Pith Number

pith:GRNX2GJM

pith:2006:GRNX2GJMJ53CR3DN4YIXA5HEA7

not attested not anchored not stored refs pending

G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Ito's type

Shige Peng

arxiv:math/0601035 v2 · 2006-01-03 · 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{GRNX2GJMJ53CR3DN4YIXA5HEA7}

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.

Cited by

1 paper in Pith

Regularity of Solutions of Mean-Field $G$-SDEs

Receipt and verification

First computed	2026-07-04T14:58:17.456261Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

345b7d192c4f7628ec6de6117074e407ec899cef45538fa7d6c824ce52907372

Aliases

arxiv: math/0601035 · arxiv_version: math/0601035v2 · doi: 10.48550/arxiv.math/0601035 · pith_short_12: GRNX2GJMJ53C · pith_short_16: GRNX2GJMJ53CR3DN · pith_short_8: GRNX2GJM

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/GRNX2GJMJ53CR3DN4YIXA5HEA7 \
  | 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: 345b7d192c4f7628ec6de6117074e407ec899cef45538fa7d6c824ce52907372

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8e3bf22fb477c2ed864e3cc22f6c3835abf484fad9229ecfb64d09b65e5388e",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2006-01-03T08:20:24Z",
    "title_canon_sha256": "e9139eb32952b0bdaff91b5d890693b61d92f2372530e576078e5d822d5159f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0601035",
    "kind": "arxiv",
    "version": 2
  }
}