Pith Number

pith:PZ2MMJQW

pith:2016:PZ2MMJQWOOY5TXSYE7NZEETHXO

not attested not anchored not stored refs pending

The emergence of a giant component in random subgraphs of pseudo-random graphs

Alan Frieze, Michael Krivelevich, Ryan R. Martin

arxiv:1605.06643 v2 · 2016-05-21 · 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{PZ2MMJQWOOY5TXSYE7NZEETHXO}

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	2026-05-18T01:13:46.734647Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e74c6261673b1d9de5827db921267bb96d24ea40bf280dacf32b824df639f2c

Aliases

arxiv: 1605.06643 · arxiv_version: 1605.06643v2 · doi: 10.48550/arxiv.1605.06643 · pith_short_12: PZ2MMJQWOOY5 · pith_short_16: PZ2MMJQWOOY5TXSY · pith_short_8: PZ2MMJQW

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/PZ2MMJQWOOY5TXSYE7NZEETHXO \
  | 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: 7e74c6261673b1d9de5827db921267bb96d24ea40bf280dacf32b824df639f2c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f02391d85317044b01303586a86aee9a1c09a4906ce2c959e1445c4c89966e19",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-05-21T13:40:46Z",
    "title_canon_sha256": "2feabe3fe2588aae0c7869127d2da773f579a8f9763416b5582b58e197dde51f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.06643",
    "kind": "arxiv",
    "version": 2
  }
}