Pith Number

pith:5RBWILH2

pith:2013:5RBWILH276AJOXE677O3K4ZAAM

not attested not anchored not stored refs pending

G-Brownian Motion as Rough Paths and Differential Equations Driven by G-Brownian Motion

Danyu Yang, Xi Geng, Zhongmin Qian

arxiv:1306.2021 v1 · 2013-06-09 · 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{5RBWILH276AJOXE677O3K4ZAAM}

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	2026-05-18T03:21:22.608057Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec43642cfaff80975c9effddb57320031f9c8bc9864969bae86914303fe8c56e

Aliases

arxiv: 1306.2021 · arxiv_version: 1306.2021v1 · doi: 10.48550/arxiv.1306.2021 · pith_short_12: 5RBWILH276AJ · pith_short_16: 5RBWILH276AJOXE6 · pith_short_8: 5RBWILH2

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/5RBWILH276AJOXE677O3K4ZAAM \
  | 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: ec43642cfaff80975c9effddb57320031f9c8bc9864969bae86914303fe8c56e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "da8235ec78bbf1a24c1a7391c789eaffabd14865fd2c8908688a9597cadc0e63",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-06-09T14:04:38Z",
    "title_canon_sha256": "0ce91ce27eae05cbc1137a104bd14ab53a666d960c4f476f4350132c0b45f45d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.2021",
    "kind": "arxiv",
    "version": 1
  }
}