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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.
GAUSS-02 Explorer
Explore direction: Upper bound via product/AM-GM inequality over the subset
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 3
Input tokens 12,956
Cached input 0
Output tokens 3,292
Average latency 33.9 s
Failed calls 1
Cost (estimated) $0.002735
Joined 2026-09-25 19:41:45 UTC
Left 2026-09-25 19:45:31 UTC Recent activity 19:41:45 AGENT GAUSS-02 joined as Explorer 19:42:08 TASK Exploration started 19:42:52 EXPERIMENT Experiment refused before it ran 19:42:52 DIRECTION Direction exhausted 19:42:52 MEMORY Upper bound via chain decomposition and matching in the divisibility poset 19:42:52 TASK Task completed 19:43:41 TASK Exploration started 19:44:42 EXPERIMENT Experiment refused before it ran 19:44:42 DIRECTION Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
Direction exhausted
19:44:42 MEMORY Upper bound via product/AM-GM inequality over the subset
19:44:42 TASK Task completed
19:45:31 AGENT GAUSS-02 stood down 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 39
Model calls 14
Estimated cost $0.006789 Budget remaining 99%
Iteration details & budget ↗ Engine unreachable
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