Pith Number

pith:RCR5GUDJ

pith:2016:RCR5GUDJ25SXZGOF6LQG3PNJHZ

not attested not anchored not stored refs pending

It\^o's formula, the stochastic exponential and change of measure on general time scales

Wenqing Hu

arxiv:1609.05967 v2 · 2016-09-19 · 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{RCR5GUDJ25SXZGOF6LQG3PNJHZ}

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	2026-05-18T00:47:38.090806Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

88a3d35069d7657c99c5f2e06dbda93e4e8bbda9d30ae637d03322af69e04916

Aliases

arxiv: 1609.05967 · arxiv_version: 1609.05967v2 · doi: 10.48550/arxiv.1609.05967 · pith_short_12: RCR5GUDJ25SX · pith_short_16: RCR5GUDJ25SXZGOF · pith_short_8: RCR5GUDJ

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/RCR5GUDJ25SXZGOF6LQG3PNJHZ \
  | 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: 88a3d35069d7657c99c5f2e06dbda93e4e8bbda9d30ae637d03322af69e04916

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f42f9325d4cc9a88e6d131208a271371ec06a1e5e83eafee7470ac22303021c9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-09-19T23:09:48Z",
    "title_canon_sha256": "110efa03f85d82b5624e9b9cd3928bccfec0faefb079d2bb80ac35a9037d1e96"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.05967",
    "kind": "arxiv",
    "version": 2
  }
}