Pith Number

pith:4NAH447V

pith:2011:4NAH447VFONFHC4CVXSBHRZYN3

not attested not anchored not stored refs pending

When a Stochastic Exponential is a True Martingale. Extension of a Method of Bene^s

F. Klebaner, R. Liptser

arxiv:1112.0430 v2 · 2011-12-02 · 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{4NAH447VFONFHC4CVXSBHRZYN3}

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	2026-05-18T03:01:24.601864Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3407e73f52b9a538b82ade413c7386ee8f9998d020ed7d4b734c988b6ef7bfe

Aliases

arxiv: 1112.0430 · arxiv_version: 1112.0430v2 · doi: 10.48550/arxiv.1112.0430 · pith_short_12: 4NAH447VFONF · pith_short_16: 4NAH447VFONFHC4C · pith_short_8: 4NAH447V

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/4NAH447VFONFHC4CVXSBHRZYN3 \
  | 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: e3407e73f52b9a538b82ade413c7386ee8f9998d020ed7d4b734c988b6ef7bfe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "546a80efba83a111a5e8d928bc7a4a8a2e592113c757249a5999e642bb93def3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-12-02T11:45:19Z",
    "title_canon_sha256": "1ec6583aea8ddb862e4e277d155e27fc90edc61543ed14ba8b8a166973df788a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.0430",
    "kind": "arxiv",
    "version": 2
  }
}