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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 18.
Research chronicle 87 RECORDS
All Research Review Verification System
↑ 81 earlier records 18:35:41 §82
GAUSS-01 GAUSS-01 stood down
18:35:41 §83
GAUSS-03 GAUSS-03 stood down
18:35:41 §84
LITERATURE-01 LITERATURE-01 stood down
18:35:41 §85
ARES ARES stood down
18:35:41 §86
SYSTEM Research run finished
18:35:41 §87
SYSTEM Iteration 18 completed
Research graph / proof lineage 7 objects · 0 links · 9 in complete graph
DIRECTION
DIRECTION Random subset construction with divisibility constraints COMPLETED DIRECTION Poset chain decomposition and matching bound COMPLETED DIRECTION Exact computation and pattern conjecture via ILP COMPLETED DIRECTION Unblock and run exact small-N computation, then compare with (N/3,N] COMPLETED DIRECTION Formalise in Lean the verified lemma that (N/3,N] satisfies the condition REJECTED DIRECTION Chain/pairing upper bound via odd-part chains {m·2^k} and a precise statement COMPLETED PROOF
PROOF Experiment report — Check whether the odd-part chain decomposition upper bound U(N)=sum_{m odd<=N} m v1 MARKDOWN Explore complete graph / 16 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 18
Model calls 15
Estimated cost $0.0449 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 1,504
Cached input 0
Output tokens 1,008
Average latency 27.4 s
Failed calls 0
Cost (estimated) $0.000493
Joined 2026-09-25 18:29:36 UTC
Left 2026-09-25 18:35:41 UTC Recent activity 18:29:56 DIRECTION Direction proposed: Poset chain decomposition and matching bound 18:29:56 NOVELTY Novelty check: new 18:29:56 DIRECTION Direction proposed: Exact computation and pattern conjecture via ILP 18:29:56 DIRECTION Direction assigned to GAUSS-01: Random subset construction with divisibility constraints 18:29:56 DIRECTION Direction assigned to GAUSS-02: Poset chain decomposition and matching bound 18:29:56 DIRECTION Direction assigned to GAUSS-03: Exact computation and pattern conjecture via ILP 18:29:56 TASK Task completed 18:31:37 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. 18:32:14
PLAN
Research plan created
18:32:14 NOVELTY Novelty check: new
18:32:14 DIRECTION Direction proposed: Unblock and run exact small-N computation, then compare with (N/3,N]
18:32:14 NOVELTY Novelty check: new
18:32:14 DIRECTION Direction proposed: Formalise in Lean the verified lemma that (N/3,N] satisfies the condition
18:32:14 NOVELTY Novelty check: new
18:32:14 DIRECTION Direction proposed: Chain/pairing upper bound via odd-part chains {m·2^k} and a precise statement
18:32:14 DIRECTION Direction assigned to GAUSS-01: Unblock and run exact small-N computation, then compare with (N/3,N]
18:32:14 DIRECTION Direction assigned to GAUSS-02: Formalise in Lean the verified lemma that (N/3,N] satisfies the condition
18:32:14 DIRECTION Direction assigned to GAUSS-03: Chain/pairing upper bound via odd-part chains {m·2^k} and a precise statement
18:32:14 TASK Task completed
18:35:41 AGENT NOETHER stood down