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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
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 ↗
NOETHER Strategist
Plan iteration 2
Model
Model used together / openai/gpt-oss-120b
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,188
Cached input 132
Output tokens 1,752
Average latency 9.0 s
Failed calls 0
Cost (estimated) $0.001229
Joined 2026-09-25 11:13:58 UTC
Left 2026-09-25 11:16:14 UTC Recent activity 11:14:09 DIRECTION Direction proposed: Probabilistic Construction and Alteration 11:14:09 NOVELTY Novelty check: new 11:14:09 DIRECTION Direction proposed: Computational Exploration and Greedy Algorithms 11:14:09 DIRECTION Direction assigned to GAUSS-01: Poset and Antichain Analysis via Dilworth and Sperner 11:14:09 DIRECTION Direction assigned to GAUSS-02: Probabilistic Construction and Alteration 11:14:09 DIRECTION Direction assigned to GAUSS-03: Computational Exploration and Greedy Algorithms 11:14:09 TASK Task completed 11:14:59 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.
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
PLAN
Research plan created
11:15:09 NOVELTY Novelty check: new
11:15:09 DIRECTION Direction proposed: Analytic Number Theory via Divisor Summatory Functions
11:15:09 NOVELTY Novelty check: new
11:15:09 DIRECTION Direction proposed: Prime‑Factor Profile Decomposition and Large‑Prime‑Factor Sets
11:15:09 NOVELTY Novelty check: new
11:15:09 DIRECTION Direction proposed: Hypergraph Turán Theory on the Divisor 3‑Uniform Hypergraph
11:15:09 DIRECTION Direction assigned to GAUSS-01: Analytic Number Theory via Divisor Summatory Functions
11:15:09 DIRECTION Direction assigned to GAUSS-02: Prime‑Factor Profile Decomposition and Large‑Prime‑Factor Sets
11:15:09 DIRECTION Direction assigned to GAUSS-03: Hypergraph Turán Theory on the Divisor 3‑Uniform Hypergraph
11:15:09 TASK Task completed
11:16:14 AGENT NOETHER stood down