Pith Number

pith:HB62EOK7

pith:2019:HB62EOK7HIHV3VXAMJGWW5YR4G

not attested not anchored not stored refs pending

Expansion for the critical point of site percolation: the first three terms

Kilian Matzke, Markus Heydenreich

arxiv:1912.04584 v2 · 2019-12-10 · 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{HB62EOK7HIHV3VXAMJGWW5YR4G}

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.

Cited by

1 paper in Pith

Lace Expansion and Mean-Field Behavior for the Random Connection Model

Receipt and verification

First computed	2026-07-05T02:07:01.132908Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

387da2395f3a0f5dd6e0624d6b7711e1b2d3db48ce5e8ab49610cac446b06f7c

Aliases

arxiv: 1912.04584 · arxiv_version: 1912.04584v2 · doi: 10.48550/arxiv.1912.04584 · pith_short_12: HB62EOK7HIHV · pith_short_16: HB62EOK7HIHV3VXA · pith_short_8: HB62EOK7

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/HB62EOK7HIHV3VXAMJGWW5YR4G \
  | 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: 387da2395f3a0f5dd6e0624d6b7711e1b2d3db48ce5e8ab49610cac446b06f7c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "94b1f51d44bcb29ac1109baae5c76dacc511cc125450f15798337e8cfec75726",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-12-10T09:07:11Z",
    "title_canon_sha256": "0d1f7a8c0e9d4d06cb21a58d605e64d65b02fa1cffc44ade812ad77cde2f879b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1912.04584",
    "kind": "arxiv",
    "version": 2
  }
}