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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 39.
Research chronicle 95 RECORDS
All Research Review Verification System
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GAUSS-01 GAUSS-01 stood down
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GAUSS-02 GAUSS-02 stood down
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GAUSS-03 GAUSS-03 stood down
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LITERATURE-01 LITERATURE-01 stood down
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SYSTEM Research run finished
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SYSTEM Iteration 39 completed
Research graph / proof lineage 7 objects · 0 links · 10 in complete graph
DIRECTION
DIRECTION Probabilistic lower bound via random subsets with divisibility constraints COMPLETED DIRECTION Upper bound via chain decomposition and matching in the divisibility poset COMPLETED DIRECTION Computational exploration and pattern detection for small intervals COMPLETED DIRECTION Constructive lower bound via threshold plus sparse small-number layer COMPLETED DIRECTION Upper bound via product/AM-GM inequality over the subset COMPLETED DIRECTION Recursive interval-splitting upper bound via block automata COMPLETED PROOF
PROOF LP optimum over all block partitions equals N for N <= 60 v1 MARKDOWN Explore complete graph / 17 objects → Research record
Agent record Close ×
GAUSS-03 Explorer
Explore direction: Recursive interval-splitting upper bound via block automata
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 3
Input tokens 8,203
Cached input 4,304
Output tokens 2,051
Average latency 38.3 s
Failed calls 1
Cost (estimated) $0.001249
Joined 2026-09-25 19:41:45 UTC
Left 2026-09-25 19:45:31 UTC Recent activity 19:41:45 AGENT GAUSS-03 joined as Explorer 19:42:08 TASK Exploration started 19:42:22 DIRECTION Direction exhausted 19:42:22 MEMORY Computational exploration and pattern detection for small intervals 19:42:22 TASK Task completed 19:43:41 TASK Exploration started 19:45:27 EXPERIMENT Experiment refused before it ran 19:45:27 DIRECTION Direction exhausted 19:45:27 MEMORY Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
Recursive interval-splitting upper bound via block automata
19:45:27 TASK Task completed
19:45:31 AGENT GAUSS-03 stood down