Pith Number

pith:F56GCZMJ

pith:2013:F56GCZMJANZTHXTLC7R7FHKF2J

not attested not anchored not stored refs pending

Optimal transportation under controlled stochastic dynamics

Nizar Touzi, Xiaolu Tan

arxiv:1310.0939 v1 · 2013-10-03 · 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{F56GCZMJANZTHXTLC7R7FHKF2J}

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	2026-05-18T03:11:24.976416Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f7c616589037333de6b17e3f29d45d2502928221e08371197e06d3989329c0b

Aliases

arxiv: 1310.0939 · arxiv_version: 1310.0939v1 · doi: 10.48550/arxiv.1310.0939 · pith_short_12: F56GCZMJANZT · pith_short_16: F56GCZMJANZTHXTL · pith_short_8: F56GCZMJ

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/F56GCZMJANZTHXTLC7R7FHKF2J \
  | 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: 2f7c616589037333de6b17e3f29d45d2502928221e08371197e06d3989329c0b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4912661156b46527d2d6e9d8dade9860dd11337fe2f4c7504d36125c70bcd5b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-10-03T10:41:11Z",
    "title_canon_sha256": "b240d611408955fb71bb688aab0c0891fac6c391607abe80d1a7d2e13f0806f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.0939",
    "kind": "arxiv",
    "version": 1
  }
}