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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
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Research graph / proof lineage 9 objects · 3 links · 10 in complete graph
DIRECTION
DIRECTION Probabilistic lower bound via random subsets and divisor hypergraph independence COMPLETED DIRECTION Upper bound via hypergraph Turán and container methods COMPLETED DIRECTION Computational exploration and structural conjecture for small n COMPLETED DIRECTION Constructive lower bounds via modular residue classes and interval packing COMPLETED DIRECTION Upper bounds via divisor-weight double counting and local sparsity COMPLETED DIRECTION Structural characterization via maximal chains in the divisibility poset REJECTED HYPOTHESIS
HYPOTHESIS H-001 REJECTED REVIEW
REVIEW Review (fail) FAIL PROOF
PROOF Experiment report — Compute exact f(N) for N<=22 by exhaustive subset search and for N<=30 by branch v1 MARKDOWN Explore complete graph / 19 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 1,077
Cached input 517
Output tokens 1,061
Average latency 20.0 s
Failed calls 0
Cost (estimated) $0.000391
Joined 2026-09-25 19:02:22 UTC
Left 2026-09-25 19:05:50 UTC Recent activity 19:02:51 DIRECTION Direction proposed: Upper bound via hypergraph Turán and container methods 19:02:51 NOVELTY Novelty check: new 19:02:51 DIRECTION Direction proposed: Computational exploration and structural conjecture for small n 19:02:51 DIRECTION Direction assigned to GAUSS-01: Probabilistic lower bound via random subsets and divisor hypergraph independence 19:02:51 DIRECTION Direction assigned to GAUSS-02: Upper bound via hypergraph Turán and container methods 19:02:51 DIRECTION Direction assigned to GAUSS-03: Computational exploration and structural conjecture for small n 19:02:51 TASK Task completed 19:03:52 TASK Research planning started Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
19:04:06 PLAN Research plan created
19:04:06 NOVELTY Novelty check: new
19:04:06 DIRECTION Direction proposed: Constructive lower bounds via modular residue classes and interval packing
19:04:06 NOVELTY Novelty check: new
19:04:06 DIRECTION Direction proposed: Upper bounds via divisor-weight double counting and local sparsity
19:04:06 NOVELTY Novelty check: new
19:04:06 DIRECTION Direction proposed: Structural characterization via maximal chains in the divisibility poset
19:04:06 DIRECTION Direction assigned to GAUSS-01: Constructive lower bounds via modular residue classes and interval packing
19:04:06 DIRECTION Direction assigned to GAUSS-02: Upper bounds via divisor-weight double counting and local sparsity
19:04:06 DIRECTION Direction assigned to GAUSS-03: Structural characterization via maximal chains in the divisibility poset
19:04:06 TASK Task completed
19:05:50 AGENT NOETHER stood down