Pith Number

pith:UP5PRFSG

pith:2018:UP5PRFSGUT6FR44J7ZV3HFCLLN

not attested not anchored not stored refs pending

Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature

David Cushing, Florentin M\"unch, Jack Koolen, Norbert Peyerimhoff, Shiping Liu, Supanat Kamtue

arxiv:1807.02384 v1 · 2018-07-06 · math.CO · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UP5PRFSGUT6FR44J7ZV3HFCLLN}

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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	2026-05-18T00:11:22.239532Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3faf89646a4fc58f389fe6bb3944b5b5a83ba1eb0947c46edb65950480dd1b3

Aliases

arxiv: 1807.02384 · arxiv_version: 1807.02384v1 · doi: 10.48550/arxiv.1807.02384 · pith_short_12: UP5PRFSGUT6F · pith_short_16: UP5PRFSGUT6FR44J · pith_short_8: UP5PRFSG

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/UP5PRFSGUT6FR44J7ZV3HFCLLN \
  | 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: a3faf89646a4fc58f389fe6bb3944b5b5a83ba1eb0947c46edb65950480dd1b3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "866e5de065f1e00acecf094e9d9d7c914c0f1653f76234f2decb45001ef389ec",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-07-06T12:45:51Z",
    "title_canon_sha256": "e4e19a1a0a051ad6bf86834f438c313811d2663433b518407247e81f24fc3929"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.02384",
    "kind": "arxiv",
    "version": 1
  }
}