Pith Number

pith:5MJWV233

pith:2017:5MJWV233YG76FUHR6LIS477GX4

not attested not anchored not stored refs pending

The phase transition in bounded-size Achlioptas processes

Lutz Warnke, Oliver Riordan

arxiv:1704.08714 v2 · 2017-04-27 · math.PR · cond-mat.stat-mech · 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{5MJWV233YG76FUHR6LIS477GX4}

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.

Cited by

2 papers in Pith

Graphon convergence of random cographs

Counting subgraphs in bounded-size Achlioptas processes

Receipt and verification

First computed	2026-07-05T10:07:36.422974Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb136aeb7bc1bfe2d0f1f2d12e7fe6bf0d878d969a43ab70bfee24288bac87f6

Aliases

arxiv: 1704.08714 · arxiv_version: 1704.08714v2 · doi: 10.48550/arxiv.1704.08714 · pith_short_12: 5MJWV233YG76 · pith_short_16: 5MJWV233YG76FUHR · pith_short_8: 5MJWV233

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/5MJWV233YG76FUHR6LIS477GX4 \
  | 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: eb136aeb7bc1bfe2d0f1f2d12e7fe6bf0d878d969a43ab70bfee24288bac87f6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d89d457fc71dcdb5502d7b1d730793cec5ee2a407e5f07d67fd1e0095dc928e5",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-04-27T18:49:03Z",
    "title_canon_sha256": "93bb5c84425ecc1f5cec87d9965c2dc68f429fb42904afeef6f3f1c5db51aef3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1704.08714",
    "kind": "arxiv",
    "version": 2
  }
}