Pith Number

pith:2GCTWJUZ

pith:2001:2GCTWJUZXK776VT6LW62GSWFRJ

not attested not anchored not stored refs pending

On the valuation of arithmetic-average Asian options: the Geman-Yor Laplace transform revisited

Michael Schr\"oder, Peter Carr

arxiv:math/0102080 v1 · 2001-02-09 · math.CA · math.PR · q-fin.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{2GCTWJUZXK776VT6LW62GSWFRJ}

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	2026-05-18T01:09:07.864347Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1853b2699babfff567e5dbda34ac58a5c5f0c04dfa4ba1745ece054a4e92f63

Aliases

arxiv: math/0102080 · arxiv_version: math/0102080v1 · doi: 10.48550/arxiv.math/0102080 · pith_short_12: 2GCTWJUZXK77 · pith_short_16: 2GCTWJUZXK776VT6 · pith_short_8: 2GCTWJUZ

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/2GCTWJUZXK776VT6LW62GSWFRJ \
  | 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: d1853b2699babfff567e5dbda34ac58a5c5f0c04dfa4ba1745ece054a4e92f63

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2e41cf714a0709da7bd5b7a670ab9db20a0f11e5d2e084e40b3093bbd544b538",
    "cross_cats_sorted": [
      "math.PR",
      "q-fin.PR"
    ],
    "license": "",
    "primary_cat": "math.CA",
    "submitted_at": "2001-02-09T12:13:33Z",
    "title_canon_sha256": "c292c8f3469a3bbe9e508a73df5f4c5f74fc5ebb629baddb9322be8c09fdad61"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0102080",
    "kind": "arxiv",
    "version": 1
  }
}