Pith Number

pith:23CVE4V5

pith:2012:23CVE4V5YRJPZQ3I2DRHP5OJLK

not attested not anchored not stored refs pending

Geodesics for a class of distances in the space of probability measures

Bruno Nazaret (CEREMADE), Guillaume Carlier (CEREMADE), Pierre Cardaliaguet (CEREMADE)

arxiv:1204.2517 v1 · 2012-04-11 · math.OC · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{23CVE4V5YRJPZQ3I2DRHP5OJLK}

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	2026-05-18T03:58:04.862334Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6c55272bdc452fcc368d0e277f5c95aa9cdfdc087c56bb9fd133b928e5db386

Aliases

arxiv: 1204.2517 · arxiv_version: 1204.2517v1 · doi: 10.48550/arxiv.1204.2517 · pith_short_12: 23CVE4V5YRJP · pith_short_16: 23CVE4V5YRJPZQ3I · pith_short_8: 23CVE4V5

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/23CVE4V5YRJPZQ3I2DRHP5OJLK \
  | 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: d6c55272bdc452fcc368d0e277f5c95aa9cdfdc087c56bb9fd133b928e5db386

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d7c83b2c674e253efc91e1296e26639892d9f070e8844274af8c65e64fab9b51",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2012-04-11T18:31:41Z",
    "title_canon_sha256": "00c587b96e4b4ece4fa4b17dec20550d08e1e54adaaf7f9faaadf00bf36af201"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.2517",
    "kind": "arxiv",
    "version": 1
  }
}