Pith Number

pith:LX3AJGVT

pith:2010:LX3AJGVTLUJFWE53P4CECP6HGE

not attested not anchored not stored refs pending

Martingale Representation Theorem for the G-expectation

H.M. Soner, J. Zhang, N. Touzi

arxiv:1001.3802 v2 · 2010-01-21 · 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{LX3AJGVTLUJFWE53P4CECP6HGE}

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	2026-05-18T03:20:57.396733Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5df6049ab35d125b13bb7f04413fc7312f206630787084dd6e4523e158817646

Aliases

arxiv: 1001.3802 · arxiv_version: 1001.3802v2 · doi: 10.48550/arxiv.1001.3802 · pith_short_12: LX3AJGVTLUJF · pith_short_16: LX3AJGVTLUJFWE53 · pith_short_8: LX3AJGVT

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/LX3AJGVTLUJFWE53P4CECP6HGE \
  | 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: 5df6049ab35d125b13bb7f04413fc7312f206630787084dd6e4523e158817646

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e3963a04467ef6ad8f1426623c72e932465be1911d3f84ad235a4ac655f8a585",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-01-21T13:47:12Z",
    "title_canon_sha256": "ddb424137c9d52aa32fb4084d16bd639aaa17dcc3e73833cd6cb28955fffc5db"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.3802",
    "kind": "arxiv",
    "version": 2
  }
}