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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 34.
Research chronicle 109 RECORDS
All Research Review Verification System
19:27:00 §1
SYSTEM Iteration 34 opened
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SYSTEM Iteration 34 started
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SYSTEM Initializing research run
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NOETHER NOETHER joined as Strategist
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SYSTEM Research started
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NOETHER Research planning started
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LITERATURE-01 Literature researcher
Reading the landscape around: Constructive CRT/block packing for large 3-divisor-free interval subsets
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,863
Cached input 0
Output tokens 434
Average latency 5.1 s
Failed calls 0
Cost (estimated) $0.000382
Joined 2026-09-25 19:27:14 UTC
Left 2026-09-25 19:30:24 UTC Recent activity 19:27:14 AGENT LITERATURE-01 joined as Literature Researcher 19:27:14 LITERATURE Literature search started 19:27:14 LITERATURE Indexed: On probabilistic inference by weighted model counting 19:27:14 LITERATURE Indexed: Probabilistic Planning via Heuristic Forward Search and Weighted Model Counting 19:27:14 LITERATURE Indexed: Exploiting Structure in Weighted Model Counting Approaches to Probabilistic Inference 19:27:14 LITERATURE Literature search: 3 new of 3 19:27:14 LITERATURE Reviewed: On probabilistic inference by weighted model counting 19:27:14 MEMORY Literature: On probabilistic inference by weighted model counting Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
09 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration.
19:29:00 LITERATURE Literature search started
19:29:00 LITERATURE Indexed: Random interval packing
19:29:00 LITERATURE Indexed: Large Zero-Free Subsets of ℤ/pℤ
19:29:00 LITERATURE Indexed: Variational Interpolation of Subsets
19:29:00 LITERATURE Literature search: 3 new of 3
19:29:00 LITERATURE Reviewed: Random interval packing
19:29:00 MEMORY Literature: Random interval packing
19:30:24 AGENT LITERATURE-01 stood down 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 34
Model calls 16
Estimated cost $0.009553 Budget remaining 99%
Iteration details & budget ↗
Research graph / proof lineage 9 objects · 3 links · 11 in complete graph
DIRECTION
DIRECTION Probabilistic construction and weighted double-counting upper bound COMPLETED DIRECTION Hypergraph matching and computational extremal search REJECTED DIRECTION Divisor-sum analytic bound via entropy or density COMPLETED DIRECTION Constructive CRT/block packing for large 3-divisor-free interval subsets COMPLETED DIRECTION Poset width and chain-decomposition upper bound via interval divisibility COMPLETED DIRECTION Forbidden pattern via prime-exponent vectors and extremal set theory REJECTED HYPOTHESIS
HYPOTHESIS H-001 REJECTED REVIEW
REVIEW Review (fail) FAIL PROOF
PROOF Odd-part chain-decomposition bound is vacuous v1 MARKDOWN Explore complete graph / 20 objects →