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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 49.
Research chronicle 96 RECORDS
All Research Review Verification System
↑ 90 earlier records 20:09:18 §91
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
20:09:18 §96
SYSTEM Iteration 49 completed
Research graph / proof lineage 7 objects · 0 links · 11 in complete graph
DIRECTION
DIRECTION Density and entropy via random subsets and divisor graph VC-dimension COMPLETED DIRECTION Constructive families via large primes and multiplicative shifts COMPLETED DIRECTION Exact values for small n via ILP and induction with a structural lemma COMPLETED DIRECTION Recursive interval-splitting with divisor-counting potential COMPLETED DIRECTION Hypergraph matching/covering on the divisibility poset COMPLETED DIRECTION CRT-based modular construction for large valid subsets COMPLETED PROOF
PROOF Dyadic-block lemma and recurrence check v1 MARKDOWN Explore complete graph / 18 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 49
Model calls 14
Estimated cost $0.006734 Budget remaining 99%
Iteration details & budget ↗
LITERATURE-01 Literature researcher
Reading the landscape around: Recursive interval-splitting with divisor-counting potential
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,911
Cached input 0
Output tokens 485
Average latency 5.5 s
Failed calls 0
Cost (estimated) $0.000403
Joined 2026-09-25 20:05:53 UTC
Left 2026-09-25 20:09:18 UTC Recent activity 20:05:53 AGENT LITERATURE-01 joined as Literature Researcher 20:05:53 LITERATURE Literature search started 20:05:53 LITERATURE Indexed: The VC‐Dimension of Random Subsets of Finite Groups 20:05:53 LITERATURE Indexed: Скобочная энтропия и VC-размерность 20:05:53 LITERATURE Indexed: VC-dimension of subsets of Hamming graphs 20:05:53 LITERATURE Literature search: 3 new of 3 20:05:53 LITERATURE Reviewed: The VC‐Dimension of Random Subsets of Finite Groups 20:05:53 MEMORY Literature: The VC‐Dimension of Random Subsets of Finite Groups 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. 20:08:21
LITERATURE
Literature search started
20:08:21 LITERATURE Indexed: A recursive formula for the convolution sum of divisor functions
20:08:21 LITERATURE Indexed: Recursive splitting of an interval when the proportions are identical and independent random variables
20:08:21 LITERATURE Indexed: Counting Problems
20:08:21 LITERATURE Literature search: 3 new of 3
20:08:21 LITERATURE Reviewed: A recursive formula for the convolution sum of divisor functions
20:08:21 MEMORY Literature: A recursive formula for the convolution sum of divisor functions
20:09:18 AGENT LITERATURE-01 stood down