Pith Number

pith:ZXSCKHM2

pith:2015:ZXSCKHM2OGKWQNSED2FZ4HKNI3

not attested not anchored not stored refs pending

On exceptional sets in Erd\H{o}s-R\'{e}nyi limit theorem revisited

Jinjun Li, Min Wu

arxiv:1511.08903 v4 · 2015-11-28 · math.PR · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZXSCKHM2OGKWQNSED2FZ4HKNI3}

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	2026-05-18T01:22:05.681870Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cde4251d9a71956836441e8b9e1d4d46e9cc49b2152d50742346617e98c5b36f

Aliases

arxiv: 1511.08903 · arxiv_version: 1511.08903v4 · doi: 10.48550/arxiv.1511.08903 · pith_short_12: ZXSCKHM2OGKW · pith_short_16: ZXSCKHM2OGKWQNSE · pith_short_8: ZXSCKHM2

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/ZXSCKHM2OGKWQNSED2FZ4HKNI3 \
  | 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: cde4251d9a71956836441e8b9e1d4d46e9cc49b2152d50742346617e98c5b36f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74dbaf8a7e77ed2c00e2662136806a29b8a3b79c399d64bf81bc6dfa4982e6a1",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-11-28T15:06:04Z",
    "title_canon_sha256": "cd111ee442d2e5dc6a8b71d788d89ae53aa03a61e1cecd96a8cad42fdb89a7fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.08903",
    "kind": "arxiv",
    "version": 4
  }
}