Pith Number

pith:CJJGZ5FN

pith:2015:CJJGZ5FNBO2YLBJGUUHBMM3XFU

not attested not anchored not stored refs pending

Self-avoiding walks and amenability

Geoffrey R. Grimmett, Zhongyang Li

arxiv:1510.08659 v2 · 2015-10-29 · math.GR · math-ph · math.CO · 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{CJJGZ5FNBO2YLBJGUUHBMM3XFU}

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	2026-05-18T01:26:09.252245Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12526cf4ad0bb5858526a50e1633772d22c876123517acaae0885dd5505f544a

Aliases

arxiv: 1510.08659 · arxiv_version: 1510.08659v2 · doi: 10.48550/arxiv.1510.08659 · pith_short_12: CJJGZ5FNBO2Y · pith_short_16: CJJGZ5FNBO2YLBJG · pith_short_8: CJJGZ5FN

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/CJJGZ5FNBO2YLBJGUUHBMM3XFU \
  | 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: 12526cf4ad0bb5858526a50e1633772d22c876123517acaae0885dd5505f544a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "715f4d8f3eb2e81580e0d523881eba690dbbe637457dbbb350b6946961b2c5f6",
    "cross_cats_sorted": [
      "math-ph",
      "math.CO",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-10-29T12:05:40Z",
    "title_canon_sha256": "9a1501c7044070d1fa8e3911e1b552d3c6788b43a778257eb8c29a91839cb6cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.08659",
    "kind": "arxiv",
    "version": 2
  }
}