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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 33.
Research chronicle 97 RECORDS
All Research Review Verification System
↑ 91 earlier records 19:27:00 §92
GAUSS-01 GAUSS-01 stood down
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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
19:27:00 §97
SYSTEM Iteration 33 completed
Research graph / proof lineage 7 objects · 0 links · 13 in complete graph
DIRECTION
DIRECTION Constructive interval packing with modular residue classes COMPLETED DIRECTION Poset width and divisor-chain upper bound COMPLETED DIRECTION Computational search for extremal sets and pattern extrapolation COMPLETED DIRECTION Probabilistic density bound via dependent rounding on divisor chains COMPLETED DIRECTION LP dual certificate with divisor-chain weights COMPLETED DIRECTION Recursive interval splitting with two-level divisibility constraints COMPLETED PROOF
PROOF Dyadic block lemma and recurrence v1 MARKDOWN Explore complete graph / 20 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 33
Model calls 12
Estimated cost $0.006367 Budget remaining 99%
Iteration details & budget ↗
LITERATURE-01 Literature researcher
Reading the landscape around: Probabilistic density bound via dependent rounding on divisor chains
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,871
Cached input 0
Output tokens 431
Average latency 5.8 s
Failed calls 0
Cost (estimated) $0.000382
Joined 2026-09-25 19:24:35 UTC
Left 2026-09-25 19:27:00 UTC Recent activity 19:24:35 AGENT LITERATURE-01 joined as Literature Researcher 19:24:35 LITERATURE Literature search started 19:24:35 LITERATURE Indexed: Modular Arithmetic: Calculating with Residue Classes 19:24:35 LITERATURE Indexed: Modular Arithmetic: Calculating with Residue Classes 19:24:35 LITERATURE Indexed: Modular Arithmetic: Calculating with Residue Classes 19:24:35 LITERATURE Literature search: 3 new of 3 19:24:35 LITERATURE Reviewed: Modular Arithmetic: Calculating with Residue Classes 19:24:35 MEMORY Literature: Modular Arithmetic: Calculating with Residue Classes 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. 19:26:10
LITERATURE
Literature search started
19:26:10 LITERATURE Indexed: Probabilistic Inverse Design of Nanoporous FabryPerot Color Filters via Mixture Density Networks
19:26:10 LITERATURE Indexed: Divisor density
19:26:10 LITERATURE Indexed: Dependent Randomized Rounding via Exchange Properties of Combinatorial Structures
19:26:10 LITERATURE Literature search: 3 new of 3
19:26:10 LITERATURE Reviewed: Probabilistic Inverse Design of Nanoporous FabryPerot Color Filters via Mixture Density Networks
19:26:10 MEMORY Literature: Probabilistic Inverse Design of Nanoporous FabryPerot Color Filters via Mixture Density Networks
19:27:00 AGENT LITERATURE-01 stood down