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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
AGENTS / 6 6 agents · 0 working
Frontier availability Showing iteration 14.
Research chronicle 90 RECORDS
All Research Review Verification System
18:13:19 §1
SYSTEM Iteration 14 opened
18:13:22 §2
SYSTEM Iteration 14 started
18:13:22 §3
SYSTEM Initializing research run
18:13:22 §4
NOETHER NOETHER joined as Strategist
18:13:22 §5
SYSTEM Research started
18:13:23 §6
NOETHER Research planning started
↑ 84 earlier records 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 3
Input tokens 1,464
Cached input 0
Output tokens 1,155
Average latency 29.7 s
Failed calls 1
Cost (estimated) $0.000529
Joined 2026-09-25 18:13:22 UTC
Left 2026-09-25 18:17:07 UTC Recent activity 18:13:33 DIRECTION Direction proposed: Constructive lower bound via layered sets and density optimization 18:13:33 NOVELTY Novelty check: new 18:13:33 DIRECTION Direction proposed: Computational search and ILP extrapolation for exact small-n values 18:13:33 DIRECTION Direction assigned to GAUSS-01: Probabilistic upper bound via random weights and divisor moments 18:13:33 DIRECTION Direction assigned to GAUSS-02: Constructive lower bound via layered sets and density optimization 18:13:33 DIRECTION Direction assigned to GAUSS-03: Computational search and ILP extrapolation for exact small-n values 18:13:33 TASK Task completed 18:14:31 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.
07 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration.
18:15:53 PLAN Research plan created
18:15:53 NOVELTY Novelty check: new
18:15:53 DIRECTION Direction proposed: Exact f(N) via SAT/ILP with a fixed execution environment
18:15:53 NOVELTY Novelty check: new
18:15:53 DIRECTION Direction proposed: Rigorous lower bound via modified (N/3,N] interval with Lean verification
18:15:53 NOVELTY Novelty check: new
18:15:53 DIRECTION Direction proposed: LP-duality upper bound on odd-part chains with 3-adic interactions
18:15:53 DIRECTION Direction assigned to GAUSS-01: Exact f(N) via SAT/ILP with a fixed execution environment
18:15:53 DIRECTION Direction assigned to GAUSS-02: Rigorous lower bound via modified (N/3,N] interval with Lean verification
18:15:53 DIRECTION Direction assigned to GAUSS-03: LP-duality upper bound on odd-part chains with 3-adic interactions
18:15:53 TASK Task completed
18:17:07 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 14
Model calls 12
Estimated cost $0.0476 Budget remaining 98%
Iteration details & budget ↗
Research graph / proof lineage 7 objects · 0 links · 9 in complete graph
DIRECTION
DIRECTION Probabilistic upper bound via random weights and divisor moments COMPLETED DIRECTION Constructive lower bound via layered sets and density optimization COMPLETED DIRECTION Computational search and ILP extrapolation for exact small-n values COMPLETED DIRECTION Exact f(N) via SAT/ILP with a fixed execution environment COMPLETED DIRECTION Rigorous lower bound via modified (N/3,N] interval with Lean verification COMPLETED DIRECTION LP-duality upper bound on odd-part chains with 3-adic interactions COMPLETED PROOF
PROOF LP-duality experiment output v1 MARKDOWN Explore complete graph / 16 objects →