Pith Number

pith:ZKYU4UOS

pith:2007:ZKYU4UOSXKOGT7MWXH7C6GIHIT

not attested not anchored not stored refs pending

A Proof of the Smoothness of the Finite Time Horizon American Put Option for Jump Diffusions

Erhan Bayraktar

arxiv:math/0703782 v12 · 2007-03-27 · math.OC · math.PR · q-fin.CP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZKYU4UOSXKOGT7MWXH7C6GIHIT}

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	2026-07-04T15:33:35.354813Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cab14e51d2ba9c69fd96b9fe2f190744eaef30c7f728e72a30ea3262b8276721

Aliases

arxiv: math/0703782 · arxiv_version: math/0703782v12 · doi: 10.48550/arxiv.math/0703782 · pith_short_12: ZKYU4UOSXKOG · pith_short_16: ZKYU4UOSXKOGT7MW · pith_short_8: ZKYU4UOS

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/ZKYU4UOSXKOGT7MWXH7C6GIHIT \
  | 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: cab14e51d2ba9c69fd96b9fe2f190744eaef30c7f728e72a30ea3262b8276721

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "77b375c60a02ebb9653cfe61167e98f221b0359a24fa7aff664ea0dbfdd269d0",
    "cross_cats_sorted": [
      "math.PR",
      "q-fin.CP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2007-03-27T14:26:53Z",
    "title_canon_sha256": "c71c53ac9f7730a2431f355576dad231170c2157fb9320920bb16ac8daa14642"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0703782",
    "kind": "arxiv",
    "version": 12
  }
}