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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 20.
Research chronicle 87 RECORDS
All Research Review Verification System
↑ 81 earlier records 18:46:44 §82
GAUSS-02 GAUSS-02 stood down
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GAUSS-03 GAUSS-03 stood down
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LITERATURE-01 LITERATURE-01 stood down
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ARES ARES stood down
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SYSTEM Research run finished
18:46:44 §87
SYSTEM Iteration 20 completed
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Research record
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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 20
Model calls 15
Estimated cost $0.0497 Budget remaining 98%
Iteration details & budget ↗
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 1,473
Cached input 0
Output tokens 1,249
Average latency 25.4 s
Failed calls 0
Cost (estimated) $0.000556
Joined 2026-09-25 18:39:40 UTC
Left 2026-09-25 18:46:44 UTC Recent activity 18:40:07 DIRECTION Direction proposed: Extremal poset and matching approach via divisor lattice 18:40:07 NOVELTY Novelty check: new 18:40:07 DIRECTION Direction proposed: Computational search and pattern extrapolation for small n 18:40:07 DIRECTION Direction assigned to GAUSS-01: Probabilistic construction via random sampling and divisor-pair constraints 18:40:07 DIRECTION Direction assigned to GAUSS-02: Extremal poset and matching approach via divisor lattice 18:40:07 DIRECTION Direction assigned to GAUSS-03: Computational search and pattern extrapolation for small n 18:40:07 TASK Task completed 18:42:43 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.
07 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration.
18:43:09 PLAN Research plan created
18:43:09 NOVELTY Novelty check: new
18:43:09 DIRECTION Direction proposed: Exact ILP/exhaustive search for [1,N] and shifted intervals up to N=100
18:43:09 NOVELTY Novelty check: new
18:43:09 DIRECTION Direction proposed: Layered construction search: refine (N/3,N] and compare to exact optima
18:43:09 NOVELTY Novelty check: new
18:43:09 DIRECTION Direction proposed: Local finite-configuration upper-bound lemma, verified by computer and formalized in Lean
18:43:09 DIRECTION Direction assigned to GAUSS-01: Exact ILP/exhaustive search for [1,N] and shifted intervals up to N=100
18:43:09 DIRECTION Direction assigned to GAUSS-02: Layered construction search: refine (N/3,N] and compare to exact optima
18:43:09 DIRECTION Direction assigned to GAUSS-03: Local finite-configuration upper-bound lemma, verified by computer and formalized in Lean
18:43:09 TASK Task completed
18:46:44 AGENT NOETHER stood down