Pith Number

pith:2GS7NXPI

pith:2026:2GS7NXPIZ2O4E43DUBQSYK43QZ

not attested not anchored not stored refs pending

Gromov-Wasserstein Quantization and Clustering: Structure, Rates, and Algorithms

Florian Beier, Stephan Eckstein

arxiv:2608.11016 v1 · 2026-08-11 · math.OC · cs.CG · cs.LG · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2GS7NXPIZ2O4E43DUBQSYK43QZ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-08-12T01:24:04.483921Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1a5f6dde8ce9dc27363a0612c2b9b86788962be4829ff53911922a4ca7faf4f

Aliases

arxiv: 2608.11016 · arxiv_version: 2608.11016v1 · doi: 10.48550/arxiv.2608.11016 · pith_short_12: 2GS7NXPIZ2O4 · pith_short_16: 2GS7NXPIZ2O4E43D · pith_short_8: 2GS7NXPI

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/2GS7NXPIZ2O4E43DUBQSYK43QZ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: d1a5f6dde8ce9dc27363a0612c2b9b86788962be4829ff53911922a4ca7faf4f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "85b88f3534e92b5326fc83fb1beaff1d059f10e83681c47ce53049ca420c07dc",
    "cross_cats_sorted": [
      "cs.CG",
      "cs.LG",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-08-11T14:58:31Z",
    "title_canon_sha256": "ad91cde213282ea5a1848cd13c114bc0b6ea34469b509a080b00275756b5ce7e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.11016",
    "kind": "arxiv",
    "version": 1
  }
}