Pith Number

pith:XTJFPFER

pith:2010:XTJFPFEROLMKQS7XPZHYH5VTHF

not attested not anchored not stored refs pending

Strict inequalities of critical values in continuum percolation

Massimo Franceschetti, Mathew D. Penrose, Tom Rosoman

arxiv:1007.3322 v1 · 2010-07-20 · 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{XTJFPFEROLMKQS7XPZHYH5VTHF}

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	2026-05-18T02:06:12.617422Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bcd257949172d8a84bf77e4f83f6b33955a0535dd1c9eb24045d269bae87cffe

Aliases

arxiv: 1007.3322 · arxiv_version: 1007.3322v1 · doi: 10.48550/arxiv.1007.3322 · pith_short_12: XTJFPFEROLMK · pith_short_16: XTJFPFEROLMKQS7X · pith_short_8: XTJFPFER

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/XTJFPFEROLMKQS7XPZHYH5VTHF \
  | 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: bcd257949172d8a84bf77e4f83f6b33955a0535dd1c9eb24045d269bae87cffe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "25c95c196b9579ac1644a2f00d69a60b9c72c65646f18e74ee32011f63acaf0e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-07-20T02:21:59Z",
    "title_canon_sha256": "3d344f0543414e05cae696f746a437018e6adb379831ee2b18fbc29b4206c064"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.3322",
    "kind": "arxiv",
    "version": 1
  }
}