Pith Number

pith:Z5FRHKLY

pith:2014:Z5FRHKLYKNA4WHCIQYN776NL7B

not attested not anchored not stored refs pending

The condensation phase transition in random graph coloring

Amin Coja-Oghlan, Dan Vilenchik, Felicia Rassmann, Samuel Hetterich, Victor Bapst

arxiv:1404.5513 v1 · 2014-04-19 · cs.DM · 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{Z5FRHKLYKNA4WHCIQYN776NL7B}

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	2026-05-18T00:29:33.953820Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf4b13a9785341cb1c48861bfff9abf86f00fbcd48aa53b3745595ea94a4794d

Aliases

arxiv: 1404.5513 · arxiv_version: 1404.5513v1 · doi: 10.48550/arxiv.1404.5513 · pith_short_12: Z5FRHKLYKNA4 · pith_short_16: Z5FRHKLYKNA4WHCI · pith_short_8: Z5FRHKLY

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/Z5FRHKLYKNA4WHCIQYN776NL7B \
  | 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: cf4b13a9785341cb1c48861bfff9abf86f00fbcd48aa53b3745595ea94a4794d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "68a81d1236692734c8ce541b51308afa4cc82a9821996b671f2d0dc079b5fa0c",
    "cross_cats_sorted": [
      "math.CO",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2014-04-19T08:17:09Z",
    "title_canon_sha256": "4678903e806a0f2ae53c7111efd633005062dec3374bba04aa999215a4285517"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1404.5513",
    "kind": "arxiv",
    "version": 1
  }
}