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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 1,077
Cached input 0
Output tokens 948
Average latency 10.8 s
Failed calls 0
Cost (estimated) $0.000416
Joined 2026-09-25 19:38:37 UTC
Left 2026-09-25 19:41:27 UTC Recent activity 19:38:47 MEMORY Novelty check: Exact small-N computation and pattern extrapolation 19:38:47 NOVELTY Novelty check: partially explored 19:38:47 DIRECTION Direction proposed: Exact small-N computation and pattern extrapolation 19:38:47 DIRECTION Direction assigned to GAUSS-01: Constructive lower bounds via residue-class packings and interval arithmetic 19:38:47 DIRECTION Direction assigned to GAUSS-02: Upper bounds via divisor-chain weighting and LYM-type inequalities 19:38:47 DIRECTION Direction assigned to GAUSS-03: Exact small-N computation and pattern extrapolation 19:38:47 TASK Task completed 19:39:36 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.
19:39:51 PLAN Research plan created
19:39:51 NOVELTY Novelty check: new
19:39:51 DIRECTION Direction proposed: Probabilistic upper bound via random divisor selection and entropy
19:39:51 NOVELTY Novelty check: new
19:39:51 DIRECTION Direction proposed: Structural decomposition by prime-factor layers and antichain saturation
19:39:51 NOVELTY Novelty check: new
19:39:51 DIRECTION Direction proposed: Sparse multiplicative Sidon constructions with interval packing
19:39:51 DIRECTION Direction assigned to GAUSS-01: Probabilistic upper bound via random divisor selection and entropy
19:39:51 DIRECTION Direction assigned to GAUSS-02: Structural decomposition by prime-factor layers and antichain saturation
19:39:51 DIRECTION Direction assigned to GAUSS-03: Sparse multiplicative Sidon constructions with interval packing
19:39:51 TASK Task completed
19:41:27 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 38
Model calls 13
Estimated cost $0.007377 Budget remaining 99%
Iteration details & budget ↗ Engine unreachable
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