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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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Research record
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Frontier availability 07 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration. 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 46
Model calls 12
Estimated cost $0.006373 Budget remaining 99%
Iteration details & budget ↗
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 1,072
Cached input 517
Output tokens 1,055
Average latency 9.4 s
Failed calls 0
Cost (estimated) $0.000389
Joined 2026-09-25 19:59:30 UTC
Left 2026-09-25 20:01:33 UTC Recent activity 19:59:39 DIRECTION Direction proposed: Constructive lower bound from prime-power layers 19:59:39 NOVELTY Novelty check: new 19:59:39 DIRECTION Direction proposed: Exact small-n computation and extremal pattern extraction 19:59:39 DIRECTION Direction assigned to GAUSS-01: Probabilistic upper bound via divisor-count weighting 19:59:39 DIRECTION Direction assigned to GAUSS-02: Constructive lower bound from prime-power layers 19:59:39 DIRECTION Direction assigned to GAUSS-03: Exact small-n computation and extremal pattern extraction 19:59:39 TASK Task completed 20:00:15 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.
20:00:29
PLAN
Research plan created
20:00:29 NOVELTY Novelty check: new
20:00:29 DIRECTION Direction proposed: Weighted density upper bound via divisor-chain penalties
20:00:29 NOVELTY Novelty check: new
20:00:29 DIRECTION Direction proposed: Block decomposition into divisor-closed intervals
20:00:29 NOVELTY Novelty check: new
20:00:29 DIRECTION Direction proposed: Greedy removal and potential-function lower bound
20:00:29 DIRECTION Direction assigned to GAUSS-01: Weighted density upper bound via divisor-chain penalties
20:00:29 DIRECTION Direction assigned to GAUSS-02: Block decomposition into divisor-closed intervals
20:00:29 DIRECTION Direction assigned to GAUSS-03: Greedy removal and potential-function lower bound
20:00:29 TASK Task completed
20:01:33 AGENT NOETHER stood down