Pith Number

pith:7NXHYKO3

pith:2014:7NXHYKO3MP5ZIDPX2RA4UZORUI

not attested not anchored not stored refs pending

The phase transition in the multi-type binomial random graph $G(\mathbf{n},P)$

Ang\'elica Pach\'on, Christoph Koch, Mihyun Kang

arxiv:1407.6248 v3 · 2014-07-17 · math.PR · 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{7NXHYKO3MP5ZIDPX2RA4UZORUI}

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	2026-05-18T01:35:22.702524Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb6e7c29db63fb940df7d441ca65d1a236fe99eb271c4ebdef418362f4c91704

Aliases

arxiv: 1407.6248 · arxiv_version: 1407.6248v3 · doi: 10.48550/arxiv.1407.6248 · pith_short_12: 7NXHYKO3MP5Z · pith_short_16: 7NXHYKO3MP5ZIDPX · pith_short_8: 7NXHYKO3

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/7NXHYKO3MP5ZIDPX2RA4UZORUI \
  | 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: fb6e7c29db63fb940df7d441ca65d1a236fe99eb271c4ebdef418362f4c91704

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "251b59b8b6d62bca0400bcf957867c5f031759e56a08a1ba208db91a77fff3b0",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-07-17T16:25:30Z",
    "title_canon_sha256": "0d4c4d7f703a1fd6a575826a2b773b81efa2e2df4319054e6c6477363a7d5ce2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.6248",
    "kind": "arxiv",
    "version": 3
  }
}