Pith Number

pith:UCU3YWLF

pith:2015:UCU3YWLFMEFGUGAIV66OPYZBOZ

not attested not anchored not stored refs pending

Connective constants and height functions for Cayley graphs

Geoffrey R. Grimmett, Zhongyang Li

arxiv:1501.00476 v5 · 2015-01-02 · math.CO · math-ph · math.GR · 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{UCU3YWLFMEFGUGAIV66OPYZBOZ}

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	2026-05-18T01:08:26.731501Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a0a9bc5965610a6a1808afbce7e32176499a6a393dda968a0883ae6bd37e88c0

Aliases

arxiv: 1501.00476 · arxiv_version: 1501.00476v5 · doi: 10.48550/arxiv.1501.00476 · pith_short_12: UCU3YWLFMEFG · pith_short_16: UCU3YWLFMEFGUGAI · pith_short_8: UCU3YWLF

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/UCU3YWLFMEFGUGAIV66OPYZBOZ \
  | 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: a0a9bc5965610a6a1808afbce7e32176499a6a393dda968a0883ae6bd37e88c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a68ccc2d121df62658ae07479fcbacc9ac4efb4a6e0a5917ea0c91b02519f4a",
    "cross_cats_sorted": [
      "math-ph",
      "math.GR",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-01-02T20:34:06Z",
    "title_canon_sha256": "a1bd960f57b2b59ae6ed5e26a6a1e48718692bc9165c9a7d507535100fbed4a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.00476",
    "kind": "arxiv",
    "version": 5
  }
}