Pith Number

pith:YZ6HDQVN

pith:2013:YZ6HDQVN5EAFXPSEOBU27GSCRY

not attested not anchored not stored refs pending

Existence and uniqueness of optimal transport maps

Fabio Cavalletti, Martin Huesmann

arxiv:1301.1782 v2 · 2013-01-09 · math.MG · math.AP · 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{YZ6HDQVN5EAFXPSEOBU27GSCRY}

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	2026-05-18T02:45:58.383462Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c67c71c2ade9005bbe447069af9a428e37789a8abfc4ad3c80ed0f8e333f7001

Aliases

arxiv: 1301.1782 · arxiv_version: 1301.1782v2 · doi: 10.48550/arxiv.1301.1782 · pith_short_12: YZ6HDQVN5EAF · pith_short_16: YZ6HDQVN5EAFXPSE · pith_short_8: YZ6HDQVN

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/YZ6HDQVN5EAFXPSEOBU27GSCRY \
  | 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: c67c71c2ade9005bbe447069af9a428e37789a8abfc4ad3c80ed0f8e333f7001

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "101357cd16f08fb019b66aa0b6b9728d017a85e26b689a3b2de7400ce9de11c1",
    "cross_cats_sorted": [
      "math.AP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2013-01-09T09:04:54Z",
    "title_canon_sha256": "3725f9140c558d39429057f0c1d32d88e71b032bc78700963e7e8fa8984c22f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.1782",
    "kind": "arxiv",
    "version": 2
  }
}