Pith Number

pith:4M5A3AUL

pith:2013:4M5A3AUL4DFJXP4U25ILFNM6JF

not attested not anchored not stored refs pending

Uniformity of the late points of random walk on Z_n^d for d >= 3

Jason Miller, Perla Sousi

arxiv:1309.3265 v1 · 2013-09-12 · math.PR · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4M5A3AUL4DFJXP4U25ILFNM6JF}

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	2026-05-18T03:13:32.410638Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e33a0d828be0ca9bbf94d750b2b59e49742338003cb60321d63d4f43c6881fbf

Aliases

arxiv: 1309.3265 · arxiv_version: 1309.3265v1 · doi: 10.48550/arxiv.1309.3265 · pith_short_12: 4M5A3AUL4DFJ · pith_short_16: 4M5A3AUL4DFJXP4U · pith_short_8: 4M5A3AUL

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/4M5A3AUL4DFJXP4U25ILFNM6JF \
  | 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: e33a0d828be0ca9bbf94d750b2b59e49742338003cb60321d63d4f43c6881fbf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6a38788c73d2ee0269e0a873ee3b0df7e111fe59e8b0ad8673bc995b74f6e6dd",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-09-12T19:57:06Z",
    "title_canon_sha256": "e49fb3e33e890fc4852368753c2a585e35eba8920f71ff56f258fe9f8a13c185"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.3265",
    "kind": "arxiv",
    "version": 1
  }
}