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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 36.
Research chronicle 91 RECORDS
All Research Review Verification System
19:33:04 §1
SYSTEM Iteration 36 opened
19:33:06 §2
SYSTEM Iteration 36 started
19:33:06 §3
SYSTEM Initializing research run
19:33:06 §4
NOETHER NOETHER joined as Strategist
19:33:06 §5
SYSTEM Research started
19:33:07 §6
NOETHER Research planning started
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GAUSS-01 Explorer
Explore direction: Density increment via divisor-neighborhood containers
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 8,040
Cached input 0
Output tokens 2,450
Average latency 12.0 s
Failed calls 0
Cost (estimated) $0.001812
Joined 2026-09-25 19:33:21 UTC
Left 2026-09-25 19:35:33 UTC Recent activity 19:33:21 AGENT GAUSS-01 joined as Explorer 19:33:37 TASK Exploration started 19:33:50 EXPERIMENT Experiment refused before it ran 19:33:50 DIRECTION Direction exhausted 19:33:50 MEMORY Random weighted subsets and divisibility-free constructions 19:33:50 TASK Task completed 19:34:23 TASK Exploration started 19:34:36 EXPERIMENT Experiment refused before it ran 19:34:36 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
19:34:36 MEMORY Density increment via divisor-neighborhood containers
19:34:36 TASK Task completed
19:35:33 AGENT GAUSS-01 stood down
Research graph / proof lineage 7 objects · 0 links · 10 in complete graph
DIRECTION
DIRECTION Random weighted subsets and divisibility-free constructions COMPLETED DIRECTION Weighted chain LP and divisor-poset upper bounds COMPLETED DIRECTION Exact small-n search and inductive pattern extrapolation COMPLETED DIRECTION Density increment via divisor-neighborhood containers COMPLETED DIRECTION Prime-power layer decomposition and CRT packing COMPLETED DIRECTION Transfer-matrix bound on the divisor poset via interval automata COMPLETED PROOF
PROOF Transfer-matrix state-space check v1 MARKDOWN Explore complete graph / 17 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 36
Model calls 14
Estimated cost $0.007647 Budget remaining 99%
Iteration details & budget ↗