Pith Number

pith:YXH4J2IR

pith:2011:YXH4J2IRUB6YEFF4BKOZDSPAK6

not attested not anchored not stored refs pending

Strong solutions of stochastic equations with rank-based coefficients

Ioannis Karatzas, Mykhaylo Shkolnikov, Tomoyuki Ichiba

arxiv:1109.3823 v1 · 2011-09-18 · 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{YXH4J2IRUB6YEFF4BKOZDSPAK6}

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	2026-05-18T04:12:45.799627Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c5cfc4e911a07d8214bc0a9d91c9e057a1807dadb869c6125853ea6b07e64e87

Aliases

arxiv: 1109.3823 · arxiv_version: 1109.3823v1 · doi: 10.48550/arxiv.1109.3823 · pith_short_12: YXH4J2IRUB6Y · pith_short_16: YXH4J2IRUB6YEFF4 · pith_short_8: YXH4J2IR

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/YXH4J2IRUB6YEFF4BKOZDSPAK6 \
  | 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: c5cfc4e911a07d8214bc0a9d91c9e057a1807dadb869c6125853ea6b07e64e87

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "238ff078d7ad18ff4244acce55a19ec6ed08c12e42ad5bbbd444ece21e9d29af",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-09-18T00:03:13Z",
    "title_canon_sha256": "0cd2a956307ea11f961d864537bb571f5ab50acc7dd4f993dd788662d16eedfb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.3823",
    "kind": "arxiv",
    "version": 1
  }
}