Pith Number

pith:5KVLDUG3

pith:2009:5KVLDUG3DFLEH7D3MM3OGR4JGJ

not attested not anchored not stored refs pending

A characterization of the martingale property of exponentially affine processes

Alexander G. Smirnov, Eberhard Mayerhofer, Johannes Muhle-Karbe

arxiv:0910.3632 v3 · 2009-10-19 · 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{5KVLDUG3DFLEH7D3MM3OGR4JGJ}

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	2026-05-18T04:22:50.196072Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eaaab1d0db195643fc7b6336e34789325a55ca8813f5a0b675f046aa9c5b0dcc

Aliases

arxiv: 0910.3632 · arxiv_version: 0910.3632v3 · doi: 10.48550/arxiv.0910.3632 · pith_short_12: 5KVLDUG3DFLE · pith_short_16: 5KVLDUG3DFLEH7D3 · pith_short_8: 5KVLDUG3

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/5KVLDUG3DFLEH7D3MM3OGR4JGJ \
  | 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: eaaab1d0db195643fc7b6336e34789325a55ca8813f5a0b675f046aa9c5b0dcc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "861cad0c15f136ac1ea2006b648fc567d6cc14050c14fd30a4a1a26911a7ddab",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-10-19T18:21:52Z",
    "title_canon_sha256": "4d329bb312489798fb9a62c955299890377a952c795c6fa3b90ab900c818f8c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.3632",
    "kind": "arxiv",
    "version": 3
  }
}