Pith Number

pith:24F453VT

pith:2010:24F453VTD4C3TKPR5L5S7TSZ2Y

not attested not anchored not stored refs pending

Two critical periods in the evolution of random planar graphs

Mihyun Kang, Tomasz {\L}uczak

arxiv:1006.0444 v2 · 2010-06-02 · 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{24F453VTD4C3TKPR5L5S7TSZ2Y}

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	2026-05-18T04:36:50.184338Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d70bceeeb31f05b9a9f1eafb2fce59d6228f25b0e18c2321267f30907b045a58

Aliases

arxiv: 1006.0444 · arxiv_version: 1006.0444v2 · doi: 10.48550/arxiv.1006.0444 · pith_short_12: 24F453VTD4C3 · pith_short_16: 24F453VTD4C3TKPR · pith_short_8: 24F453VT

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/24F453VTD4C3TKPR5L5S7TSZ2Y \
  | 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: d70bceeeb31f05b9a9f1eafb2fce59d6228f25b0e18c2321267f30907b045a58

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf86eba3f86e4bad1f5e62da0f18c1577b13f3f17f672ba700b3011cb975d94a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-06-02T16:57:26Z",
    "title_canon_sha256": "fe646a720d43e4b541f1a92137a4d69f5ed92569d71ab81ecca82692efbbd40c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.0444",
    "kind": "arxiv",
    "version": 2
  }
}