Pith Number

pith:WZD7NGYP

pith:2012:WZD7NGYPZOMO7CNIFUYIF75Q6O

not attested not anchored not stored refs pending

Linear stochastic equations in the critical case

Dariusz Buraczewski, Konrad Kolesko

arxiv:1210.7732 v1 · 2012-10-29 · 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{WZD7NGYPZOMO7CNIFUYIF75Q6O}

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	2026-05-18T03:41:59.490428Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b647f69b0fcb98ef89a82d3082ffb0f3a3a57b23c24b0bea4150cfff29bda57c

Aliases

arxiv: 1210.7732 · arxiv_version: 1210.7732v1 · doi: 10.48550/arxiv.1210.7732 · pith_short_12: WZD7NGYPZOMO · pith_short_16: WZD7NGYPZOMO7CNI · pith_short_8: WZD7NGYP

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/WZD7NGYPZOMO7CNIFUYIF75Q6O \
  | 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: b647f69b0fcb98ef89a82d3082ffb0f3a3a57b23c24b0bea4150cfff29bda57c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72b99c996ddb7dcd47cdd5087cfd8ffaddc24a4c0a67c60d140ac56925d7050d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-10-29T17:10:32Z",
    "title_canon_sha256": "6b198f1884e8745bdbf98d60bf69b1b267d8edb566e003a8de5e28847a1bfdec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.7732",
    "kind": "arxiv",
    "version": 1
  }
}