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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-03 Explorer
Explore direction: Recursive interval splitting with two-level divisibility constraints
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 8,345
Cached input 0
Output tokens 2,826
Average latency 20.3 s
Failed calls 0
Cost (estimated) $0.001960
Joined 2026-09-25 19:24:35 UTC
Left 2026-09-25 19:27:00 UTC Recent activity 19:24:35 AGENT GAUSS-03 joined as Explorer 19:24:54 TASK Exploration started 19:25:11 EXPERIMENT Experiment refused before it ran 19:25:11 DIRECTION Direction exhausted 19:25:11 MEMORY Computational search for extremal sets and pattern extrapolation 19:25:11 TASK Task completed 19:26:28 TASK Exploration started 19:26:57 EXPERIMENT Experiment refused before it ran 19:26:57 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
19:26:57 MEMORY Recursive interval splitting with two-level divisibility constraints
19:26:57 TASK Task completed
19:27:00 AGENT GAUSS-03 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 33
Model calls 12
Estimated cost $0.006367 Budget remaining 99%
Iteration details & budget ↗ Engine unreachable
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