Pith Number

pith:2ISFBJT3

pith:2012:2ISFBJT3IXDX6QMESYGRYNEBCS

not attested not anchored not stored refs pending

Bounds on connective constants of regular graphs

Geoffrey R. Grimmett, Zhongyang Li

arxiv:1210.6277 v2 · 2012-10-23 · 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{2ISFBJT3IXDX6QMESYGRYNEBCS}

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	2026-05-18T03:26:42.759957Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d22450a67b45c77f4184960d1c34811487d6bddf4b2e1abc4dc7fb5aa2dd7134

Aliases

arxiv: 1210.6277 · arxiv_version: 1210.6277v2 · doi: 10.48550/arxiv.1210.6277 · pith_short_12: 2ISFBJT3IXDX · pith_short_16: 2ISFBJT3IXDX6QME · pith_short_8: 2ISFBJT3

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/2ISFBJT3IXDX6QMESYGRYNEBCS \
  | 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: d22450a67b45c77f4184960d1c34811487d6bddf4b2e1abc4dc7fb5aa2dd7134

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d03372662dc8c9fde2dfb219e58f509339d450466243203cf7dc94974ae40b55",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-10-23T16:05:33Z",
    "title_canon_sha256": "73cac46b173e073cb90b4356c7c6eeab0bf237c5ea2eb69785ef44e22ef94e51"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.6277",
    "kind": "arxiv",
    "version": 2
  }
}