Pith Number

pith:3BHJS5YR

pith:2013:3BHJS5YRIEITLJNZ5OUGOVHG2U

not attested not anchored not stored refs pending

Pathwise solvability of stochastic integral equations with generalized drift and non-smooth dispersion functions

Ioannis Karatzas, Johannes Ruf

arxiv:1312.7257 v4 · 2013-12-27 · math.PR · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3BHJS5YRIEITLJNZ5OUGOVHG2U}

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	2026-05-18T01:21:23.314122Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d84e997711411135a5b9eba86754e6d519f063e17deebab11c114f9be71544db

Aliases

arxiv: 1312.7257 · arxiv_version: 1312.7257v4 · doi: 10.48550/arxiv.1312.7257 · pith_short_12: 3BHJS5YRIEIT · pith_short_16: 3BHJS5YRIEITLJNZ · pith_short_8: 3BHJS5YR

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/3BHJS5YRIEITLJNZ5OUGOVHG2U \
  | 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: d84e997711411135a5b9eba86754e6d519f063e17deebab11c114f9be71544db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f4792c1d305a54a37d1a379ce3b2f5f61221c26751eb16b63c6ca78e5cb2161",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-12-27T13:19:49Z",
    "title_canon_sha256": "c633949e8c9eb780fa25f903869a0b6a44f431e2500596ac796e64a1d6649d6b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.7257",
    "kind": "arxiv",
    "version": 4
  }
}