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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: Structural decomposition by divisor poset layers with interval-specific chain constraints
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 8,326
Cached input 0
Output tokens 2,585
Average latency 34.1 s
Failed calls 0
Cost (estimated) $0.001889
Joined 2026-09-25 20:16:52 UTC
Left 2026-09-25 20:19:14 UTC Recent activity 20:16:52 AGENT GAUSS-02 joined as Explorer 20:17:09 TASK Exploration started 20:18:04 EXPERIMENT Experiment refused before it ran 20:18:04 DIRECTION Direction exhausted 20:18:04 MEMORY Construction with large primes and near-prime intervals 20:18:04 TASK Task completed 20:18:44 TASK Exploration started 20:19:00 EXPERIMENT Experiment refused before it ran 20:19:00 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
20:19:00 MEMORY Structural decomposition by divisor poset layers with interval-specific chain constraints
20:19:00 TASK Task completed
20:19:14 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 53
Model calls 12
Estimated cost $0.006474 Budget remaining 99%
Iteration details & budget ↗ Engine unreachable
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