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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: Local finite-configuration upper-bound lemma, verified by computer and formalized in Lean
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 3
Input tokens 10,435
Cached input 0
Output tokens 1,769
Average latency 18.3 s
Failed calls 1
Cost (estimated) $0.001956
Joined 2026-09-25 18:40:07 UTC
Left 2026-09-25 18:46:44 UTC Recent activity 18:40:07 AGENT GAUSS-03 joined as Explorer 18:40:31 TASK Exploration started 18:40:44 DIRECTION Direction exhausted 18:40:44 MEMORY Computational search and pattern extrapolation for small n 18:40:44 TASK Task completed 18:43:41 TASK Exploration started 18:44:27 EXPERIMENT Experiment refused before it ran 18:44:27 DIRECTION Direction exhausted 18:44:27 MEMORY Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
Local finite-configuration upper-bound lemma, verified by computer and formalized in Lean
18:44:27 TASK Task completed
18:46:44 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 20
Model calls 15
Estimated cost $0.0497 Budget remaining 98%
Iteration details & budget ↗ Engine unreachable
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