Pith Number

pith:SOLVXNBW

pith:2013:SOLVXNBW4A4GYFS2MRQ4S6XJER

not attested not anchored not stored refs pending

A geometric study of Wasserstein spaces: ultrametrics

Beno\^it Kloeckner (IF)

arxiv:1304.5219 v2 · 2013-04-18 · math.FA · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SOLVXNBW4A4GYFS2MRQ4S6XJER}

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	2026-05-18T02:50:34.157456Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93975bb436e0386c165a6461c97ae92457b02abd92a5b5ab26e5458d2ce99c80

Aliases

arxiv: 1304.5219 · arxiv_version: 1304.5219v2 · doi: 10.48550/arxiv.1304.5219 · pith_short_12: SOLVXNBW4A4G · pith_short_16: SOLVXNBW4A4GYFS2 · pith_short_8: SOLVXNBW

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/SOLVXNBW4A4GYFS2MRQ4S6XJER \
  | 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: 93975bb436e0386c165a6461c97ae92457b02abd92a5b5ab26e5458d2ce99c80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fabcf5213ffd7d7e439fe071b5cac157e1ba8bbc367d9ad152f781a5d97b9118",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-04-18T18:46:20Z",
    "title_canon_sha256": "00730d481ca14bd67d15689e4046bff3d385a73c8e26429b1c9de1db9562c3f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.5219",
    "kind": "arxiv",
    "version": 2
  }
}