{
  "story_id": "adf66faffdc2d7498723916e78f2f3ea",
  "desk": "drm3",
  "revision": 1,
  "published_at": "2026-09-02T04:00:00.000Z",
  "content_hash": "6f417d73d3386ee1e6c21fa49731a943a065bc63a0b5cb4c0c827aa59ed40328",
  "hash_basis": "sha256 over `headline\\ndek\\nprose`, plus `\\n` + the canonical citations JSON when any source is placed, plus `\\n#blog` for blogs",
  "basis": {
    "headline": "New Sierpiński-Knopp Wasserstein distance accelerates persistence diagram comparisons 626x",
    "dek": "SK-Wasserstein distance maps persistence diagrams to a space-filling curve, achieving 626x median speedup over W2 approximations.",
    "prose": "Sebastien Tchitchek and co-authors, in a paper submitted to arXiv on 2026-09-01, introduce the Sierpiński-Knopp (SK) Wasserstein distance, a fast metric between persistence diagrams. [^1]\n\nThe paper reports that experiments on 12 scientific collections comprising 227 diagrams show a median per-collection speedup of d_SK over state-of-the-art approximations of W_2 of 626x, with an aggregate speedup of 2100x. [^2]\n\nThe authors claim that the encoded point sets are matched via one-dimensional optimal assignment in O(N log N) steps, yielding an explicit diagonal-aware point assignment. [^3]\n\nThe paper asserts that the SK-Wasserstein distance controls the classical 2-Wasserstein distance, admits an explicit isometric embedding into a Hilbert space, and induces a positive-definite Gaussian kernel. [^4]\n\nThe Sierpiński--Knopp Wasserstein Distance is intended for applications involving 2-Wasserstein approximation. [^5]\n\nThe authors suggest that this new distance metric addresses limitations in existing methods for analyzing persistence diagrams. [^6]\n\nThe research paper associated with this metric has been assigned the identifier 2609.01528. [^7]",
    "cited": "[{\"statement\":\"Sebastien Tchitchek and co-authors, in a paper submitted to arXiv on 2026-09-01, introduce the Sierpiński-Knopp (SK) Wasserstein distance, a fast metric between persistence diagrams.\",\"source\":\"arXiv.org\",\"instrument\":\"News\",\"claim_key\":null,\"published_at\":\"2026-09-02T04:00:00.000Z\",\"publisher_count\":1,\"sources\":[\"arXiv.org\"]},{\"statement\":\"The paper reports that experiments on 12 scientific collections comprising 227 diagrams show a median per-collection speedup of d_SK over state-of-the-art approximations of W_2 of 626x, with an aggregate speedup of 2100x.\",\"source\":\"arXiv.org\",\"instrument\":\"News\",\"claim_key\":null,\"published_at\":\"2026-09-02T04:00:00.000Z\",\"publisher_count\":1,\"sources\":[\"arXiv.org\"]},{\"statement\":\"The authors claim that the encoded point sets are matched via one-dimensional optimal assignment in O(N log N) steps, yielding an explicit diagonal-aware point assignment.\",\"source\":\"arXiv.org\",\"instrument\":\"News\",\"claim_key\":null,\"published_at\":\"2026-09-02T04:00:00.000Z\",\"publisher_count\":1,\"sources\":[\"arXiv.org\"]},{\"statement\":\"The paper asserts that the SK-Wasserstein distance controls the classical 2-Wasserstein distance, admits an explicit isometric embedding into a Hilbert space, and induces a positive-definite Gaussian kernel.\",\"source\":\"arXiv.org\",\"instrument\":\"News\",\"claim_key\":null,\"published_at\":\"2026-09-02T04:00:00.000Z\",\"publisher_count\":1,\"sources\":[\"arXiv.org\"]},{\"statement\":\"The Sierpiński--Knopp Wasserstein Distance is intended for applications involving 2-Wasserstein approximation.\",\"source\":\"takara.ai\",\"instrument\":\"News\",\"claim_key\":null,\"published_at\":\"2026-09-01T16:57:04.000Z\",\"publisher_count\":1,\"sources\":[\"takara.ai\"]},{\"statement\":\"The authors suggest that this new distance metric addresses limitations in existing methods for analyzing persistence diagrams.\",\"source\":\"takara.ai\",\"instrument\":\"News\",\"claim_key\":null,\"published_at\":\"2026-09-01T16:57:04.000Z\",\"publisher_count\":1,\"sources\":[\"takara.ai\"]},{\"statement\":\"The research paper associated with this metric has been assigned the identifier 2609.01528.\",\"source\":\"takara.ai\",\"instrument\":\"News\",\"claim_key\":null,\"published_at\":\"2026-09-01T16:57:04.000Z\",\"publisher_count\":1,\"sources\":[\"takara.ai\"]}]",
    "kind": "news"
  },
  "receipt_verify": "Ed25519 over the dot-joined string `slice_hash.cursor_from.cursor_to.view.view_version.row_count`; public_key and sig are base64url of the raw 32-byte key / 64-byte signature",
