Pith Number

pith:SGHV3YBD

pith:2016:SGHV3YBDDH6YXMZ6XIJSPKZEHO

not attested not anchored not stored refs pending

The associativity rule in pathwise functional It\^o calculus

Alexander Schied, Iryna Voloshchenko

arxiv:1605.08861 v5 · 2016-05-28 · math.PR · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SGHV3YBDDH6YXMZ6XIJSPKZEHO}

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	2026-05-18T00:15:31.135625Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

918f5de02319fd8bb33eba1327ab243b981f854a3c98bcf06d598404e0cc85c2

Aliases

arxiv: 1605.08861 · arxiv_version: 1605.08861v5 · doi: 10.48550/arxiv.1605.08861 · pith_short_12: SGHV3YBDDH6Y · pith_short_16: SGHV3YBDDH6YXMZ6 · pith_short_8: SGHV3YBD

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/SGHV3YBDDH6YXMZ6XIJSPKZEHO \
  | 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: 918f5de02319fd8bb33eba1327ab243b981f854a3c98bcf06d598404e0cc85c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72a61b8d5e6d4c53553cf11f6156b8afa6c33332067cd9abba9cd48a3a294318",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-05-28T08:16:16Z",
    "title_canon_sha256": "d6d161159d196f7d5f7b4c2fa22c5a02065f92bf0151c884c6ee6d4504052ec1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.08861",
    "kind": "arxiv",
    "version": 5
  }
}