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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-01 Explorer
Explore direction: Random subset with dependent rounding and divisor-count weighting
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 8,501
Cached input 0
Output tokens 2,400
Average latency 13.1 s
Failed calls 0
Cost (estimated) $0.001862
Joined 2026-09-25 19:55:42 UTC
Left 2026-09-25 19:57:46 UTC Recent activity 19:55:42 AGENT GAUSS-01 joined as Explorer 19:55:58 TASK Exploration started 19:56:10 EXPERIMENT Experiment refused before it ran 19:56:10 DIRECTION Direction exhausted 19:56:10 MEMORY Density via multiplicative chains and interval blocking 19:56:10 TASK Task completed 19:57:12 TASK Exploration started 19:57:28 EXPERIMENT Experiment refused before it ran 19:57:28 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
19:57:28 MEMORY Random subset with dependent rounding and divisor-count weighting
19:57:28 TASK Task completed
19:57:46 AGENT GAUSS-01 stood down Engine unreachable
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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 44
Model calls 13
Estimated cost $0.007170 Budget remaining 99%
Iteration details & budget ↗