Pith Number

pith:O3Y3BLE2

pith:2011:O3Y3BLE2GQOAERK42W5YBU7UGU

not attested not anchored not stored refs pending

An Optional Stopping-like theorem for large stopping times on birth-death chains

Greg Markowsky

arxiv:1103.4973 v1 · 2011-03-24 · 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{O3Y3BLE2GQOAERK42W5YBU7UGU}

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	2026-05-18T04:25:48.279113Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76f1b0ac9a341c02455cd5bb80d3f43527540fe1c3549dada14063edfc24d146

Aliases

arxiv: 1103.4973 · arxiv_version: 1103.4973v1 · doi: 10.48550/arxiv.1103.4973 · pith_short_12: O3Y3BLE2GQOA · pith_short_16: O3Y3BLE2GQOAERK4 · pith_short_8: O3Y3BLE2

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/O3Y3BLE2GQOAERK42W5YBU7UGU \
  | 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: 76f1b0ac9a341c02455cd5bb80d3f43527540fe1c3549dada14063edfc24d146

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8782888b1f3893c7375c0799ca849105f2f57a54bf5538b9ef9f9a8558853dd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-03-24T06:20:21Z",
    "title_canon_sha256": "25594204ae548cc2a90f8e7cd9a666d6d7c84a11f668fa7f1d97c0867466eef1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.4973",
    "kind": "arxiv",
    "version": 1
  }
}