Pith Number

pith:O2ZO6LHG

pith:2016:O2ZO6LHGFLQB4HAHMBDXMRDGL3

not attested not anchored not stored refs pending

The Ricci curvature on directed graphs

Taiki Yamada

arxiv:1602.07779 v6 · 2016-02-25 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{O2ZO6LHGFLQB4HAHMBDXMRDGL3}

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.

Cited by

1 paper in Pith

Ollivier-Ricci Curvature of Riemannian Manifolds and Directed Graphs with Applications to Graph Neural Networks

Receipt and verification

First computed	2026-05-18T00:07:28.620571Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76b2ef2ce62ae01e1c0760477644665ee3633492f5c8f7f1ccf98a43abdcb517

Aliases

arxiv: 1602.07779 · arxiv_version: 1602.07779v6 · doi: 10.48550/arxiv.1602.07779 · pith_short_12: O2ZO6LHGFLQB · pith_short_16: O2ZO6LHGFLQB4HAH · pith_short_8: O2ZO6LHG

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/O2ZO6LHGFLQB4HAHMBDXMRDGL3 \
  | 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: 76b2ef2ce62ae01e1c0760477644665ee3633492f5c8f7f1ccf98a43abdcb517

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba66c94390977a72c5ee79763c5edaaab04611db5091adfef819f36681a4dee4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-02-25T03:02:22Z",
    "title_canon_sha256": "cf134455de3c056f4fa83d07923b11c9e291232861c45feb38e5a4ee9634af98"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.07779",
    "kind": "arxiv",
    "version": 6
  }
}