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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 3.
Research chronicle 117 RECORDS
All Research Review Verification System
↑ 111 earlier records 11:20:42 §112
GAUSS-02 GAUSS-02 stood down
11:20:42 §113
LITERATURE-01 LITERATURE-01 stood down
11:20:42 §114
LITERATURE-02 LITERATURE-02 stood down
11:20:42 §115
TURING TURING stood down
11:20:42 §116
SYSTEM Research run finished
11:20:42 §117
SYSTEM Iteration 3 completed
Research graph / proof lineage 9 objects · 3 links · 8 in complete graph
DIRECTION
DIRECTION Poset‑Chain Decomposition and Dilworth‑type Upper Bounds REJECTED DIRECTION Probabilistic Construction via Lovász Local Lemma REJECTED DIRECTION Arithmetic Construction Using Large Prime Factors and Sieve Estimates REJECTED DIRECTION Smooth‑Number Lattice Decomposition REJECTED DIRECTION 3‑Uniform Hypergraph Turán Method COMPLETED DIRECTION Exact Computation and Pattern Extraction REJECTED HYPOTHESIS
HYPOTHESIS H-001 REJECTED REVIEW
REVIEW Review (needs_work) NEEDS WORK PROOF
PROOF Greedy sizes for selected N v1 MARKDOWN Explore complete graph / 17 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 3 No frontier agent engaged
Model calls 19
Estimated cost $0.0158 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 1,340
Cached input 136
Output tokens 1,763
Average latency 8.2 s
Failed calls 0
Cost (estimated) $0.001259
Joined 2026-09-25 11:18:29 UTC
Left 2026-09-25 11:20:42 UTC Recent activity 11:18:41 DIRECTION Direction proposed: Probabilistic Construction via Lovász Local Lemma 11:18:41 NOVELTY Novelty check: new 11:18:41 DIRECTION Direction proposed: Arithmetic Construction Using Large Prime Factors and Sieve Estimates 11:18:41 DIRECTION Direction assigned to GAUSS-01: Poset‑Chain Decomposition and Dilworth‑type Upper Bounds 11:18:41 DIRECTION Direction assigned to GAUSS-02: Probabilistic Construction via Lovász Local Lemma 11:18:41 DIRECTION Direction assigned to GAUSS-03: Arithmetic Construction Using Large Prime Factors and Sieve Estimates 11:18:41 TASK Task completed 11:19:44 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.
11:19:51 PLAN Research plan created
11:19:51 NOVELTY Novelty check: new
11:19:51 DIRECTION Direction proposed: Smooth‑Number Lattice Decomposition
11:19:51 NOVELTY Novelty check: new
11:19:51 DIRECTION Direction proposed: 3‑Uniform Hypergraph Turán Method
11:19:51 NOVELTY Novelty check: new
11:19:51 DIRECTION Direction proposed: Exact Computation and Pattern Extraction
11:19:51 DIRECTION Direction assigned to GAUSS-01: Smooth‑Number Lattice Decomposition
11:19:51 DIRECTION Direction assigned to GAUSS-02: 3‑Uniform Hypergraph Turán Method
11:19:51 DIRECTION Direction assigned to GAUSS-03: Exact Computation and Pattern Extraction
11:19:51 TASK Task completed
11:20:42 AGENT NOETHER stood down