Pith Number

pith:QZ6HHP6S

pith:2015:QZ6HHP6SMIWFB3QMFZH7P3KFU7

not attested not anchored not stored refs pending

A zero-one law for recurrence and transience of frog processes

Elena Kosygina, Martin P.W. Zerner

arxiv:1508.01953 v2 · 2015-08-08 · 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{QZ6HHP6SMIWFB3QMFZH7P3KFU7}

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	2026-05-18T01:20:16.968868Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

867c73bfd2622c50ee0c2e4ff7ed45a7e7535bbc2fea047b06ec71603e7f1725

Aliases

arxiv: 1508.01953 · arxiv_version: 1508.01953v2 · doi: 10.48550/arxiv.1508.01953 · pith_short_12: QZ6HHP6SMIWF · pith_short_16: QZ6HHP6SMIWFB3QM · pith_short_8: QZ6HHP6S

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/QZ6HHP6SMIWFB3QMFZH7P3KFU7 \
  | 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: 867c73bfd2622c50ee0c2e4ff7ed45a7e7535bbc2fea047b06ec71603e7f1725

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80a0836e24fbb2246c5578b631803ed84a1d9f096a402e079df8bc9ce8c44fb4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-08-08T20:56:11Z",
    "title_canon_sha256": "05aa4255da7bce1c472bf86f61c146f946e330cfa0bc8db13d7acf05a91677c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.01953",
    "kind": "arxiv",
    "version": 2
  }
}