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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 42.
Research chronicle 89 RECORDS
All Research Review Verification System
↑ 83 earlier records 19:53:50 §84
NOETHER NOETHER stood down
19:53:50 §85
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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SYSTEM Research run finished
19:53:50 §89
SYSTEM Iteration 42 completed
Research graph / proof lineage 7 objects · 0 links · 7 in complete graph
DIRECTION
DIRECTION Constructive extremal families via layered residue classes COMPLETED DIRECTION Analytic upper bound via multiple-counting and interval compression REJECTED DIRECTION Graph-theoretic reformulation and computational pattern mining COMPLETED DIRECTION Recursive parity-layer decomposition for exact extremal recurrences REJECTED DIRECTION Divisor-graph matching and König-type upper bounds COMPLETED DIRECTION Periodic block constructions via CRT and residue-class designs COMPLETED PROOF
PROOF LP bound vs true f(N) for N up to 20 v1 MARKDOWN Explore complete graph / 14 objects → Research record
Agent record Close ×
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 42
Model calls 14
Estimated cost $0.008357 Budget remaining 99%
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 1,074
Cached input 0
Output tokens 964
Average latency 13.4 s
Failed calls 0
Cost (estimated) $0.000420
Joined 2026-09-25 19:50:38 UTC
Left 2026-09-25 19:53:50 UTC Recent activity 19:50:55 DIRECTION Direction proposed: Analytic upper bound via multiple-counting and interval compression 19:50:55 NOVELTY Novelty check: new 19:50:55 DIRECTION Direction proposed: Graph-theoretic reformulation and computational pattern mining 19:50:55 DIRECTION Direction assigned to GAUSS-01: Constructive extremal families via layered residue classes 19:50:55 DIRECTION Direction assigned to GAUSS-02: Analytic upper bound via multiple-counting and interval compression 19:50:55 DIRECTION Direction assigned to GAUSS-03: Graph-theoretic reformulation and computational pattern mining 19:50:55 TASK Task completed 19:52:09 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.
19:52:22 PLAN Research plan created
19:52:22 NOVELTY Novelty check: new
19:52:22 DIRECTION Direction proposed: Recursive parity-layer decomposition for exact extremal recurrences
19:52:22 NOVELTY Novelty check: new
19:52:22 DIRECTION Direction proposed: Divisor-graph matching and König-type upper bounds
19:52:22 NOVELTY Novelty check: new
19:52:22 DIRECTION Direction proposed: Periodic block constructions via CRT and residue-class designs
19:52:22 DIRECTION Direction assigned to GAUSS-01: Recursive parity-layer decomposition for exact extremal recurrences
19:52:22 DIRECTION Direction assigned to GAUSS-02: Divisor-graph matching and König-type upper bounds
19:52:22 DIRECTION Direction assigned to GAUSS-03: Periodic block constructions via CRT and residue-class designs
19:52:22 TASK Task completed
19:53:50 AGENT NOETHER stood down