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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 47.
Research chronicle 90 RECORDS
All Research Review Verification System
20:01:33 §1
SYSTEM Iteration 47 opened
20:01:35 §2
SYSTEM Iteration 47 started
20:01:35 §3
SYSTEM Initializing research run
20:01:35 §4
NOETHER NOETHER joined as Strategist
20:01:35 §5
SYSTEM Research started
20:01:36 §6
NOETHER Research planning started
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GAUSS-03 Explorer
Explore direction: Lower bound from semiprime and almost-prime families
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 8,389
Cached input 1,152
Output tokens 1,284
Average latency 8.3 s
Failed calls 0
Cost (estimated) $0.001407
Joined 2026-09-25 20:01:51 UTC
Left 2026-09-25 20:03:41 UTC Recent activity 20:01:51 AGENT GAUSS-03 joined as Explorer 20:02:09 TASK Exploration started 20:02:19 DIRECTION Direction exhausted 20:02:19 MEMORY Exact computation for small n and pattern-driven conjecture 20:02:19 TASK Task completed 20:03:03 TASK Exploration started 20:03:14 EXPERIMENT Experiment refused before it ran 20:03:14 DIRECTION Direction exhausted 20:03:14 MEMORY 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. Lower bound from semiprime and almost-prime families
20:03:14 TASK Task completed
20:03:41 AGENT GAUSS-03 stood down
Research graph / proof lineage 7 objects · 0 links · 11 in complete graph
DIRECTION
DIRECTION Probabilistic upper bound via weighted divisor counting COMPLETED DIRECTION Constructive lower bound from geometric progressions and residue classes COMPLETED DIRECTION Exact computation for small n and pattern-driven conjecture COMPLETED DIRECTION Weighted entropy upper bound via divisor chains COMPLETED DIRECTION Recursive interval splitting and extremal recurrence COMPLETED DIRECTION Lower bound from semiprime and almost-prime families COMPLETED PROOF
PROOF Weighted triple-counting inequality v1 MARKDOWN Explore complete graph / 18 objects → 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 47
Model calls 12
Estimated cost $0.005795 Budget remaining 99%
Iteration details & budget ↗