Pith Number

pith:YA47LIH7

pith:2013:YA47LIH7OSC47PEU4L6I35TIDJ

not attested not anchored not stored refs pending

Branching random walks and multi-type contact-processes on the percolation cluster of ${\mathbb{Z}}^{d}$

Daniela Bertacchi, Fabio Zucca

arxiv:1311.5369 v2 · 2013-11-21 · 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{YA47LIH7OSC47PEU4L6I35TIDJ}

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	2026-05-18T01:42:57.636065Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c039f5a0ff7485cfbc94e2fc8df6681a43d6b7acf7edf38aabe64a930f90c57e

Aliases

arxiv: 1311.5369 · arxiv_version: 1311.5369v2 · doi: 10.48550/arxiv.1311.5369 · pith_short_12: YA47LIH7OSC4 · pith_short_16: YA47LIH7OSC47PEU · pith_short_8: YA47LIH7

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/YA47LIH7OSC47PEU4L6I35TIDJ \
  | 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: c039f5a0ff7485cfbc94e2fc8df6681a43d6b7acf7edf38aabe64a930f90c57e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5d85f2d6592ddbc47a6e44d21d33e86ac29cb6380f9d45666da472f03f7353b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-11-21T11:21:35Z",
    "title_canon_sha256": "0adeaff525f104276145f857d57250dc4edd6264d91ab443d748672a584d5bcd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.5369",
    "kind": "arxiv",
    "version": 2
  }
}