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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 517
Output tokens 1,226
Average latency 14.2 s
Failed calls 0
Cost (estimated) $0.000436
Joined 2026-09-25 19:24:19 UTC
Left 2026-09-25 19:27:00 UTC Recent activity 19:24:35 NOVELTY Novelty check: new 19:24:35 DIRECTION Direction proposed: Computational search for extremal sets and pattern extrapolation 19:24:35 DIRECTION Direction assigned to GAUSS-01: Constructive interval packing with modular residue classes 19:24:35 DIRECTION Direction assigned to GAUSS-02: Poset width and divisor-chain upper bound 19:24:35 DIRECTION Direction assigned to GAUSS-03: Computational search for extremal sets and pattern extrapolation 19:24:35 TASK Task completed 19:25:54 TASK Research planning started 19:26:10 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.
19:26:10
MEMORY
Novelty check: Probabilistic density bound via dependent rounding on divisor chains
19:26:10 NOVELTY Novelty check: partially explored
19:26:10 DIRECTION Direction proposed: Probabilistic density bound via dependent rounding on divisor chains
19:26:10 NOVELTY Novelty check: new
19:26:10 DIRECTION Direction proposed: LP dual certificate with divisor-chain weights
19:26:10 NOVELTY Novelty check: new
19:26:10 DIRECTION Direction proposed: Recursive interval splitting with two-level divisibility constraints
19:26:10 DIRECTION Direction assigned to GAUSS-01: Probabilistic density bound via dependent rounding on divisor chains
19:26:10 DIRECTION Direction assigned to GAUSS-02: LP dual certificate with divisor-chain weights
19:26:10 DIRECTION Direction assigned to GAUSS-03: Recursive interval splitting with two-level divisibility constraints
19:26:10 TASK Task completed
19:27:00 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 33
Model calls 12
Estimated cost $0.006367 Budget remaining 99%
Iteration details & budget ↗ Engine unreachable
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