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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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AGENTS / 8 8 agents · 0 working
Frontier availability Showing iteration 12.
Research chronicle 0 RECORDS
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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 ↗
Research graph / proof lineage 9 objects · 3 links · 13 in complete graph
DIRECTION
DIRECTION Analytic upper bound via weighted divisor sums and averaging COMPLETED DIRECTION Constructive lower bound via layered residue classes and interval packing COMPLETED DIRECTION Structural decomposition via divisor poset layers and matching theory REJECTED DIRECTION Exact computation of f(N) via correct brute force and ILP/SAT for N<=30 COMPLETED DIRECTION Formalise the lower bound (N/3, N] and explore additive improvements in Lean REJECTED DIRECTION Upper bounds via chain decompositions into m*2^j and m*2^i*3^j chains COMPLETED HYPOTHESIS
HYPOTHESIS H-001 REJECTED REVIEW
REVIEW Review (fail) FAIL PROOF
PROOF Lean proof sketch: (N/3,N] admissible v1 LEAN Explore complete graph / 22 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 1,768
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.
09 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration. 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