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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 22.
Research chronicle 89 RECORDS
All Research Review Verification System
↑ 83 earlier records 18:53:53 §84
GAUSS-02 GAUSS-02 stood down
18:53:53 §85
GAUSS-03 GAUSS-03 stood down
18:53:53 §86
LITERATURE-01 LITERATURE-01 stood down
18:53:53 §87
ARES ARES stood down
18:53:53 §88
SYSTEM Research run finished
18:53:53 §89
SYSTEM Iteration 22 completed
Research graph / proof lineage 7 objects · 0 links · 9 in complete graph
DIRECTION
DIRECTION Probabilistic construction via random sparse sets COMPLETED DIRECTION Hypergraph container and extremal upper bound COMPLETED DIRECTION Computational search and inductive pattern discovery COMPLETED DIRECTION Exact computation of f(N) for N up to 200 and comparison with 2N/3 COMPLETED DIRECTION Chain-decomposition upper bound and Lean formalisation COMPLETED DIRECTION 2D grid upper bound and pattern-based lower bound improvement COMPLETED PROOF
PROOF Experiment report — For N up to 2000, compute the 2D-grid upper bound (sum over m coprime to 6 of th v1 MARKDOWN Explore complete graph / 16 objects → Research record
Agent record Close ×
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 22
Model calls 11
Estimated cost $0.0561 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 1,489
Cached input 0
Output tokens 1,248
Average latency 23.9 s
Failed calls 0
Cost (estimated) $0.000558
Joined 2026-09-25 18:50:26 UTC
Left 2026-09-25 18:53:53 UTC Recent activity 18:50:41 DIRECTION Direction proposed: Hypergraph container and extremal upper bound 18:50:41 NOVELTY Novelty check: new 18:50:41 DIRECTION Direction proposed: Computational search and inductive pattern discovery 18:50:41 DIRECTION Direction assigned to GAUSS-01: Probabilistic construction via random sparse sets 18:50:41 DIRECTION Direction assigned to GAUSS-02: Hypergraph container and extremal upper bound 18:50:41 DIRECTION Direction assigned to GAUSS-03: Computational search and inductive pattern discovery 18:50:41 TASK Task completed 18:52:04 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. 18:52:39
PLAN
Research plan created
18:52:39 NOVELTY Novelty check: new
18:52:39 DIRECTION Direction proposed: Exact computation of f(N) for N up to 200 and comparison with 2N/3
18:52:39 NOVELTY Novelty check: new
18:52:39 DIRECTION Direction proposed: Chain-decomposition upper bound and Lean formalisation
18:52:39 NOVELTY Novelty check: new
18:52:39 DIRECTION Direction proposed: 2D grid upper bound and pattern-based lower bound improvement
18:52:39 DIRECTION Direction assigned to GAUSS-01: Exact computation of f(N) for N up to 200 and comparison with 2N/3
18:52:39 DIRECTION Direction assigned to GAUSS-02: Chain-decomposition upper bound and Lean formalisation
18:52:39 DIRECTION Direction assigned to GAUSS-03: 2D grid upper bound and pattern-based lower bound improvement
18:52:39 TASK Task completed
18:53:53 AGENT NOETHER stood down