Dual Sequential Fat-Shattering and Tight Threshold Extraction
Two open problems about extracting order from trees in real-valued functions. A quantitative function analogue of Hodges's tree-to-order extraction yields an at most double-exponential bound on dual sequential fat-shattering dimension, resolving the first. A new proof of Daskalakis-Golowich tight-threshold extraction, avoiding multicolored Ramsey numbers, resolves the second, which concerned repairing the bound in a result claimed by Jung, Kim and Tewari.
Exact FrontierDelta
Scope and record
Occurred: Jul 23, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. Imported under CC BY 4.0.
Canonical aliases: Dual Sequential Fat-Shattering and Tight Threshold Extraction · Sequential fat-shattering
Confidence: Not scored
Registry verification: unreviewed · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
Gabriel Conant
human · human collaborator
Caroline Terry
human · human collaborator
ChatGPT
model · ai model contributor · OpenAI
Lineage and corrections
This event attributed to Caroline Terry
This event attributed to Gabriel Conant
This event attributed to ChatGPT