Pith Number

pith:NNHBQ7DC

pith:2015:NNHBQ7DCNGKKJR2RSMCJGD4EJ5

not attested not anchored not stored refs pending

Generalized couplings and convergence of transition probabilities

Alexei Kulik, Michael Scheutzow

arxiv:1512.06359 v2 · 2015-12-20 · 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{NNHBQ7DCNGKKJR2RSMCJGD4EJ5}

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	2026-05-18T01:22:00.010158Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6b4e187c626994a4c7519304930f844f6c7d300e513483f1fe4593c2698d5c8f

Aliases

arxiv: 1512.06359 · arxiv_version: 1512.06359v2 · doi: 10.48550/arxiv.1512.06359 · pith_short_12: NNHBQ7DCNGKK · pith_short_16: NNHBQ7DCNGKKJR2R · pith_short_8: NNHBQ7DC

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/NNHBQ7DCNGKKJR2RSMCJGD4EJ5 \
  | 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: 6b4e187c626994a4c7519304930f844f6c7d300e513483f1fe4593c2698d5c8f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e7592ce199b203034b091700b39d13303d622a8d85ac6d977d6e23dc0629982f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-12-20T11:46:21Z",
    "title_canon_sha256": "c0c3b5918fd3f2d584c9698b7b247dd89f5fcd26695cf1401b44d1ca0f6bc51e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.06359",
    "kind": "arxiv",
    "version": 2
  }
}