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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
18:39:36 §1
SYSTEM Iteration 20 opened
18:39:40 §2
SYSTEM Iteration 20 started
18:39:40 §3
SYSTEM Initializing research run
18:39:40 §4
NOETHER NOETHER joined as Strategist
18:39:40 §5
SYSTEM Research started
18:39:40 §6
NOETHER Research planning started
↑ 81 earlier records Research record
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GAUSS-02 Explorer
Explore direction: Layered construction search: refine (N/3,N] and compare to exact optima
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 3
Input tokens 7,460
Cached input 0
Output tokens 2,520
Average latency 47.7 s
Failed calls 1
Cost (estimated) $0.001750
Joined 2026-09-25 18:40:07 UTC
Left 2026-09-25 18:46:44 UTC Recent activity 18:40:07 AGENT GAUSS-02 joined as Explorer 18:40:31 TASK Exploration started 18:42:17 EXPERIMENT Experiment refused before it ran 18:42:17 DIRECTION Direction exhausted 18:42:17 MEMORY Extremal poset and matching approach via divisor lattice 18:42:17 TASK Task completed 18:43:41 TASK Exploration started 18:44:21 EXPERIMENT Experiment refused before it ran 18:44:21 DIRECTION 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. Direction exhausted
18:44:21 MEMORY Layered construction search: refine (N/3,N] and compare to exact optima
18:44:21 TASK Task completed
18:46:44 AGENT GAUSS-02 stood down
Research graph / proof lineage 7 objects · 0 links · 7 in complete graph
DIRECTION
DIRECTION Probabilistic construction via random sampling and divisor-pair constraints COMPLETED DIRECTION Extremal poset and matching approach via divisor lattice COMPLETED DIRECTION Computational search and pattern extrapolation for small n COMPLETED DIRECTION Exact ILP/exhaustive search for [1,N] and shifted intervals up to N=100 REJECTED DIRECTION Layered construction search: refine (N/3,N] and compare to exact optima COMPLETED DIRECTION Local finite-configuration upper-bound lemma, verified by computer and formalized in Lean COMPLETED PROOF
PROOF Local configuration check results v1 MARKDOWN Explore complete graph / 14 objects → 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 ↗