Pith Number

pith:KURJSUXH

pith:2015:KURJSUXH4IX4INRFYIHH2IEF7K

not attested not anchored not stored refs pending

Invariance, quasi-invariance and unimodularity for random graphs

Vadim A. Kaimanovich

arxiv:1512.08479 v1 · 2015-12-28 · math.PR · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KURJSUXH4IX4INRFYIHH2IEF7K}

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	2026-05-18T01:23:40.600453Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

55229952e7e22fc43625c20e7d2085fa8804f9dedabccc00a71bef8ac843671f

Aliases

arxiv: 1512.08479 · arxiv_version: 1512.08479v1 · doi: 10.48550/arxiv.1512.08479 · pith_short_12: KURJSUXH4IX4 · pith_short_16: KURJSUXH4IX4INRF · pith_short_8: KURJSUXH

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/KURJSUXH4IX4INRFYIHH2IEF7K \
  | 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: 55229952e7e22fc43625c20e7d2085fa8804f9dedabccc00a71bef8ac843671f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd73f317c370845978d797d577028825095fcb209fe3da2add35033658c0fd6f",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-12-28T18:44:25Z",
    "title_canon_sha256": "8894883e9018b936bdfd21fb8b9c5d73ebd8f442cdd1386ac0da42132da2c94f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.08479",
    "kind": "arxiv",
    "version": 1
  }
}