Pith Number

pith:3STE5D4A

pith:2013:3STE5D4AY7C4WIILA57UE7C2OY

not attested not anchored not stored refs pending

A Discrete-Time Clark-Ocone Formula and its Application to an Error Analysis

Jir\^o Akahori, Kaori Okuma, Takafumi Amaba

arxiv:1307.0673 v2 · 2013-07-02 · 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{3STE5D4AY7C4WIILA57UE7C2OY}

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	2026-05-18T03:14:38.844717Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dca64e8f80c7c5cb210b077f427c5a7619ad39f0aa59f5f6f22ebb64ace75e86

Aliases

arxiv: 1307.0673 · arxiv_version: 1307.0673v2 · doi: 10.48550/arxiv.1307.0673 · pith_short_12: 3STE5D4AY7C4 · pith_short_16: 3STE5D4AY7C4WIIL · pith_short_8: 3STE5D4A

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/3STE5D4AY7C4WIILA57UE7C2OY \
  | 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: dca64e8f80c7c5cb210b077f427c5a7619ad39f0aa59f5f6f22ebb64ace75e86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6cebbd6fa1ee56267c08d0f015a7a6313510c44bb1ec1a671faf00f55598278",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-07-02T10:41:35Z",
    "title_canon_sha256": "20d9d08677ffbb58081e6f25c2f1ce6722ee4620e3e90fa7aaace81cd78ab9b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.0673",
    "kind": "arxiv",
    "version": 2
  }
}