Pith Number

pith:232SDEOK

pith:2010:232SDEOKKCGCP3QVZDQEALZ6JW

not attested not anchored not stored refs pending

Monotonicity of Percolation Probability on $\Z^d$ with Long Range Connections

Bernardo N. B. de Lima, R\'emy Sanchis, Roger W.C. Silva

arxiv:1006.4191 v3 · 2010-06-21 · 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{232SDEOKKCGCP3QVZDQEALZ6JW}

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	2026-05-18T04:21:29.987160Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6f52191ca508c27ee15c8e0402f3e4dbe41c9866bdf23c8c77894129fd3f496

Aliases

arxiv: 1006.4191 · arxiv_version: 1006.4191v3 · doi: 10.48550/arxiv.1006.4191 · pith_short_12: 232SDEOKKCGC · pith_short_16: 232SDEOKKCGCP3QV · pith_short_8: 232SDEOK

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/232SDEOKKCGCP3QVZDQEALZ6JW \
  | 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: d6f52191ca508c27ee15c8e0402f3e4dbe41c9866bdf23c8c77894129fd3f496

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63e09ce81e6f55d5efa89caf5d7a80c45fd8c273529f821579e2d28808f2d5aa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-06-21T23:38:03Z",
    "title_canon_sha256": "e5cddb5f1305bb45fb965c55f38f80ff9d2c5d802666d0dd814eff6276ceb9be"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.4191",
    "kind": "arxiv",
    "version": 3
  }
}