Pith Number

pith:4YGCTIIJ

pith:2017:4YGCTIIJ7UV3X3AR4DP5IGLVWE

not attested not anchored not stored refs pending

Geodesic of minimal length in the set of probability measures on graphs

Chenchen Mou, Wilfrid Gangbo, Wuchen Li

arxiv:1712.09266 v1 · 2017-12-26 · math.CA · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4YGCTIIJ7UV3X3AR4DP5IGLVWE}

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	2026-05-18T00:27:14.053007Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e60c29a109fd2bbbec11e0dfd41975b11d4276d6523ca8472470d4451101d990

Aliases

arxiv: 1712.09266 · arxiv_version: 1712.09266v1 · doi: 10.48550/arxiv.1712.09266 · pith_short_12: 4YGCTIIJ7UV3 · pith_short_16: 4YGCTIIJ7UV3X3AR · pith_short_8: 4YGCTIIJ

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/4YGCTIIJ7UV3X3AR4DP5IGLVWE \
  | 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: e60c29a109fd2bbbec11e0dfd41975b11d4276d6523ca8472470d4451101d990

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "975ff0097fe227abdfd8cdf13c94abfab3588ba8515d6e8e17487d54e83af714",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2017-12-26T13:33:43Z",
    "title_canon_sha256": "028d826cd069b563144e1618b34e94c371a690cc4ff8d695ea05a6f96f1f42cd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.09266",
    "kind": "arxiv",
    "version": 1
  }
}