Pith Number

pith:U2XZ6ZP2

pith:2010:U2XZ6ZP2EOFA3I6Z3TQD2JASYN

not attested not anchored not stored refs pending

A Functional Approach to FBSDEs and Its Application in Optimal Portfolios

G. Liang, T. Lyons, Z. Qian

arxiv:1011.4499 v1 · 2010-11-19 · math.PR · q-fin.PM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U2XZ6ZP2EOFA3I6Z3TQD2JASYN}

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	2026-05-18T04:35:14.021452Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a6af9f65fa238a0da3d9dce03d2412c37367dca763d15cf69d80a6f9c40746b3

Aliases

arxiv: 1011.4499 · arxiv_version: 1011.4499v1 · doi: 10.48550/arxiv.1011.4499 · pith_short_12: U2XZ6ZP2EOFA · pith_short_16: U2XZ6ZP2EOFA3I6Z · pith_short_8: U2XZ6ZP2

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/U2XZ6ZP2EOFA3I6Z3TQD2JASYN \
  | 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: a6af9f65fa238a0da3d9dce03d2412c37367dca763d15cf69d80a6f9c40746b3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3684631951bf95a7515ba1c01bd660a9cccac2a6c9261f8277b91e188e5f5da3",
    "cross_cats_sorted": [
      "q-fin.PM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-11-19T19:05:50Z",
    "title_canon_sha256": "338b8e2e44cd0a8bdb33555abba6ef22d9d8cfd3c528acf3c927b30a1ae50dbf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.4499",
    "kind": "arxiv",
    "version": 1
  }
}