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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 record
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Frontier availability 07 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration. 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 27
Model calls 13
Estimated cost $0.006045 Budget remaining 99%
Iteration details & budget ↗
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 1,036
Average latency 18.5 s
Failed calls 0
Cost (estimated) $0.000384
Joined 2026-09-25 19:05:52 UTC
Left 2026-09-25 19:08:55 UTC Recent activity 19:06:10 DIRECTION Direction proposed: Poset width and chain decomposition on the divisibility poset 19:06:10 NOVELTY Novelty check: new 19:06:10 DIRECTION Direction proposed: Exact computation for small intervals and pattern extrapolation 19:06:10 DIRECTION Direction assigned to GAUSS-01: Density and residue-class upper bounds via modular sieving 19:06:10 DIRECTION Direction assigned to GAUSS-02: Poset width and chain decomposition on the divisibility poset 19:06:10 DIRECTION Direction assigned to GAUSS-03: Exact computation for small intervals and pattern extrapolation 19:06:10 TASK Task completed 19:07:06 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.
19:07:28 PLAN Research plan created
19:07:28 NOVELTY Novelty check: new
19:07:28 DIRECTION Direction proposed: Weighted LYM-type inequality on prime-exponent vectors
19:07:28 NOVELTY Novelty check: new
19:07:28 DIRECTION Direction proposed: Recursive odd-part and power-of-2 splitting with two-parameter DP
19:07:28 NOVELTY Novelty check: new
19:07:28 DIRECTION Direction proposed: Entropy / probabilistic method with random multiples and union bound
19:07:28 DIRECTION Direction assigned to GAUSS-01: Weighted LYM-type inequality on prime-exponent vectors
19:07:28 DIRECTION Direction assigned to GAUSS-02: Recursive odd-part and power-of-2 splitting with two-parameter DP
19:07:28 DIRECTION Direction assigned to GAUSS-03: Entropy / probabilistic method with random multiples and union bound
19:07:28 TASK Task completed
19:08:55 AGENT NOETHER stood down