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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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AGENTS / 6 6 agents · 0 working
Frontier availability 07 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration. Mission
Runtime 8 h 14 min
Iteration 34 of 34
Directions 196
Hypotheses 16
Experiments 145
Rejected paths 59 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 73
Highly relevant 1 Iteration 10
Model calls 13
Estimated cost $0.0524 Budget remaining 97%
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 1,450
Cached input 0
Output tokens 1,104
Average latency 13.9 s
Failed calls 0
Cost (estimated) $0.000512
Joined 2026-09-25 17:26:09 UTC
Left 2026-09-25 18:00:49 UTC Recent activity 17:26:27 DIRECTION Direction proposed: Explicit construction via residue classes and interval packing 17:26:27 NOVELTY Novelty check: new 17:26:27 DIRECTION Direction proposed: Computational search and pattern extrapolation for exact small-n values 17:26:27 DIRECTION Direction assigned to GAUSS-01: Probabilistic upper bound via divisor-count concentration 17:26:27 DIRECTION Direction assigned to GAUSS-02: Explicit construction via residue classes and interval packing 17:26:27 DIRECTION Direction assigned to GAUSS-03: Computational search and pattern extrapolation for exact small-n values 17:26:27 TASK Task completed 17:59:44 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.
17:59:57 PLAN Research plan created
17:59:57 NOVELTY Novelty check: new
17:59:57 DIRECTION Direction proposed: Exact solver for f(N) and interval variants via ILP/SAT
17:59:57 NOVELTY Novelty check: new
17:59:57 DIRECTION Direction proposed: Construction: verify (N/3, N] and add lower layers for density above 2/3
17:59:57 NOVELTY Novelty check: new
17:59:57 DIRECTION Direction proposed: Upper bound via chain decomposition into m·2^i·3^j families and literature search
17:59:57 DIRECTION Direction assigned to GAUSS-01: Exact solver for f(N) and interval variants via ILP/SAT
17:59:57 DIRECTION Direction assigned to GAUSS-02: Construction: verify (N/3, N] and add lower layers for density above 2/3
17:59:57 DIRECTION Direction assigned to GAUSS-03: Upper bound via chain decomposition into m·2^i·3^j families and literature search
17:59:57 TASK Task completed
18:00:49 AGENT NOETHER stood down