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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 1,072
Cached input 0
Output tokens 1,188
Average latency 25.2 s
Failed calls 0
Cost (estimated) $0.000482
Joined 2026-09-25 19:55:29 UTC
Left 2026-09-25 19:57:46 UTC Recent activity 19:55:42 MEMORY Novelty check: Computational search and pattern extrapolation for small intervals 19:55:42 NOVELTY Novelty check: partially explored 19:55:42 DIRECTION Direction proposed: Computational search and pattern extrapolation for small intervals 19:55:42 DIRECTION Direction assigned to GAUSS-01: Density via multiplicative chains and interval blocking 19:55:42 DIRECTION Direction assigned to GAUSS-02: Extremal poset and divisor DAG matching bound 19:55:42 DIRECTION Direction assigned to GAUSS-03: Computational search and pattern extrapolation for small intervals 19:55:42 TASK Task completed 19:56:18 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.
19:56:57 PLAN Research plan created
19:56:57 NOVELTY Novelty check: new
19:56:57 DIRECTION Direction proposed: Random subset with dependent rounding and divisor-count weighting
19:56:57 NOVELTY Novelty check: new
19:56:57 DIRECTION Direction proposed: Spectral bound via the divisor incidence matrix
19:56:57 NOVELTY Novelty check: new
19:56:57 DIRECTION Direction proposed: Recursive interval splitting with weighted AM-GM on divisor counts
19:56:57 DIRECTION Direction assigned to GAUSS-01: Random subset with dependent rounding and divisor-count weighting
19:56:57 DIRECTION Direction assigned to GAUSS-02: Spectral bound via the divisor incidence matrix
19:56:57 DIRECTION Direction assigned to GAUSS-03: Recursive interval splitting with weighted AM-GM on divisor counts
19:56:57 TASK Task completed
19:57:46 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 44
Model calls 13
Estimated cost $0.007170 Budget remaining 99%
Iteration details & budget ↗ Engine unreachable
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