Pith Number

pith:QVJUPPIC

pith:2012:QVJUPPICFNQVQL3NUK24CB4FFM

not attested not anchored not stored refs pending

Sobolev estimates for optimal transport maps on Gaussian spaces

Shizan Fang, Vincent Nolot

arxiv:1207.4907 v1 · 2012-07-20 · 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{QVJUPPICFNQVQL3NUK24CB4FFM}

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	2026-05-18T03:50:34.816850Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

855347bd022b61582f6da2b5c107852b1b5738e6d38ba6d85d610bc4ca18893a

Aliases

arxiv: 1207.4907 · arxiv_version: 1207.4907v1 · doi: 10.48550/arxiv.1207.4907 · pith_short_12: QVJUPPICFNQV · pith_short_16: QVJUPPICFNQVQL3N · pith_short_8: QVJUPPIC

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/QVJUPPICFNQVQL3NUK24CB4FFM \
  | 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: 855347bd022b61582f6da2b5c107852b1b5738e6d38ba6d85d610bc4ca18893a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8cbfcb456583cacce270902362ca18e6adfc81c83b604c62e253a12ad663a6e0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-07-20T10:30:16Z",
    "title_canon_sha256": "3c67af8459ac12f0511575e6fc30616249dd9dedb345490eaa205bb217e7a0a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.4907",
    "kind": "arxiv",
    "version": 1
  }
}