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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 17.
Research chronicle 93 RECORDS
All Research Review Verification System
↑ 87 earlier records 18:29:32 §88
GAUSS-02 GAUSS-02 stood down
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GAUSS-03 GAUSS-03 stood down
18:29:32 §90
LITERATURE-01 LITERATURE-01 stood down
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ARES ARES stood down
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SYSTEM Research run finished
18:29:32 §93
SYSTEM Iteration 17 completed
Research graph / proof lineage 7 objects · 0 links · 15 in complete graph
DIRECTION
DIRECTION Probabilistic construction with random multiples and density optimization COMPLETED DIRECTION Poset chain decomposition and weighted Dilworth-type bound COMPLETED DIRECTION Exact computation for small n and induction with block decomposition COMPLETED DIRECTION Exact brute-force and layered-construction benchmark for [1,N] and short intervals COMPLETED DIRECTION Lower-bound construction family from layered intervals with controlled multiple counts COMPLETED DIRECTION Upper bound by grouping each element with its first two multiples and charging deletions COMPLETED PROOF
PROOF Exact maxima for [1,N], N<=24 v1 MARKDOWN Explore complete graph / 22 objects → Research record
Agent record Close ×
NOETHER Strategist
Plan iteration 2
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,430
Cached input 517
Output tokens 1,100
Average latency 28.5 s
Failed calls 0
Cost (estimated) $0.000451
Joined 2026-09-25 18:23:34 UTC
Left 2026-09-25 18:29:32 UTC Recent activity 18:23:59 NOVELTY Novelty check: new 18:23:59 DIRECTION Direction proposed: Exact computation for small n and induction with block decomposition 18:23:59 DIRECTION Direction assigned to GAUSS-01: Probabilistic construction with random multiples and density optimization 18:23:59 DIRECTION Direction assigned to GAUSS-02: Poset chain decomposition and weighted Dilworth-type bound 18:23:59 DIRECTION Direction assigned to GAUSS-03: Exact computation for small n and induction with block decomposition 18:23:59 TASK Task completed 18:26:41 TASK Research planning started 18:27:15 PLAN Research plan created Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
18:27:15
NOVELTY
Novelty check: new
18:27:15 DIRECTION Direction proposed: Exact brute-force and layered-construction benchmark for [1,N] and short intervals
18:27:15 MEMORY Novelty check: Lower-bound construction family from layered intervals with controlled multiple counts
18:27:15 NOVELTY Novelty check: partially explored
18:27:15 DIRECTION Direction proposed: Lower-bound construction family from layered intervals with controlled multiple counts
18:27:15 NOVELTY Novelty check: new
18:27:15 DIRECTION Direction proposed: Upper bound by grouping each element with its first two multiples and charging deletions
18:27:15 DIRECTION Direction assigned to GAUSS-01: Exact brute-force and layered-construction benchmark for [1,N] and short intervals
18:27:15 DIRECTION Direction assigned to GAUSS-02: Lower-bound construction family from layered intervals with controlled multiple counts
18:27:15 DIRECTION Direction assigned to GAUSS-03: Upper bound by grouping each element with its first two multiples and charging deletions
18:27:15 TASK Task completed
18:29:32 AGENT NOETHER stood down