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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
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Showing iteration 7.
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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 7 No frontier agent engaged
Model calls 44
Estimated cost $0.0449 Budget remaining 98%
Iteration details & budget ↗
Research graph / proof lineage 18 objects · 3 links · 8 in complete graph
DIRECTION
DIRECTION Poset & Chain Decomposition Bounds REJECTED DIRECTION Probabilistic Construction via Lovász Local Lemma REJECTED DIRECTION Greedy/Sieve Method with Harmonic Estimates REJECTED DIRECTION Divisor‑Graph Turán Approach COMPLETED DIRECTION Primitive‑Set Extension via Prime‑Factor Constraints REJECTED DIRECTION 3‑Uniform Hypergraph Turán / Dependent Random Choice COMPLETED DIRECTION Spectral bound on the divisor graph with out‑degree constraint REJECTED DIRECTION Mixed‑factor construction with large‑prime anchors REJECTED DIRECTION Exact ILP for moderate N and pattern extraction REJECTED DIRECTION Entropy‑Based Upper Bound via Shearer’s Inequality COMPLETED DIRECTION Largest‑Prime‑Factor Partition and Smooth‑Number Estimates REJECTED DIRECTION Exact Extremal Computation via SAT/SMT with Symmetry Breaking REJECTED DIRECTION Exponent‑vector antichain via Sperner theory REJECTED DIRECTION Adaptation of multiplicative Sidon set results REJECTED DIRECTION Recursive block decomposition and symmetry‑reduced integer programming REJECTED HYPOTHESIS
HYPOTHESIS H-001 REJECTED REVIEW
REVIEW Review (needs_work) NEEDS WORK PROOF
PROOF Experiment report — Verify that for all N ≤ 2000 the greedy set S_N satisfies |S_N| ≥ N / (3*log(N)) v1 MARKDOWN Explore complete graph / 26 objects → Research record
Agent record Close ×
NOETHER Strategist
Plan iteration 6
Blocked: The model returned an unusable response
Model
Model used together / openai/gpt-oss-120b
Routing profile cheap_reasoning
Usage
Model calls 8
Input tokens 6,147
Cached input 2,041
Output tokens 10,147
Average latency 10.7 s
Failed calls 3
Cost (estimated) $0.007011
Joined 2026-09-25 11:36:06 UTC
Left 2026-09-25 11:41:48 UTC Recent activity 11:39:45 NOVELTY Novelty check: new 11:39:45 DIRECTION Direction proposed: Exact Extremal Computation via SAT/SMT with Symmetry Breaking 11:39:45 DIRECTION Direction assigned to GAUSS-01: Entropy‑Based Upper Bound via Shearer’s Inequality 11:39:45 DIRECTION Direction assigned to GAUSS-02: Largest‑Prime‑Factor Partition and Smooth‑Number Estimates 11:39:45 DIRECTION Direction assigned to GAUSS-03: Exact Extremal Computation via SAT/SMT with Symmetry Breaking 11:39:45 TASK Task completed 11:40:29 TASK Research planning started 11:40:42 PLAN Research plan created 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. 11:40:42
NOVELTY
Novelty check: new
11:40:42 DIRECTION Direction proposed: Exponent‑vector antichain via Sperner theory
11:40:42 NOVELTY Novelty check: new
11:40:42 DIRECTION Direction proposed: Adaptation of multiplicative Sidon set results
11:40:42 NOVELTY Novelty check: new
11:40:42 DIRECTION Direction proposed: Recursive block decomposition and symmetry‑reduced integer programming
11:40:42 DIRECTION Direction assigned to GAUSS-01: Exponent‑vector antichain via Sperner theory
11:40:42 DIRECTION Direction assigned to GAUSS-02: Adaptation of multiplicative Sidon set results
11:40:42 DIRECTION Direction assigned to GAUSS-03: Recursive block decomposition and symmetry‑reduced integer programming
11:40:42 TASK Task completed
11:41:21 TASK Research planning started
11:41:48 TASK Task completed