  "receipt": null,
  "receipt_note": "this revision predates receipt-keeping (before v0.37.0); the filed row lives in the record",
  "generation_chain": {
    "wire": {
      "stream": "fountain_news",
      "story_id": "a546cf1c725e55a0ca09bf0fb571427b",
      "thread_id": "d62cfb898cc8d2f26f801e286e79d695",
      "thread_label": "Sebastien Tchitchek",
      "novelty": "UPDATE",
      "content_hash": "5b56a4013aa74d8969784056460e3ba2dce25ade6e566f2d401030486a6bdf1b",
      "last_published_at": "2026-09-02T04:00:00.000Z",
      "read_receipt": {
        "slice_hash": "3905664cf10c2126ea131af76eb59a4e670141af2a4606d101f9336a8aaf6e3e",
        "cursor_from": "eyJ0cyI6IjIwMjYtMDktMDJUMDM6NDM6MDAuMDAwMDAwWiIsImlkIjoiZjIzZjc5YTk3YjM4MGMyNDgzZTRlNzYxMjNlZjg2M2QiLCJ2IjoiMSJ9",
        "cursor_to": "eyJ0cyI6IjIwMjYtMDktMDJUMDQ6MDQ6MjYuMDAwMDAwWiIsImlkIjoiN2M3MjY3YjA5MzczMjU3ZjI0ZDZiY2NmZWY3ZDVjNGUiLCJ2IjoiMSJ9",
        "view": "v_fountain_news",
        "view_version": "1",
        "row_count": 100,
        "window_days": 3,
        "bytes_scanned": 12017721,
        "credits": 8,
        "price_per_100_rows": 8,
        "sig": "juwMycx6aGSQfawfzLUaISZZUKKkbvDiOPDpZxKn6fmy0KIBoISR1qDjkJuogjQ0TUgCk4tYeoc9JF0bPKfOCw",
        "public_key": "bMUigy8O0jOnBxQ4Sc-5lwhIZ8LQVAhxMbR7qESVuUE",
        "signer_path": "lakehouse/data-extract/v1",
        "alg": "Ed25519",
        "signed": true
      }
    },
    "written_at": "2026-09-02T22:36:00.930Z"
  },
  "cited_facts": [
    {
      "statement": "Sebastien Tchitchek and co-authors, in a paper submitted to arXiv on 2026-09-01, introduce the Sierpiński-Knopp (SK) Wasserstein distance, a fast metric between persistence diagrams.",
      "source": "arXiv.org",
      "instrument": "News",
      "claim_key": null,
      "published_at": "2026-09-02T04:00:00.000Z",
      "publisher_count": 1,
      "sources": [
        "arXiv.org"
      ]
    },
    {
      "statement": "The paper reports that experiments on 12 scientific collections comprising 227 diagrams show a median per-collection speedup of d_SK over state-of-the-art approximations of W_2 of 626x, with an aggregate speedup of 2100x.",
      "source": "arXiv.org",
      "instrument": "News",
      "claim_key": null,
      "published_at": "2026-09-02T04:00:00.000Z",
      "publisher_count": 1,
      "sources": [
        "arXiv.org"
      ]
    },
    {
      "statement": "The authors claim that the encoded point sets are matched via one-dimensional optimal assignment in O(N log N) steps, yielding an explicit diagonal-aware point assignment.",
      "source": "arXiv.org",
      "instrument": "News",
      "claim_key": null,
      "published_at": "2026-09-02T04:00:00.000Z",
      "publisher_count": 1,
      "sources": [
        "arXiv.org"
      ]
    },
    {
      "statement": "The paper asserts that the SK-Wasserstein distance controls the classical 2-Wasserstein distance, admits an explicit isometric embedding into a Hilbert space, and induces a positive-definite Gaussian kernel.",
      "source": "arXiv.org",
      "instrument": "News",
      "claim_key": null,
      "published_at": "2026-09-02T04:00:00.000Z",
      "publisher_count": 1,
      "sources": [
        "arXiv.org"
      ]
    },
    {
      "statement": "The Sierpiński--Knopp Wasserstein Distance is intended for applications involving 2-Wasserstein approximation.",
      "source": "takara.ai",
      "instrument": "News",
      "claim_key": null,
      "published_at": "2026-09-01T16:57:04.000Z",
      "publisher_count": 1,
      "sources": [
        "takara.ai"
      ]
    },
    {
      "statement": "The authors suggest that this new distance metric addresses limitations in existing methods for analyzing persistence diagrams.",
      "source": "takara.ai",
      "instrument": "News",
      "claim_key": null,
      "published_at": "2026-09-01T16:57:04.000Z",
      "publisher_count": 1,
      "sources": [
        "takara.ai"
      ]
    },
    {
      "statement": "The research paper associated with this metric has been assigned the identifier 2609.01528.",
      "source": "takara.ai",
      "instrument": "News",
      "claim_key": null,
      "published_at": "2026-09-01T16:57:04.000Z",
      "publisher_count": 1,
      "sources": [
        "takara.ai"
      ]
    }
  ],
  "note": "A signature proves who filed this and that it has not changed since. It never makes a claim true."
}