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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 48.
Research chronicle 93 RECORDS
All Research Review Verification System
↑ 87 earlier records 20:05:18 §88
GAUSS-01 GAUSS-01 stood down
20:05:18 §89
GAUSS-02 GAUSS-02 stood down
20:05:18 §90
GAUSS-03 GAUSS-03 stood down
20:05:18 §91
LITERATURE-01 LITERATURE-01 stood down
20:05:18 §92
SYSTEM Research run finished
20:05:18 §93
SYSTEM Iteration 48 completed
Research graph / proof lineage 7 objects · 0 links · 12 in complete graph
DIRECTION
DIRECTION Extremal density via chain-free poset and LYM-type inequalities COMPLETED DIRECTION Greedy/random construction and matching lower bounds COMPLETED DIRECTION Finite interval exact computation and pattern extrapolation COMPLETED DIRECTION Multiplicative Dilates and Interval Partition into Chains COMPLETED DIRECTION Fourier-Analytic and Additive-Combinatorial Bound via Divisor Graph Eigenvalues COMPLETED DIRECTION Probabilistic Method with Entropy and Local Centrality Constraints COMPLETED PROOF
PROOF Entropy/Shearer direction analysis v1 MARKDOWN Explore complete graph / 19 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 48
Model calls 13
Estimated cost $0.006627 Budget remaining 99%
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 1,077
Cached input 517
Output tokens 1,110
Average latency 7.2 s
Failed calls 0
Cost (estimated) $0.000404
Joined 2026-09-25 20:03:43 UTC
Left 2026-09-25 20:05:18 UTC Recent activity 20:03:50 DIRECTION Direction proposed: Greedy/random construction and matching lower bounds 20:03:50 NOVELTY Novelty check: new 20:03:50 DIRECTION Direction proposed: Finite interval exact computation and pattern extrapolation 20:03:50 DIRECTION Direction assigned to GAUSS-01: Extremal density via chain-free poset and LYM-type inequalities 20:03:50 DIRECTION Direction assigned to GAUSS-02: Greedy/random construction and matching lower bounds 20:03:50 DIRECTION Direction assigned to GAUSS-03: Finite interval exact computation and pattern extrapolation 20:03:50 TASK Task completed 20:04:31 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.
20:04:41 PLAN Research plan created
20:04:41 NOVELTY Novelty check: new
20:04:41 DIRECTION Direction proposed: Multiplicative Dilates and Interval Partition into Chains
20:04:41 NOVELTY Novelty check: new
20:04:41 DIRECTION Direction proposed: Fourier-Analytic and Additive-Combinatorial Bound via Divisor Graph Eigenvalues
20:04:41 NOVELTY Novelty check: new
20:04:41 DIRECTION Direction proposed: Probabilistic Method with Entropy and Local Centrality Constraints
20:04:41 DIRECTION Direction assigned to GAUSS-01: Multiplicative Dilates and Interval Partition into Chains
20:04:41 DIRECTION Direction assigned to GAUSS-02: Fourier-Analytic and Additive-Combinatorial Bound via Divisor Graph Eigenvalues
20:04:41 DIRECTION Direction assigned to GAUSS-03: Probabilistic Method with Entropy and Local Centrality Constraints
20:04:41 TASK Task completed
20:05:18 AGENT NOETHER stood down