Pith Number

pith:DZ6Z3XGD

pith:2016:DZ6Z3XGDYYDJREKQ5U6K7NSZ4X

not attested not anchored not stored refs pending

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

Amine Asselah, Bruno Schapira, Perla Sousi

arxiv:1602.03499 v1 · 2016-02-10 · 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{DZ6Z3XGDYYDJREKQ5U6K7NSZ4X}

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	2026-05-18T01:20:59.810971Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e7d9ddcc3c606989150ed3cafb659e5dcb6f912425b5dba07375c2680574ccb

Aliases

arxiv: 1602.03499 · arxiv_version: 1602.03499v1 · doi: 10.48550/arxiv.1602.03499 · pith_short_12: DZ6Z3XGDYYDJ · pith_short_16: DZ6Z3XGDYYDJREKQ · pith_short_8: DZ6Z3XGD

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/DZ6Z3XGDYYDJREKQ5U6K7NSZ4X \
  | 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: 1e7d9ddcc3c606989150ed3cafb659e5dcb6f912425b5dba07375c2680574ccb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e4ed0433c7575a762852f77d8b1fd2bffdc0437a462e2de9dff1a1881778c592",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-02-10T20:06:47Z",
    "title_canon_sha256": "de6162842624dc6a5822fd59765844fef0bec589d6d5855fac4e1de08216a44e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.03499",
    "kind": "arxiv",
    "version": 1
  }
}