Pith Number

pith:HOX3DTV4

pith:2012:HOX3DTV4OKUY64Z6DPBGFZYRUW

not attested not anchored not stored refs pending

Largest sparse subgraphs of random graphs

Colin McDiarmid, Nikolaos Fountoulakis, Ross J. Kang

arxiv:1203.0132 v1 · 2012-03-01 · math.CO · 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{HOX3DTV4OKUY64Z6DPBGFZYRUW}

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	2026-05-18T03:14:26.990430Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3bafb1cebc72a98f733e1bc262e711a5845be8811e57ad5e97008cff52ecb733

Aliases

arxiv: 1203.0132 · arxiv_version: 1203.0132v1 · doi: 10.48550/arxiv.1203.0132 · pith_short_12: HOX3DTV4OKUY · pith_short_16: HOX3DTV4OKUY64Z6 · pith_short_8: HOX3DTV4

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/HOX3DTV4OKUY64Z6DPBGFZYRUW \
  | 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: 3bafb1cebc72a98f733e1bc262e711a5845be8811e57ad5e97008cff52ecb733

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b261677b0bc4f17317cdcb303311db46c600b6d4d5fde45b758591d46794e428",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-03-01T10:18:47Z",
    "title_canon_sha256": "4aae709e89f38b7ecb4205f270741222895ba1498c5e15eafe5f83b18a1b502a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.0132",
    "kind": "arxiv",
    "version": 1
  }
}