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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: Density increment via divisibility hypergraph containers
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 2,314
Cached input 0
Output tokens 575
Average latency 10.0 s
Failed calls 0
Cost (estimated) $0.000485
Joined 2026-09-25 19:00:17 UTC
Left 2026-09-25 19:02:20 UTC Recent activity 19:00:17 AGENT LITERATURE-01 joined as Literature Researcher 19:00:17 LITERATURE Literature search started 19:00:17 LITERATURE Indexed: Self-Organized Construction in Sparse Random Arrays of Conway’s Game of Life 19:00:17 LITERATURE Literature search: 3 new of 3 19:00:17 LITERATURE Reviewed: Self-Organized Construction in Sparse Random Arrays of Conway’s Game of Life 19:00:17 MEMORY Literature: Self-Organized Construction in Sparse Random Arrays of Conway’s Game of Life 19:01:09 LITERATURE Literature search started 19:01:09 LITERATURE Indexed: Increment Boring Containers Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
19:01:09
LITERATURE
Indexed: Hypergraph Containers and Their Generalization to Super-Hyper-Graph Containers
19:01:09 LITERATURE Literature search: 3 new of 3
19:01:09 LITERATURE Reviewed: Hypergraph Containers
19:01:09 MEMORY Literature: Hypergraph Containers
19:02:20 AGENT LITERATURE-01 stood down Engine unreachable
The research engine answered a mission's knowledge in a shape this page cannot read.
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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 25
Model calls 12
Estimated cost $0.005948 Budget remaining 99%
Iteration details & budget ↗