Pith Number

pith:CKAWRWXB

pith:2015:CKAWRWXBOMOSNDGZASJ7SESUXH

not attested not anchored not stored refs pending

On the trace of random walks on random graphs

Alan Frieze, Michael Krivelevich, Peleg Michaeli, Ron Peled

arxiv:1508.07355 v2 · 2015-08-28 · math.CO · 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{CKAWRWXBOMOSNDGZASJ7SESUXH}

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	2026-05-18T00:28:19.199529Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

128168dae1731d268cd90493f91254b9c47c8b03eaea5feab57df72b6c7cc986

Aliases

arxiv: 1508.07355 · arxiv_version: 1508.07355v2 · doi: 10.48550/arxiv.1508.07355 · pith_short_12: CKAWRWXBOMOS · pith_short_16: CKAWRWXBOMOSNDGZ · pith_short_8: CKAWRWXB

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/CKAWRWXBOMOSNDGZASJ7SESUXH \
  | 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: 128168dae1731d268cd90493f91254b9c47c8b03eaea5feab57df72b6c7cc986

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f69d0b71ccd1da45f1865aff288a4260bd37e1f61fdcbd5ef0710ea9fdcef77",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-08-28T21:33:19Z",
    "title_canon_sha256": "aa4238dade03fe7eb4f839e2bc4a83368dc7ad9cbb4aea043e4a9aa160d1bf77"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.07355",
    "kind": "arxiv",
    "version": 2
  }
}