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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
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.
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 1,075
Cached input 517
Output tokens 970
Average latency 11.0 s
Failed calls 0
Cost (estimated) $0.000365
Joined 2026-09-25 20:01:35 UTC
Left 2026-09-25 20:03:41 UTC Recent activity 20:01:51 DIRECTION Direction proposed: Constructive lower bound from geometric progressions and residue classes 20:01:51 NOVELTY Novelty check: new 20:01:51 DIRECTION Direction proposed: Exact computation for small n and pattern-driven conjecture 20:01:51 DIRECTION Direction assigned to GAUSS-01: Probabilistic upper bound via weighted divisor counting 20:01:51 DIRECTION Direction assigned to GAUSS-02: Constructive lower bound from geometric progressions and residue classes 20:01:51 DIRECTION Direction assigned to GAUSS-03: Exact computation for small n and pattern-driven conjecture 20:01:51 TASK Task completed 20:02:37 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.
20:02:46 PLAN Research plan created
20:02:46 NOVELTY Novelty check: new
20:02:46 DIRECTION Direction proposed: Weighted entropy upper bound via divisor chains
20:02:46 NOVELTY Novelty check: new
20:02:46 DIRECTION Direction proposed: Recursive interval splitting and extremal recurrence
20:02:46 NOVELTY Novelty check: new
20:02:46 DIRECTION Direction proposed: Lower bound from semiprime and almost-prime families
20:02:46 DIRECTION Direction assigned to GAUSS-01: Weighted entropy upper bound via divisor chains
20:02:46 DIRECTION Direction assigned to GAUSS-02: Recursive interval splitting and extremal recurrence
20:02:46 DIRECTION Direction assigned to GAUSS-03: Lower bound from semiprime and almost-prime families
20:02:46 TASK Task completed
20:03:41 AGENT NOETHER stood down 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 47
Model calls 12
Estimated cost $0.005795 Budget remaining 99%
Iteration details & budget ↗ Engine unreachable
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