Pith Number

pith:4AXHQIPG

pith:2015:4AXHQIPG6CE5RPKBLXI27UMPW6

not attested not anchored not stored refs pending

The cone percolation model on Galton-Watson and on spherically symmetric trees

F\'abio Prates Machado, Krishnamurthi Ravishankar, Valdivino Vargas Junior

arxiv:1510.02821 v3 · 2015-10-09 · 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{4AXHQIPG6CE5RPKBLXI27UMPW6}

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	2026-05-18T00:59:42.254787Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e02e7821e6f089d8bd415dd1afd18fb7b7ed60362e7cc8cdfa1257612643e046

Aliases

arxiv: 1510.02821 · arxiv_version: 1510.02821v3 · doi: 10.48550/arxiv.1510.02821 · pith_short_12: 4AXHQIPG6CE5 · pith_short_16: 4AXHQIPG6CE5RPKB · pith_short_8: 4AXHQIPG

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/4AXHQIPG6CE5RPKBLXI27UMPW6 \
  | 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: e02e7821e6f089d8bd415dd1afd18fb7b7ed60362e7cc8cdfa1257612643e046

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f019e4ed35f860052ef721d963f798d062a6d9f5ee6392bc1179c0d0fbd14aee",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-10-09T20:46:39Z",
    "title_canon_sha256": "fd5c6a178c365a0e408668c041d653415d4ca3390e7cdd81afe6ac041bcf409e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.02821",
    "kind": "arxiv",
    "version": 3
  }
}