Pith Number

pith:XK5SHOZG

pith:2018:XK5SHOZGHDR6RRYOWNJ3ZVOM4P

not attested not anchored not stored refs pending

Critical Percolation and the Incipient Infinite Cluster on Galton-Watson Trees

Marcus Michelen

arxiv:1806.00888 v2 · 2018-06-03 · 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{XK5SHOZGHDR6RRYOWNJ3ZVOM4P}

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	2026-05-17T23:53:44.016029Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

babb23bb2638e3e8c70eb353bcd5cce3f705fcc8250067034ab71eb7e1cfdeae

Aliases

arxiv: 1806.00888 · arxiv_version: 1806.00888v2 · doi: 10.48550/arxiv.1806.00888 · pith_short_12: XK5SHOZGHDR6 · pith_short_16: XK5SHOZGHDR6RRYO · pith_short_8: XK5SHOZG

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/XK5SHOZGHDR6RRYOWNJ3ZVOM4P \
  | 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: babb23bb2638e3e8c70eb353bcd5cce3f705fcc8250067034ab71eb7e1cfdeae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b35f0dae305e315ab31eac24d2f395dbea415e6e6b4cfb6b13c09fa5fa5754e4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-06-03T21:46:49Z",
    "title_canon_sha256": "d6b5d3fdd687bbbbc4fc14ed7264905721cd583dc2373c155e52a9c8261711a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.00888",
    "kind": "arxiv",
    "version": 2
  }
}