Pith Number

pith:VTNTN67U

pith:2000:VTNTN67UUA7LVGGPLMUGG4TDY3

not attested not anchored not stored refs pending

On the valuation of arithmetic-average Asian options: Laguerre series and Theta integrals

Michael Schr\"oder

arxiv:math/0012072 v1 · 2000-12-11 · 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{VTNTN67UUA7LVGGPLMUGG4TDY3}

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	2026-05-18T01:09:07.883588Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

acdb36fbf4a03eba98cf5b28637263c6d841cc3e0cee37ceed2771edc4399083

Aliases

arxiv: math/0012072 · arxiv_version: math/0012072v1 · doi: 10.48550/arxiv.math/0012072 · pith_short_12: VTNTN67UUA7L · pith_short_16: VTNTN67UUA7LVGGP · pith_short_8: VTNTN67U

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/VTNTN67UUA7LVGGPLMUGG4TDY3 \
  | 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: acdb36fbf4a03eba98cf5b28637263c6d841cc3e0cee37ceed2771edc4399083

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d414c97e9778d4994e7decf5c0e2281d6b5b72334262b0dbb8048d0271098548",
    "cross_cats_sorted": [
      "math.PR",
      "q-fin.PR"
    ],
    "license": "",
    "primary_cat": "math.CA",
    "submitted_at": "2000-12-11T09:11:00Z",
    "title_canon_sha256": "8158fd45a154354685d16890e831c4644f378823477e40933164fbbedb22d594"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0012072",
    "kind": "arxiv",
    "version": 1
  }
}