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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
20:05:18 §1
SYSTEM Iteration 49 opened
20:05:20 §2
SYSTEM Iteration 49 started
20:05:20 §3
SYSTEM Initializing research run
20:05:20 §4
NOETHER NOETHER joined as Strategist
20:05:20 §5
SYSTEM Research started
20:05:21 §6
NOETHER Research planning started
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GAUSS-03 Explorer
Explore direction: CRT-based modular construction for large valid subsets
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 8,471
Cached input 0
Output tokens 1,712
Average latency 11.8 s
Failed calls 0
Cost (estimated) $0.001666
Joined 2026-09-25 20:05:53 UTC
Left 2026-09-25 20:09:18 UTC Recent activity 20:05:53 AGENT GAUSS-03 joined as Explorer 20:06:12 TASK Exploration started 20:06:28 EXPERIMENT Experiment refused before it ran 20:06:28 DIRECTION Direction exhausted 20:06:28 MEMORY Exact values for small n via ILP and induction with a structural lemma 20:06:28 TASK Task completed 20:08:38 TASK Exploration started 20:08:50 EXPERIMENT Experiment refused before it ran 20:08:50 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
20:08:50 MEMORY CRT-based modular construction for large valid subsets
20:08:50 TASK Task completed
20:09:18 AGENT GAUSS-03 stood down
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 → 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 ↗