Pith Number

pith:IHK5WWA6

pith:2013:IHK5WWA6MCNKE3TGZNI6UGZN6X

not attested not anchored not stored refs pending

G-Expectation Weighted Sobolev Spaces, Backward SDE and Path Dependent PDE

Shige Peng, Yongsheng Song

arxiv:1305.4722 v2 · 2013-05-21 · 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{IHK5WWA6MCNKE3TGZNI6UGZN6X}

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	2026-05-18T02:56:11.648747Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

41d5db581e609aa26e66cb51ea1b2df5dea82aacf3741e4bea6318f229e67ff3

Aliases

arxiv: 1305.4722 · arxiv_version: 1305.4722v2 · doi: 10.48550/arxiv.1305.4722 · pith_short_12: IHK5WWA6MCNK · pith_short_16: IHK5WWA6MCNKE3TG · pith_short_8: IHK5WWA6

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/IHK5WWA6MCNKE3TGZNI6UGZN6X \
  | 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: 41d5db581e609aa26e66cb51ea1b2df5dea82aacf3741e4bea6318f229e67ff3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "daa2df8f5e640926b73bb38a23a6cd36fe4f8a7fd7014c6d46149529f85d9835",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-05-21T06:12:12Z",
    "title_canon_sha256": "5c1ff68ebda6976f69a8339fa70583ae5cedda88854ae7dd90df8db2d4f5e737"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.4722",
    "kind": "arxiv",
    "version": 2
  }
}