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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
AGENTS / 6 6 agents · 0 working
Frontier availability Showing iteration 17.
Research chronicle 93 RECORDS
All Research Review Verification System
↑ 87 earlier records 18:29:32 §88
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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ARES ARES stood down
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SYSTEM Research run finished
18:29:32 §93
SYSTEM Iteration 17 completed
Research graph / proof lineage 7 objects · 0 links · 15 in complete graph
DIRECTION
DIRECTION Probabilistic construction with random multiples and density optimization COMPLETED DIRECTION Poset chain decomposition and weighted Dilworth-type bound COMPLETED DIRECTION Exact computation for small n and induction with block decomposition COMPLETED DIRECTION Exact brute-force and layered-construction benchmark for [1,N] and short intervals COMPLETED DIRECTION Lower-bound construction family from layered intervals with controlled multiple counts COMPLETED DIRECTION Upper bound by grouping each element with its first two multiples and charging deletions COMPLETED PROOF
PROOF Exact maxima for [1,N], N<=24 v1 MARKDOWN Explore complete graph / 22 objects → Research record
Agent record Close ×
Mission
Runtime 9 h 10 min
Iteration 55 of 55
Directions 325
Hypotheses 17
Experiments 260
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 108
Highly relevant 1 Iteration 17
Model calls 13
Estimated cost $0.0486 Budget remaining 98%
Iteration details & budget ↗
LITERATURE-01 Literature researcher
Reading the landscape around: Exact brute-force and layered-construction benchmark for [1,N] short intervals
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,862
Cached input 0
Output tokens 437
Average latency 7.1 s
Failed calls 0
Cost (estimated) $0.000383
Joined 2026-09-25 18:23:59 UTC
Left 2026-09-25 18:29:32 UTC Recent activity 18:23:59 AGENT LITERATURE-01 joined as Literature Researcher 18:23:59 LITERATURE Literature search started 18:23:59 LITERATURE Indexed: Probabilistic analyses of combinatorial optimization problems on random shortest path metrics 18:23:59 LITERATURE Indexed: Stochastic model construction of observed random phenomena 18:23:59 LITERATURE Indexed: Probabilistic construction of proportional graphs 18:23:59 LITERATURE Literature search: 3 new of 3 18:23:59 LITERATURE Reviewed: Probabilistic analyses of combinatorial optimization problems on random shortest path metrics 18:23:59 MEMORY Literature: Probabilistic analyses of combinatorial optimization problems on random shortest path metrics 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.
18:27:15 LITERATURE Literature search started
18:27:15 LITERATURE Indexed: Short Circuit
18:27:15 LITERATURE Indexed: brute-force attack
18:27:15 LITERATURE Literature search: 3 new of 3
18:27:15 LITERATURE Reviewed: Short Circuit
18:27:15 MEMORY Literature: Short Circuit
18:29:32 AGENT LITERATURE-01 stood down