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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing all iterations.
Research chronicle 501 RECORDS
All Research Review Verification System
↑ 495 earlier records 16:46:48 §5
NOETHER NOETHER joined as Strategist
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SYSTEM Research started
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NOETHER Research planning started
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NOETHER Task completed
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SYSTEM Research run finished
16:46:50 §10
SYSTEM Iteration 4 completed
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Research record
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Mission
Runtime 5 h 32 min
Iteration 7 of 7
Directions 33
Hypotheses 7
Experiments 3
Rejected paths 34 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 18
Highly relevant 0 Iteration 7 No frontier agent engaged
Model calls 44
Estimated cost $0.0449 Budget remaining 98%
Iteration details & budget ↗
LITERATURE-01 Literature researcher
Reading the landscape around: Exponent‑vector antichain via Sperner theory
Model
Model used together / openai/gpt-oss-120b
Routing profile cheap_reasoning
Usage
Model calls 5
Input tokens 5,598
Cached input 345
Output tokens 2,821
Average latency 4.3 s
Failed calls 0
Cost (estimated) $0.002532
Joined 2026-09-25 11:36:16 UTC
Left 2026-09-25 11:41:48 UTC Recent activity 11:38:50 LITERATURE Indexed: An upper bound for the minimum degree of a graph 11:38:50 LITERATURE Indexed: Number of irreducible factors and degree in divisor graph of Zp[x,n] 11:38:50 LITERATURE Literature search: 3 new of 3 11:38:50 LITERATURE Reviewed: Degree Distance of Zero-Divisor Graph Г[Z_n ] 11:38:50 MEMORY Literature: Degree Distance of Zero-Divisor Graph Г[Z_n ] 11:39:45 LITERATURE Literature search started 11:39:45 LITERATURE Indexed: Refinements and Generalizations of the Shannon Lower Bound via Extensions of the Kraft Inequality 11:39:45 LITERATURE Indexed: Shearer’s inequality and infimum rule for Shannon entropy and topological entropy Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
08 Research director Not started On the roster; the workflow has not woken it in this iteration. 09 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration.
11:39:45 LITERATURE Indexed: New Upper Bound and Lower Bound for Degree-Based Network Entropy
11:39:45 LITERATURE Literature search: 3 new of 3
11:39:45 LITERATURE Reviewed: Refinements and Generalizations of the Shannon Lower Bound via Extensions of the Kraft Inequality
11:39:45 MEMORY Literature: Refinements and Generalizations of the Shannon Lower Bound via Extensions of the Kraft Inequality
11:40:42 LITERATURE Literature search started
11:40:42 LITERATURE Indexed: Algebraic methods in Sperner theory
11:40:42 LITERATURE Indexed: The flow-theoretic approach in Sperner theory
11:40:42 LITERATURE Indexed: Optimal Error-Detecting Codes for General Asymmetric Channels via Sperner Theory
11:40:42 LITERATURE Literature search: 3 new of 3
11:40:42 LITERATURE Reviewed: Algebraic methods in Sperner theory
11:40:42 MEMORY Literature: Algebraic methods in Sperner theory
11:41:48 AGENT LITERATURE-01 stood down