Pith Number

pith:HBIFA75Z

pith:2009:HBIFA75ZKQ5IVTL3DM4XZJFRKZ

not attested not anchored not stored refs pending

Entropy of Random Walk Range

Amir Yehudayoff, Ariel Yadin, Gady Kozma, Itai Benjamini

arxiv:0903.3179 v1 · 2009-03-18 · math.PR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HBIFA75ZKQ5IVTL3DM4XZJFRKZ}

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	2026-05-18T02:14:27.502066Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3850507fb9543a8acd7b1b397ca4b1567959d4d3641e6eb8daff146dbf3260c9

Aliases

arxiv: 0903.3179 · arxiv_version: 0903.3179v1 · doi: 10.48550/arxiv.0903.3179 · pith_short_12: HBIFA75ZKQ5I · pith_short_16: HBIFA75ZKQ5IVTL3 · pith_short_8: HBIFA75Z

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/HBIFA75ZKQ5IVTL3DM4XZJFRKZ \
  | 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: 3850507fb9543a8acd7b1b397ca4b1567959d4d3641e6eb8daff146dbf3260c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa104b2e780981e05ff4b1c2880c5d9ef3c27ec00ee599666582fe5d822ada5d",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-03-18T15:11:04Z",
    "title_canon_sha256": "d43f1ab206eb4a3c4c11f6a64b0d016eb88e1be473815581c7946f38543f28f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.3179",
    "kind": "arxiv",
    "version": 1
  }
}