Pith Number

pith:GC6CUUBA

pith:2015:GC6CUUBA6JLNWKNJR2H4TR5XPP

not attested not anchored not stored refs pending

Asymptotic Expansion for Forward-Backward SDEs with Jumps

Akihiko Takahashi, Masaaki Fujii

arxiv:1510.03220 v4 · 2015-10-12 · q-fin.CP · q-fin.MF

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GC6CUUBA6JLNWKNJR2H4TR5XPP}

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	2026-05-18T00:06:21.126223Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30bc2a5020f256db29a98e8fc9c7b77bcd7aa9c270cbb1f179c56ae8e7bbd06b

Aliases

arxiv: 1510.03220 · arxiv_version: 1510.03220v4 · doi: 10.48550/arxiv.1510.03220 · pith_short_12: GC6CUUBA6JLN · pith_short_16: GC6CUUBA6JLNWKNJ · pith_short_8: GC6CUUBA

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/GC6CUUBA6JLNWKNJR2H4TR5XPP \
  | 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: 30bc2a5020f256db29a98e8fc9c7b77bcd7aa9c270cbb1f179c56ae8e7bbd06b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2d9bcec265ed8746d40798bc54346b7d89028fdf471a78728e761d7dbae3fdd8",
    "cross_cats_sorted": [
      "q-fin.MF"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "q-fin.CP",
    "submitted_at": "2015-10-12T10:57:53Z",
    "title_canon_sha256": "3d3298faa1042197a5abbbdec496c2d019b9e2b595f09174812d484adc974f72"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.03220",
    "kind": "arxiv",
    "version": 4
  }
}