Pith Number

pith:5NAZBSE5

pith:2013:5NAZBSE5YRDQOR65BCQ42HCCGM

not attested not anchored not stored refs pending

Strict inequalities for connective constants of transitive graphs

Geoffrey R. Grimmett, Zhongyang Li

arxiv:1301.3091 v2 · 2013-01-14 · math.CO · math-ph · math.MP · 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{5NAZBSE5YRDQOR65BCQ42HCCGM}

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	2026-05-18T02:53:27.209555Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb4190c89dc4470747dd08a1cd1c423310a1d1bdc96137a640a92887476443a4

Aliases

arxiv: 1301.3091 · arxiv_version: 1301.3091v2 · doi: 10.48550/arxiv.1301.3091 · pith_short_12: 5NAZBSE5YRDQ · pith_short_16: 5NAZBSE5YRDQOR65 · pith_short_8: 5NAZBSE5

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/5NAZBSE5YRDQOR65BCQ42HCCGM \
  | 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: eb4190c89dc4470747dd08a1cd1c423310a1d1bdc96137a640a92887476443a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f41271663b376045101b07d1038fc03a2b7e1bc81b0fb83150953bd71455927",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-01-14T18:42:41Z",
    "title_canon_sha256": "5d2325a49316b11607c6d2961779c90a7c225f0f5ef5b9c0500de7ec08f072c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.3091",
    "kind": "arxiv",
    "version": 2
  }
}