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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 / 8 8 agents · 0 working
Frontier availability 09 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 12
Model calls 16
Estimated cost $0.0577 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 1,768
Cached input 0
Output tokens 1,270
Average latency 14.3 s
Failed calls 0
Cost (estimated) $0.000603
Joined 2026-09-25 18:05:10 UTC
Left 2026-09-25 18:08:56 UTC Recent activity 18:05:29 DIRECTION Direction proposed: Constructive lower bound via layered residue classes and interval packing 18:05:29 NOVELTY Novelty check: new 18:05:29 DIRECTION Direction proposed: Structural decomposition via divisor poset layers and matching theory 18:05:29 DIRECTION Direction assigned to GAUSS-01: Analytic upper bound via weighted divisor sums and averaging 18:05:29 DIRECTION Direction assigned to GAUSS-02: Constructive lower bound via layered residue classes and interval packing 18:05:29 DIRECTION Direction assigned to GAUSS-03: Structural decomposition via divisor poset layers and matching theory 18:05:29 TASK Task completed 18:07:08 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
18:07:21 PLAN Research plan created
18:07:21 NOVELTY Novelty check: new
18:07:21 DIRECTION Direction proposed: Exact computation of f(N) via correct brute force and ILP/SAT for N<=30
18:07:21 NOVELTY Novelty check: new
18:07:21 DIRECTION Direction proposed: Formalise the lower bound (N/3, N] and explore additive improvements in Lean
18:07:21 NOVELTY Novelty check: new
18:07:21 DIRECTION Direction proposed: Upper bounds via chain decompositions into m*2^j and m*2^i*3^j chains
18:07:21 DIRECTION Direction assigned to GAUSS-01: Exact computation of f(N) via correct brute force and ILP/SAT for N<=30
18:07:21 DIRECTION Direction assigned to GAUSS-02: Formalise the lower bound (N/3, N] and explore additive improvements in Lean
18:07:21 DIRECTION Direction assigned to GAUSS-03: Upper bounds via chain decompositions into m*2^j and m*2^i*3^j chains
18:07:21 TASK Task completed
18:08:56 AGENT NOETHER stood down