Pith Number

pith:4D6ES6WU

pith:2012:4D6ES6WUI77LVVGS4U5JIGFOX5

not attested not anchored not stored refs pending

Decomposition of geodesics in the Wasserstein space and the globalization property

Fabio Cavalletti

arxiv:1209.5909 v4 · 2012-09-26 · math.MG · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4D6ES6WUI77LVVGS4U5JIGFOX5}

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	2026-05-18T03:15:34.527299Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0fc497ad447febad4d2e53a9418aebf510aa18356c3219448da5e399b47f90b

Aliases

arxiv: 1209.5909 · arxiv_version: 1209.5909v4 · doi: 10.48550/arxiv.1209.5909 · pith_short_12: 4D6ES6WUI77L · pith_short_16: 4D6ES6WUI77LVVGS · pith_short_8: 4D6ES6WU

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/4D6ES6WUI77LVVGS4U5JIGFOX5 \
  | 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: e0fc497ad447febad4d2e53a9418aebf510aa18356c3219448da5e399b47f90b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7589de9e9f8a75662ec8898d9e5b6704ea0147e80f0c9c8189f722fa6535b523",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2012-09-26T11:53:13Z",
    "title_canon_sha256": "09edf0425a416778a9cf6976ca2afcec8974ea2c62b25789d04d776e2d807115"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.5909",
    "kind": "arxiv",
    "version": 4
  }
}