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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
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.
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 1,466
Cached input 0
Output tokens 1,287
Average latency 27.3 s
Failed calls 0
Cost (estimated) $0.000565
Joined 2026-09-25 18:35:44 UTC
Left 2026-09-25 18:39:36 UTC Recent activity 18:36:14 DIRECTION Direction proposed: Density/entropy approach via random subsets and multiplicative structure 18:36:14 NOVELTY Novelty check: new 18:36:14 DIRECTION Direction proposed: Computational search and induction for small intervals to guess exact extremal function 18:36:14 DIRECTION Direction assigned to GAUSS-01: Extremal construction and divisor-chain counting upper bound 18:36:14 DIRECTION Direction assigned to GAUSS-02: Density/entropy approach via random subsets and multiplicative structure 18:36:14 DIRECTION Direction assigned to GAUSS-03: Computational search and induction for small intervals to guess exact extremal function 18:36:14 TASK Task completed 18:37:49 TASK Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
Research planning started
18:38:16 PLAN Research plan created
18:38:16 NOVELTY Novelty check: new
18:38:16 DIRECTION Direction proposed: Exact f(N) for N up to 30 and canonical problem statement
18:38:16 NOVELTY Novelty check: new
18:38:16 DIRECTION Direction proposed: Per-chain upper bound via 2^a 3^b m decomposition
18:38:16 NOVELTY Novelty check: new
18:38:16 DIRECTION Direction proposed: Literature check and comparison against ceil(2N/3) baseline
18:38:16 DIRECTION Direction assigned to GAUSS-01: Exact f(N) for N up to 30 and canonical problem statement
18:38:16 DIRECTION Direction assigned to GAUSS-02: Per-chain upper bound via 2^a 3^b m decomposition
18:38:16 DIRECTION Direction assigned to GAUSS-03: Literature check and comparison against ceil(2N/3) baseline
18:38:16 TASK Task completed
18:39:36 AGENT NOETHER stood down 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 19
Model calls 11
Estimated cost $0.0475 Budget remaining 98%
Iteration details & budget ↗ Engine unreachable
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