Pith Number

pith:XYYUQKAU

pith:2011:XYYUQKAU57WM7DFAU6VOALXTIH

not attested not anchored not stored refs pending

Densities of short uniform random walks

Armin Straub, James Wan, Jonathan M. Borwein, Wadim Zudilin

arxiv:1103.2995 v2 · 2011-03-15 · math.CA · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XYYUQKAU57WM7DFAU6VOALXTIH}

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	2026-05-18T02:22:18.952587Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be31482814efeccf8ca0a7aae02ef341eee29eb27fc661fbfae0d525f555bfe2

Aliases

arxiv: 1103.2995 · arxiv_version: 1103.2995v2 · doi: 10.48550/arxiv.1103.2995 · pith_short_12: XYYUQKAU57WM · pith_short_16: XYYUQKAU57WM7DFA · pith_short_8: XYYUQKAU

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/XYYUQKAU57WM7DFAU6VOALXTIH \
  | 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: be31482814efeccf8ca0a7aae02ef341eee29eb27fc661fbfae0d525f555bfe2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fca44608e75ddab2d3042a9e67be240afa6345d0b4cffe02ec82fdd15b6d8718",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-03-15T19:08:45Z",
    "title_canon_sha256": "1a58ab51b3640cf8e1baabb8ecb931f84b0b6be8d5666476b315d0cee656a776"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.2995",
    "kind": "arxiv",
    "version": 2
  }
}