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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 8.
Research chronicle 92 RECORDS
All Research Review Verification System
↑ 86 earlier records 17:00:48 §87
NOETHER NOETHER stood down
17:00:48 §88
GAUSS-01 GAUSS-01 stood down
17:00:48 §89
GAUSS-03 GAUSS-03 stood down
17:00:48 §90
LITERATURE-01 LITERATURE-01 stood down
17:00:48 §91
SYSTEM Research run finished
17:00:48 §92
SYSTEM Iteration 8 completed
Research graph / proof lineage 7 objects · 0 links · 10 in complete graph
DIRECTION
DIRECTION Extremal density via double-counting over divisor chains COMPLETED DIRECTION Hypergraph independence number via container method COMPLETED DIRECTION Probabilistic construction and lower bound via random subsets with divisor-pair avoidance COMPLETED DIRECTION CRT residue-class decomposition and local forbidden-pattern bounds COMPLETED DIRECTION Recursive interval-splitting with rigorous upper bounds via dynamic programming REJECTED DIRECTION Spectral / Lagrangian relaxation on the divisor hypergraph via weighted Motzkin-Straus COMPLETED PROOF
PROOF CRT residue-class density check v1 MARKDOWN Explore complete graph / 17 objects → Research record
Agent record Close ×
Mission
Runtime 8 h 13 min
Iteration 34 of 34
Directions 193
Hypotheses 16
Experiments 143
Rejected paths 59 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 The corpus is not published by the engine.
Iteration 8
Model calls 16
Estimated cost $0.1684 Budget remaining 93%
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 1,078
Cached input 0
Output tokens 1,388
Average latency 16.9 s
Failed calls 0
Cost (estimated) $0.000540
Joined 2026-09-25 16:56:39 UTC
Left 2026-09-25 17:00:48 UTC Recent activity 16:57:04 DIRECTION Direction proposed: Hypergraph independence number via container method 16:57:04 NOVELTY Novelty check: new 16:57:04 DIRECTION Direction proposed: Probabilistic construction and lower bound via random subsets with divisor-pair avoidance 16:57:04 DIRECTION Direction assigned to GAUSS-01: Extremal density via double-counting over divisor chains 16:57:04 DIRECTION Direction assigned to GAUSS-02: Hypergraph independence number via container method 16:57:04 DIRECTION Direction assigned to GAUSS-03: Probabilistic construction and lower bound via random subsets with divisor-pair avoidance 16:57:04 TASK Task completed 16:58:21 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.
16:58:34 PLAN Research plan created
16:58:34 NOVELTY Novelty check: new
16:58:34 DIRECTION Direction proposed: CRT residue-class decomposition and local forbidden-pattern bounds
16:58:34 NOVELTY Novelty check: new
16:58:34 DIRECTION Direction proposed: Recursive interval-splitting with rigorous upper bounds via dynamic programming
16:58:34 NOVELTY Novelty check: new
16:58:34 DIRECTION Direction proposed: Spectral / Lagrangian relaxation on the divisor hypergraph via weighted Motzkin-Straus
16:58:34 DIRECTION Direction assigned to GAUSS-01: CRT residue-class decomposition and local forbidden-pattern bounds
16:58:34 DIRECTION Direction assigned to GAUSS-02: Recursive interval-splitting with rigorous upper bounds via dynamic programming
16:58:34 DIRECTION Direction assigned to GAUSS-03: Spectral / Lagrangian relaxation on the divisor hypergraph via weighted Motzkin-Straus
16:58:34 TASK Task completed
17:00:48 AGENT NOETHER stood down