{
  "$type": "site.standard.document",
  "bskyPostRef": {
    "cid": "bafyreihrnucp4oi4y3kpisj5fppltg4ddepm72ihiv6vfor5vkmo2ntmzq",
    "uri": "at://did:plc:3fychdutjjusoqeq24ljch6q/app.bsky.feed.post/3mkosggrbgw62"
  },
  "coverImage": {
    "$type": "blob",
    "ref": {
      "$link": "bafkreiflo6xt7is6b2iafwghkjahlgggocme5jwjsbeuqqwcywuvjhmszm"
    },
    "mimeType": "image/png",
    "size": 24783
  },
  "path": "/abs/2604.26068v1",
  "publishedAt": "2026-04-30T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Alexander Kalinowski"
  ],
  "textContent": "**Authors:** Alexander Kalinowski\n\nWe study detection of collapse in high-dimensional point clouds, where mass concentrates near a lower-dimensional set relative to a non-collapsed geometry. We propose persistent homology-based test statistics under two well-studied filtrations, with cutoffs calibrated under a broad set of non-collapsed reference models. We benchmark power across three alternative collapse mechanisms (linear/spectral, nonlinear-support, and contamination/heterogeneity) and distill the results into a mechanism map guiding the choice of filtration and statistic.",
  "title": "Calibrated Persistent Homology Tests for High-dimensional Collapse Detection"
}