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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 33.
Research chronicle 97 RECORDS
All Research Review Verification System
↑ 91 earlier records 19:27:00 §92
GAUSS-01 GAUSS-01 stood down
19:27:00 §93
GAUSS-02 GAUSS-02 stood down
19:27:00 §94
GAUSS-03 GAUSS-03 stood down
19:27:00 §95
LITERATURE-01 LITERATURE-01 stood down
19:27:00 §96
SYSTEM Research run finished
19:27:00 §97
SYSTEM Iteration 33 completed
Research graph / proof lineage 7 objects · 0 links · 13 in complete graph
DIRECTION
DIRECTION Constructive interval packing with modular residue classes COMPLETED DIRECTION Poset width and divisor-chain upper bound COMPLETED DIRECTION Computational search for extremal sets and pattern extrapolation COMPLETED DIRECTION Probabilistic density bound via dependent rounding on divisor chains COMPLETED DIRECTION LP dual certificate with divisor-chain weights COMPLETED DIRECTION Recursive interval splitting with two-level divisibility constraints COMPLETED PROOF
PROOF Dyadic block lemma and recurrence v1 MARKDOWN Explore complete graph / 20 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 The corpus is not published by the engine.
Iteration 33
Model calls 12
Estimated cost $0.006367 Budget remaining 99%
Iteration details & budget ↗
NOETHER Strategist
Plan iteration 2
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,072
Cached input 517
Output tokens 1,226
Average latency 14.2 s
Failed calls 0
Cost (estimated) $0.000436
Joined 2026-09-25 19:24:19 UTC
Left 2026-09-25 19:27:00 UTC Recent activity 19:24:35 NOVELTY Novelty check: new 19:24:35 DIRECTION Direction proposed: Computational search for extremal sets and pattern extrapolation 19:24:35 DIRECTION Direction assigned to GAUSS-01: Constructive interval packing with modular residue classes 19:24:35 DIRECTION Direction assigned to GAUSS-02: Poset width and divisor-chain upper bound 19:24:35 DIRECTION Direction assigned to GAUSS-03: Computational search for extremal sets and pattern extrapolation 19:24:35 TASK Task completed 19:25:54 TASK Research planning started 19:26:10 PLAN Research plan created 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. 19:26:10
MEMORY
Novelty check: Probabilistic density bound via dependent rounding on divisor chains
19:26:10 NOVELTY Novelty check: partially explored
19:26:10 DIRECTION Direction proposed: Probabilistic density bound via dependent rounding on divisor chains
19:26:10 NOVELTY Novelty check: new
19:26:10 DIRECTION Direction proposed: LP dual certificate with divisor-chain weights
19:26:10 NOVELTY Novelty check: new
19:26:10 DIRECTION Direction proposed: Recursive interval splitting with two-level divisibility constraints
19:26:10 DIRECTION Direction assigned to GAUSS-01: Probabilistic density bound via dependent rounding on divisor chains
19:26:10 DIRECTION Direction assigned to GAUSS-02: LP dual certificate with divisor-chain weights
19:26:10 DIRECTION Direction assigned to GAUSS-03: Recursive interval splitting with two-level divisibility constraints
19:26:10 TASK Task completed
19:27:00 AGENT NOETHER stood down