Pith Number

pith:NZJ46WD5

pith:2009:NZJ46WD5GEWYDUQPHT7T7PKYAS

not attested not anchored not stored refs pending

Stochastic Calculus for a Time-changed Semimartingale and the Associated Stochastic Differential Equations

Kei Kobayashi

arxiv:0906.5385 v2 · 2009-06-29 · 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{NZJ46WD5GEWYDUQPHT7T7PKYAS}

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	2026-05-18T04:38:50.887899Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6e53cf587d312d81d20f3cff3fbd58048ba9eb4c099aaaf8250e785f65629559

Aliases

arxiv: 0906.5385 · arxiv_version: 0906.5385v2 · doi: 10.48550/arxiv.0906.5385 · pith_short_12: NZJ46WD5GEWY · pith_short_16: NZJ46WD5GEWYDUQP · pith_short_8: NZJ46WD5

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/NZJ46WD5GEWYDUQPHT7T7PKYAS \
  | 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: 6e53cf587d312d81d20f3cff3fbd58048ba9eb4c099aaaf8250e785f65629559

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "88d734824473778192cfc1782049c4a36ccd0ac01c11b72fa3e6687fe91fd6b9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-06-29T23:30:04Z",
    "title_canon_sha256": "86db1ee18cb2afe89e74d66bc80d50e4ff41c95e175f3444b5c4809c562380e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.5385",
    "kind": "arxiv",
    "version": 2
  }
}