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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
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LITERATURE-01 LITERATURE-01 stood down
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LITERATURE-02 LITERATURE-02 stood down
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TURING TURING stood down
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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-01 Literature researcher
Reading the landscape around: Analytic Number Theory via Divisor Summatory Functions
Model
Model used together / openai/gpt-oss-120b
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,989
Cached input 132
Output tokens 1,003
Average latency 4.3 s
Failed calls 0
Cost (estimated) $0.000900
Joined 2026-09-25 11:14:09 UTC
Left 2026-09-25 11:16:14 UTC Recent activity 11:14:09 AGENT LITERATURE-01 joined as Literature Researcher 11:14:09 LITERATURE Literature search started 11:14:09 LITERATURE Indexed: Families of chains of a poset and Sperner properties 11:14:09 LITERATURE Indexed: No Finite–Infinite Antichain Duality in the Homomorphism Poset of Directed Graphs 11:14:09 LITERATURE Indexed: A chain complete poset with no infinite antichain has a finite core 11:14:09 LITERATURE Literature search: 3 new of 3 11:14:09 LITERATURE Reviewed: Families of chains of a poset and Sperner properties 11:14:09 MEMORY Literature: Families of chains of a poset and Sperner properties 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. 11:15:09
LITERATURE
Literature search started
11:15:09 LITERATURE Indexed: Summatory Functions
11:15:09 LITERATURE Indexed: Summatory Functions
11:15:09 LITERATURE Indexed: On the representation of the summatory functions of a class of arithmetical functions
11:15:09 LITERATURE Literature search: 3 new of 3
11:15:09 LITERATURE Reviewed: Summatory Functions
11:15:09 MEMORY Literature: Summatory Functions
11:16:14 AGENT LITERATURE-01 stood down