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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 16.
Research chronicle 92 RECORDS
All Research Review Verification System
↑ 86 earlier records 18:23:31 §87
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
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SYSTEM Iteration 16 completed
Research graph / proof lineage 7 objects · 0 links · 10 in complete graph
DIRECTION
DIRECTION Random subset construction with divisor-free triples COMPLETED DIRECTION Poset rank-layer and chain-decomposition upper bound COMPLETED DIRECTION Computational search and extremal pattern extraction COMPLETED DIRECTION Exhaustive/ILP computation of f(N) for N<=40 and density benchmark COMPLETED DIRECTION Lower-bound construction: augment (N/3,N] with small elements COMPLETED DIRECTION Upper bound via multiplicative-chain decompositions and Lean lemma COMPLETED PROOF
PROOF Experiment report — Verify that for all N<=200, the maximum f(N) of a subset of {1..N} with no eleme v1 MARKDOWN Explore complete graph / 17 objects → Research record
Agent record Close ×
Mission
Runtime 9 h 10 min
Iteration 55 of 55
Directions 325
Hypotheses 17
Experiments 259
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 16
Model calls 11
Estimated cost $0.0507 Budget remaining 97%
Iteration details & budget ↗
LITERATURE-01 Literature researcher
Reading the landscape around: Exhaustive/ILP computation of f(N) for 40 and density benchmark
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,882
Cached input 0
Output tokens 442
Average latency 6.2 s
Failed calls 0
Cost (estimated) $0.000387
Joined 2026-09-25 18:20:29 UTC
Left 2026-09-25 18:23:31 UTC Recent activity 18:20:29 AGENT LITERATURE-01 joined as Literature Researcher 18:20:29 LITERATURE Literature search started 18:20:29 LITERATURE Indexed: Figure 6: Turtle representation of the subset of triples from the MetaRecord metadata pertaining to the two DCAT Distributions. 18:20:29 LITERATURE Literature search: 1 new of 1 18:20:29 LITERATURE Reviewed: Figure 6: Turtle representation of the subset of triples from the MetaRecord metadata pertaining to the two DCAT Distributions. 18:20:29 MEMORY Literature: Figure 6: Turtle representation of the subset of triples from the MetaRecord metadata pertaining to the two DCAT Distributions. 18:22:28 LITERATURE Literature search started 18:22:28 LITERATURE 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. Indexed: Integer Linear Programming (ILP)
18:22:28 LITERATURE Indexed: Precision Modular Flow: Exhaustive Human Computation Of Exponentiations
18:22:28 LITERATURE Indexed: Integer Linear Programming (ILP)
18:22:28 LITERATURE Literature search: 3 new of 3
18:22:28 LITERATURE Reviewed: Integer Linear Programming (ILP)
18:22:28 MEMORY Literature: Integer Linear Programming (ILP)
18:23:31 AGENT LITERATURE-01 stood down