Pith Number

pith:RZLCIF4S

pith:2012:RZLCIF4S3RTX7AMWOGNA2WJIVA

not attested not anchored not stored refs pending

A Semi-group Expansion for Pricing Barrier Options

Akihiko Takahashi, Takashi Kato, Toshihiro Yamada

arxiv:1202.3002 v5 · 2012-02-14 · q-fin.CP · math.AP · 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{RZLCIF4S3RTX7AMWOGNA2WJIVA}

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	2026-05-18T02:41:17.352634Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8e56241792dc677f8196719a0d5928a817d180a05b06bc4953e9a4c04a6a493d

Aliases

arxiv: 1202.3002 · arxiv_version: 1202.3002v5 · doi: 10.48550/arxiv.1202.3002 · pith_short_12: RZLCIF4S3RTX · pith_short_16: RZLCIF4S3RTX7AMW · pith_short_8: RZLCIF4S

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/RZLCIF4S3RTX7AMWOGNA2WJIVA \
  | 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: 8e56241792dc677f8196719a0d5928a817d180a05b06bc4953e9a4c04a6a493d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40deae54aa3514e0e2d1c23587010e0b81b4a3de6cf08304c868fa0728ed627e",
    "cross_cats_sorted": [
      "math.AP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "q-fin.CP",
    "submitted_at": "2012-02-14T11:25:38Z",
    "title_canon_sha256": "96357b9a766e5ec90c89fc933a159304772dea58be024da9a029238bf1dd1547"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.3002",
    "kind": "arxiv",
    "version": 5
  }
}