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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 49.
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Mission
Runtime 9 h 14 min
Iteration 57 of 57
Directions 331
Hypotheses 17
Experiments 266
Rejected paths 64 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 109
Highly relevant 1 Iteration 49
Model calls 14
Estimated cost $0.006734 Budget remaining 99%
Iteration details & budget ↗
Research graph / proof lineage 7 objects · 0 links · 11 in complete graph
DIRECTION
DIRECTION Density and entropy via random subsets and divisor graph VC-dimension COMPLETED DIRECTION Constructive families via large primes and multiplicative shifts COMPLETED DIRECTION Exact values for small n via ILP and induction with a structural lemma COMPLETED DIRECTION Recursive interval-splitting with divisor-counting potential COMPLETED DIRECTION Hypergraph matching/covering on the divisibility poset COMPLETED DIRECTION CRT-based modular construction for large valid subsets COMPLETED PROOF
PROOF Dyadic-block lemma and recurrence check v1 MARKDOWN Explore complete graph / 18 objects → Research record
Agent record Close ×
NOETHER Strategist
Plan iteration 2
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,081
Cached input 517
Output tokens 1,137
Average latency 26.7 s
Failed calls 0
Cost (estimated) $0.000412
Joined 2026-09-25 20:05:20 UTC
Left 2026-09-25 20:09:18 UTC Recent activity 20:05:53 DIRECTION Direction proposed: Constructive families via large primes and multiplicative shifts 20:05:53 NOVELTY Novelty check: new 20:05:53 DIRECTION Direction proposed: Exact values for small n via ILP and induction with a structural lemma 20:05:53 DIRECTION Direction assigned to GAUSS-01: Density and entropy via random subsets and divisor graph VC-dimension 20:05:53 DIRECTION Direction assigned to GAUSS-02: Constructive families via large primes and multiplicative shifts 20:05:53 DIRECTION Direction assigned to GAUSS-03: Exact values for small n via ILP and induction with a structural lemma 20:05:53 TASK Task completed 20:07:58 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.
07 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration.
20:08:21 PLAN Research plan created
20:08:21 NOVELTY Novelty check: new
20:08:21 DIRECTION Direction proposed: Recursive interval-splitting with divisor-counting potential
20:08:21 NOVELTY Novelty check: new
20:08:21 DIRECTION Direction proposed: Hypergraph matching/covering on the divisibility poset
20:08:21 NOVELTY Novelty check: new
20:08:21 DIRECTION Direction proposed: CRT-based modular construction for large valid subsets
20:08:21 DIRECTION Direction assigned to GAUSS-01: Recursive interval-splitting with divisor-counting potential
20:08:21 DIRECTION Direction assigned to GAUSS-02: Hypergraph matching/covering on the divisibility poset
20:08:21 DIRECTION Direction assigned to GAUSS-03: CRT-based modular construction for large valid subsets
20:08:21 TASK Task completed
20:09:18 AGENT NOETHER stood down