Skip to content
How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
AGENTS / 7 7 agents · 0 working
Frontier availability Showing iteration 1.
Research chronicle 104 RECORDS
All Research Review Verification System
↑ 98 earlier records 11:16:14 §99
GAUSS-03 GAUSS-03 stood down
11:16:14 §100
LITERATURE-01 LITERATURE-01 stood down
11:16:14 §101
LITERATURE-02 LITERATURE-02 stood down
11:16:14 §102
TURING TURING stood down
11:16:14 §103
SYSTEM Research run finished
11:16:14 §104
SYSTEM Iteration 1 completed
Research graph / proof lineage 9 objects · 3 links · 5 in complete graph
DIRECTION
DIRECTION Poset and Antichain Analysis via Dilworth and Sperner REJECTED DIRECTION Probabilistic Construction and Alteration REJECTED DIRECTION Computational Exploration and Greedy Algorithms REJECTED DIRECTION Analytic Number Theory via Divisor Summatory Functions REJECTED DIRECTION Prime‑Factor Profile Decomposition and Large‑Prime‑Factor Sets REJECTED DIRECTION Hypergraph Turán Theory on the Divisor 3‑Uniform Hypergraph COMPLETED HYPOTHESIS
HYPOTHESIS H-001 REJECTED REVIEW
REVIEW Review (needs_work) NEEDS WORK PROOF
PROOF Experiment report — Compute the exact maximum size f(N) for N ≤ 30 for the property that no element v1 MARKDOWN Explore complete graph / 14 objects → Research record
Agent record Close ×
Mission
Runtime 5 h 32 min
Iteration 7 of 7
Directions 33
Hypotheses 7
Experiments 3
Rejected paths 34 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 18
Highly relevant 0 Iteration 1 No frontier agent engaged
Model calls 18
Estimated cost $0.0161 Budget remaining 99%
Iteration details & budget ↗
LITERATURE-02 Literature researcher
Checking prior art and known barriers for: Maximum size ≈ N/2
Model
Model used together / openai/gpt-oss-120b
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,976
Cached input 132
Output tokens 636
Average latency 3.0 s
Failed calls 0
Cost (estimated) $0.000678
Joined 2026-09-25 11:15:37 UTC
Left 2026-09-25 11:16:14 UTC Recent activity 11:15:37 AGENT LITERATURE-02 joined as Literature Researcher 11:15:37 LITERATURE Literature search started 11:15:37 LITERATURE Indexed: Asymptotic Formulae for Restricted Unimodal Sequences 11:15:37 LITERATURE Indexed: Covering systems with restricted divisibility 11:15:37 LITERATURE Indexed: Asymptotic Results for Class Number Divisibility in Cyclotomic Fields 11:15:37 LITERATURE Literature search: 3 new of 3 11:15:37 LITERATURE Reviewed: Asymptotic Formulae for Restricted Unimodal Sequences 11:15:37 MEMORY Literature: Asymptotic Formulae for Restricted Unimodal Sequences Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
08 Research director Not started On the roster; the workflow has not woken it in this iteration. 09 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration. 11:15:52
LITERATURE
Literature search started
11:15:52 LITERATURE Indexed: Figure 2: Barnacle density and maximum body size.
11:15:52 LITERATURE Indexed: Estimation of Population Size Using Sample Maximum
11:15:52 LITERATURE Indexed: Review for "The Relationship Between Maturation Size and Maximum Tree Size From Tropical to Boreal Climates"
11:15:52 LITERATURE Literature search: 3 new of 3
11:15:52 LITERATURE Reviewed: Figure 2: Barnacle density and maximum body size.
11:15:52 MEMORY Literature: Figure 2: Barnacle density and maximum body size.
11:16:14 AGENT LITERATURE-02 stood down