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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 56.
Research chronicle 96 RECORDS
All Research Review Verification System
20:24:53 §1
SYSTEM Iteration 56 opened
20:24:55 §2
SYSTEM Iteration 56 started
20:24:55 §3
SYSTEM Initializing research run
20:24:55 §4
NOETHER NOETHER joined as Strategist
20:24:55 §5
SYSTEM Research started
20:24:56 §6
NOETHER Research planning started
↑ 90 earlier records Research record
Agent record Close ×
Research graph / proof lineage 7 objects · 0 links · 11 in complete graph
DIRECTION
DIRECTION Probabilistic extremal bound via divisor-count concentration COMPLETED DIRECTION Constructive family via prime-power intervals COMPLETED DIRECTION Computational search and structural conjecture on small intervals COMPLETED DIRECTION Weighted pair-counting upper bound via divisor-sum weights COMPLETED DIRECTION 2-adic valuation decomposition and bipartite matching bound COMPLETED DIRECTION Asymptotic upper bound via divisor function and covering by multiples COMPLETED PROOF
PROOF LP bound vs ceil(N/2) v1 MARKDOWN Explore complete graph / 18 objects →
GAUSS-02 Explorer
Explore direction: 2-adic valuation decomposition and bipartite matching bound
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 8,198
Cached input 0
Output tokens 2,955
Average latency 40.6 s
Failed calls 0
Cost (estimated) $0.001976
Joined 2026-09-25 20:25:11 UTC
Left 2026-09-25 20:28:34 UTC Recent activity 20:25:11 AGENT GAUSS-02 joined as Explorer 20:25:28 TASK Exploration started 20:26:13 EXPERIMENT Experiment refused before it ran 20:26:13 DIRECTION Direction exhausted 20:26:13 MEMORY Constructive family via prime-power intervals 20:26:13 TASK Task completed 20:27:10 TASK Exploration started 20:27:50 EXPERIMENT Experiment refused before it ran 20:27:50 DIRECTION 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. Direction exhausted
20:27:50 MEMORY 2-adic valuation decomposition and bipartite matching bound
20:27:50 TASK Task completed
20:28:34 AGENT GAUSS-02 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 56
Model calls 13
Estimated cost $0.005336 Budget remaining 99%
Iteration details & budget ↗