Pith Number

pith:KBFCMEZC

pith:2011:KBFCMEZCGTMQ5Z3DZT4CYGHCBV

not attested not anchored not stored refs pending

A new proof for the conditions of Novikov and Kazamaki

Johannes Ruf

arxiv:1111.5583 v4 · 2011-11-23 · 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{KBFCMEZCGTMQ5Z3DZT4CYGHCBV}

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	2026-05-18T03:37:53.213426Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

504a26132234d90ee763ccf82c18e20d75b0c2409e3067db32e6cb76fea54516

Aliases

arxiv: 1111.5583 · arxiv_version: 1111.5583v4 · doi: 10.48550/arxiv.1111.5583 · pith_short_12: KBFCMEZCGTMQ · pith_short_16: KBFCMEZCGTMQ5Z3D · pith_short_8: KBFCMEZC

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/KBFCMEZCGTMQ5Z3DZT4CYGHCBV \
  | 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: 504a26132234d90ee763ccf82c18e20d75b0c2409e3067db32e6cb76fea54516

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f7b2a04ad574375e072f116f7ec88433544c2eba919d2b25eb3b80f379ef055",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-11-23T19:00:58Z",
    "title_canon_sha256": "18e4d501c6760b722054ce852de972394a0a91611e4086690bd2cf1da41c0f90"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.5583",
    "kind": "arxiv",
    "version": 4
  }
}