Pith Number

pith:VGUXTTIW

pith:2016:VGUXTTIWVQNPVATEX44OKZIY5U

not attested not anchored not stored refs pending

Capacity of the range of random walk on $\mathbb{Z}^4$

Amine Asselah, Bruno Schapira, Perla Sousi

arxiv:1611.04567 v2 · 2016-11-14 · 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{VGUXTTIWVQNPVATEX44OKZIY5U}

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	2026-05-18T00:53:47.582503Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9a979cd16ac1afa8264bf38e56518ed0b4ee10bb8bef2e1e1d2bb0eb42ac925

Aliases

arxiv: 1611.04567 · arxiv_version: 1611.04567v2 · doi: 10.48550/arxiv.1611.04567 · pith_short_12: VGUXTTIWVQNP · pith_short_16: VGUXTTIWVQNPVATE · pith_short_8: VGUXTTIW

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/VGUXTTIWVQNPVATEX44OKZIY5U \
  | 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: a9a979cd16ac1afa8264bf38e56518ed0b4ee10bb8bef2e1e1d2bb0eb42ac925

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a04000b7da8a94549824164dfff0852fcdc7bb64151d2dbc83cc2730c065473f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-11-14T20:44:16Z",
    "title_canon_sha256": "91ee2593a79752707bb699cc8f787fb87a59e59bdc11ba5c8a8e93027976630b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.04567",
    "kind": "arxiv",
    "version": 2
  }
}