Pith Number

pith:Q6DLE5CA

pith:2015:Q6DLE5CA5WODWX3C5DK4SGU5VW

not attested not anchored not stored refs pending

Random Walks on countable groups

Michael Bj\"orklund

arxiv:1502.04038 v2 · 2015-02-13 · math.DS · math.GR · 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{Q6DLE5CA5WODWX3C5DK4SGU5VW}

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	2026-05-18T01:22:08.222671Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8786b27440ed9c3b5f62e8d5c91a9dadb4b5d60b053db86f804107fcb59f5cc8

Aliases

arxiv: 1502.04038 · arxiv_version: 1502.04038v2 · doi: 10.48550/arxiv.1502.04038 · pith_short_12: Q6DLE5CA5WOD · pith_short_16: Q6DLE5CA5WODWX3C · pith_short_8: Q6DLE5CA

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/Q6DLE5CA5WODWX3C5DK4SGU5VW \
  | 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: 8786b27440ed9c3b5f62e8d5c91a9dadb4b5d60b053db86f804107fcb59f5cc8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80757facc91bad70920b9829387d27fe4dc563d2f1d7469c4e51b5b754b19211",
    "cross_cats_sorted": [
      "math.GR",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-02-13T16:02:44Z",
    "title_canon_sha256": "f08a2b95d252cd1cd053c57a14d0ed5f26aceb3d8c27983752462bebf7abf04b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.04038",
    "kind": "arxiv",
    "version": 2
  }
}