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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 1,080
Cached input 517
Output tokens 1,212
Average latency 10.3 s
Failed calls 0
Cost (estimated) $0.000434
Joined 2026-09-25 20:19:15 UTC
Left 2026-09-25 20:21:19 UTC Recent activity 20:19:25 NOVELTY Novelty check: new 20:19:25 DIRECTION Direction proposed: Exact computation and pattern detection for small n 20:19:25 DIRECTION Direction assigned to GAUSS-01: Density/entropy upper bound via random sampling and divisor graph 20:19:25 DIRECTION Direction assigned to GAUSS-02: Constructive lower bound via multiples of a large prime or near-n intervals 20:19:25 DIRECTION Direction assigned to GAUSS-03: Exact computation and pattern detection for small n 20:19:25 TASK Task completed 20:20:18 TASK Research planning started 20:20:32 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.
20:20:32
NOVELTY
Novelty check: new
20:20:32 DIRECTION Direction proposed: Poset chain-decomposition and LP dual upper bounds
20:20:32 MEMORY Novelty check: Residue-class and dyadic block decomposition
20:20:32 NOVELTY Novelty check: partially explored
20:20:32 DIRECTION Direction proposed: Residue-class and dyadic block decomposition
20:20:32 NOVELTY Novelty check: new
20:20:32 DIRECTION Direction proposed: Second-moment and divisor-sum analytic bounds
20:20:32 DIRECTION Direction assigned to GAUSS-01: Poset chain-decomposition and LP dual upper bounds
20:20:32 DIRECTION Direction assigned to GAUSS-02: Residue-class and dyadic block decomposition
20:20:32 DIRECTION Direction assigned to GAUSS-03: Second-moment and divisor-sum analytic bounds
20:20:32 TASK Task completed
20:21:19 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 54
Model calls 13
Estimated cost $0.006917 Budget remaining 99%
Iteration details & budget ↗ Engine unreachable
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