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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 1,076
Cached input 517
Output tokens 973
Average latency 9.1 s
Failed calls 0
Cost (estimated) $0.000366
Joined 2026-09-25 20:14:42 UTC
Left 2026-09-25 20:16:42 UTC Recent activity 20:14:54 NOVELTY Novelty check: new 20:14:54 DIRECTION Direction proposed: Exact extremal computation for small intervals and pattern detection 20:14:54 DIRECTION Direction assigned to GAUSS-01: Random greedy and probabilistic lower bound constructions 20:14:54 DIRECTION Direction assigned to GAUSS-02: Weighted chain/LYM-type upper bound on the divisor poset 20:14:54 DIRECTION Direction assigned to GAUSS-03: Exact extremal computation for small intervals and pattern detection 20:14:54 TASK Task completed 20:15:38 TASK Research planning started 20:15:47 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.
20:15:47
MEMORY
Novelty check: Block-product lower bound via residue classes and CRT
20:15:47 NOVELTY Novelty check: partially explored
20:15:47 DIRECTION Direction proposed: Block-product lower bound via residue classes and CRT
20:15:47 NOVELTY Novelty check: new
20:15:47 DIRECTION Direction proposed: Upper bound via interval partition into divisor-free layers
20:15:47 NOVELTY Novelty check: new
20:15:47 DIRECTION Direction proposed: Recursive interval-splitting with formalized certificates
20:15:47 DIRECTION Direction assigned to GAUSS-01: Block-product lower bound via residue classes and CRT
20:15:47 DIRECTION Direction assigned to GAUSS-02: Upper bound via interval partition into divisor-free layers
20:15:47 DIRECTION Direction assigned to GAUSS-03: Recursive interval-splitting with formalized certificates
20:15:47 TASK Task completed
20:16:42 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 52
Model calls 13
Estimated cost $0.006897 Budget remaining 99%
Iteration details & budget ↗ Engine unreachable
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