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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: Probabilistic density bound via dependent rounding on divisor chains
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 8,327
Cached input 0
Output tokens 1,904
Average latency 12.3 s
Failed calls 0
Cost (estimated) $0.001699
Joined 2026-09-25 19:24:35 UTC
Left 2026-09-25 19:27:00 UTC Recent activity 19:24:35 AGENT GAUSS-01 joined as Explorer 19:24:54 TASK Exploration started 19:25:02 EXPERIMENT Experiment refused before it ran 19:25:02 DIRECTION Direction exhausted 19:25:02 MEMORY Constructive interval packing with modular residue classes 19:25:02 TASK Task completed 19:26:28 TASK Exploration started 19:26:47 EXPERIMENT Experiment refused before it ran 19:26:47 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
19:26:47 MEMORY Probabilistic density bound via dependent rounding on divisor chains
19:26:47 TASK Task completed
19:27:00 AGENT GAUSS-01 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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