literature search: 3 new of 3
19:49:37 LITERATURE Reviewed: Distribution-Dependent Weighted Union Bound
19:49:37 MEMORY Literature: Distribution-Dependent Weighted Union Bound
19:50:36 AGENT LITERATURE-01 stood down