Pith Number

pith:62VJUG6U

pith:2011:62VJUG6UCL66TKYUKSAIVKFGT3

not attested not anchored not stored refs pending

The Complete Convergence Theorem Holds for Contact Processes in a Random Environment on $Z^d\times Z^+$

Qiang Yao, Xinxing Chen

arxiv:1102.3020 v4 · 2011-02-15 · 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{62VJUG6UCL66TKYUKSAIVKFGT3}

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	2026-05-18T02:22:31.730267Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f6aa9a1bd412fde9ab1454808aa8a69ed9186f66838849d843601aca3d6fd801

Aliases

arxiv: 1102.3020 · arxiv_version: 1102.3020v4 · doi: 10.48550/arxiv.1102.3020 · pith_short_12: 62VJUG6UCL66 · pith_short_16: 62VJUG6UCL66TKYU · pith_short_8: 62VJUG6U

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/62VJUG6UCL66TKYUKSAIVKFGT3 \
  | 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: f6aa9a1bd412fde9ab1454808aa8a69ed9186f66838849d843601aca3d6fd801

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad18f1ddb1e1d82222c6f443724c5f9a9026b9ee8b5125884ed8a084497feaa9",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-02-15T10:10:08Z",
    "title_canon_sha256": "57c35e0532065851056bb54a84863123bf9a5be4e7b2005df0ac148b202287a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.3020",
    "kind": "arxiv",
    "version": 4
  }
}