Pith Number

pith:RXXUGXOK

pith:2016:RXXUGXOKBQCS4EZXSXN4S6NYBS

not attested not anchored not stored refs pending

Average Entropy of the Ranges for Simple Random Walks on Discrete Groups

Jian-Sheng Xie, Min-Zhi Zhao, Xin-Xing Chen

arxiv:1612.00917 v2 · 2016-12-03 · 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{RXXUGXOKBQCS4EZXSXN4S6NYBS}

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	2026-05-18T00:50:28.846827Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8def435dca0c052e133795dbc979b80c92e77f141b8768dd56f8461c4d7a707c

Aliases

arxiv: 1612.00917 · arxiv_version: 1612.00917v2 · doi: 10.48550/arxiv.1612.00917 · pith_short_12: RXXUGXOKBQCS · pith_short_16: RXXUGXOKBQCS4EZX · pith_short_8: RXXUGXOK

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/RXXUGXOKBQCS4EZXSXN4S6NYBS \
  | 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: 8def435dca0c052e133795dbc979b80c92e77f141b8768dd56f8461c4d7a707c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b044a38ad3ea4d83b84c029af07d8f52c2ae5115e93a98b8569b659c95667a0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-12-03T03:14:09Z",
    "title_canon_sha256": "ff665cd310179242b0afa3c6b55ba0ab9378d4f75695ee8dbd8cee6a9f47462f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.00917",
    "kind": "arxiv",
    "version": 2
  }
}