Pith Number

pith:K4LPOYFN

pith:2016:K4LPOYFNLMQL4QWACULM6U7XRU

not attested not anchored not stored refs pending

How to determine if a random graph with a fixed degree sequence has a giant component

Bruce Reed, Dieter Rautenbach, Felix Joos, Guillem Perarnau

arxiv:1601.03714 v3 · 2016-01-14 · math.CO · cs.DM · 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{K4LPOYFNLMQL4QWACULM6U7XRU}

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	2026-05-18T00:51:51.986519Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5716f760ad5b20be42c01516cf53f78d3bc55e53553492a696568ea1a506c647

Aliases

arxiv: 1601.03714 · arxiv_version: 1601.03714v3 · doi: 10.48550/arxiv.1601.03714 · pith_short_12: K4LPOYFNLMQL · pith_short_16: K4LPOYFNLMQL4QWA · pith_short_8: K4LPOYFN

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/K4LPOYFNLMQL4QWACULM6U7XRU \
  | 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: 5716f760ad5b20be42c01516cf53f78d3bc55e53553492a696568ea1a506c647

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0c555abfac689bf818cb9902393c049959c5c41e5edec15dfa9c8ace067dd4c0",
    "cross_cats_sorted": [
      "cs.DM",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-01-14T20:19:33Z",
    "title_canon_sha256": "6d8e24cee141f2fc0cb08925b7d2330557aca58dce521c78d98270974999a58f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.03714",
    "kind": "arxiv",
    "version": 3
  }
}