Pith Number

pith:IG33OU64

pith:2007:IG33OU64AMYKMYR4CDOUPDSUNN

not attested not anchored not stored refs pending

The number of open paths in an oriented $\rho$-percolation model

Francis Comets, Marina Vachkovskaia, Serguei Popov

arxiv:0707.0818 v1 · 2007-07-05 · 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{IG33OU64AMYKMYR4CDOUPDSUNN}

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	2026-05-18T04:03:44.179831Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

41b7b753dc0330a6623c10dd478e546b5b255aa2fc83a97288bf24c26a3242d4

Aliases

arxiv: 0707.0818 · arxiv_version: 0707.0818v1 · doi: 10.48550/arxiv.0707.0818 · pith_short_12: IG33OU64AMYK · pith_short_16: IG33OU64AMYKMYR4 · pith_short_8: IG33OU64

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/IG33OU64AMYKMYR4CDOUPDSUNN \
  | 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: 41b7b753dc0330a6623c10dd478e546b5b255aa2fc83a97288bf24c26a3242d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "530f55665de5b3c840c98c371b32becb5597fa8d0ebf2f41602d230a038ef803",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2007-07-05T15:50:06Z",
    "title_canon_sha256": "568d91f8fa674428e6f8ff829dcaf56b6ef1036eb9292f66d4cc055e32c89286"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0707.0818",
    "kind": "arxiv",
    "version": 1
  }
}