Pith Number

pith:7FZLRI3G

pith:2011:7FZLRI3G36GCZTQFUHBVOBBFII

not attested not anchored not stored refs pending

Consensus over Random Graph Processes: Network Borel-Cantelli Lemmas for Almost Sure Convergence

Brian D. O. Anderson, Guodong Shi, Karl Henrik Johansson

arxiv:1112.1336 v5 · 2011-12-06 · cs.DC

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7FZLRI3G36GCZTQFUHBVOBBFII}

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	2026-05-18T00:57:57.157150Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f972b8a366df8c2cce05a1c35704254206685bc57a0aef096580700e22ea25e9

Aliases

arxiv: 1112.1336 · arxiv_version: 1112.1336v5 · doi: 10.48550/arxiv.1112.1336 · pith_short_12: 7FZLRI3G36GC · pith_short_16: 7FZLRI3G36GCZTQF · pith_short_8: 7FZLRI3G

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/7FZLRI3G36GCZTQFUHBVOBBFII \
  | 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: f972b8a366df8c2cce05a1c35704254206685bc57a0aef096580700e22ea25e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1addee836b93fd9cdd8efc5cad604790eb01ef5a8474eb4814340c9de8cdcdb8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DC",
    "submitted_at": "2011-12-06T16:33:04Z",
    "title_canon_sha256": "0a25808ac216c3021dc5415ca469a0057bc9067e54c30c439fe7e2c2d20607a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.1336",
    "kind": "arxiv",
    "version": 5
  }
}