Pith Number

pith:NMUMCOG6

pith:2015:NMUMCOG6XETEPD2JEU7NT42DKP

not attested not anchored not stored refs pending

Multivariate approximation in total variation, I: equilibrium distributions of Markov jump processes

A. D. Barbour, Aihua Xia, Malwina J. Luczak

arxiv:1512.07400 v2 · 2015-12-23 · 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{NMUMCOG6XETEPD2JEU7NT42DKP}

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	2026-05-18T00:54:09.016338Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6b28c138deb926478f49253ed9f34353d7c934f3f24516a4cfb5ef04b8543eec

Aliases

arxiv: 1512.07400 · arxiv_version: 1512.07400v2 · doi: 10.48550/arxiv.1512.07400 · pith_short_12: NMUMCOG6XETE · pith_short_16: NMUMCOG6XETEPD2J · pith_short_8: NMUMCOG6

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/NMUMCOG6XETEPD2JEU7NT42DKP \
  | 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: 6b28c138deb926478f49253ed9f34353d7c934f3f24516a4cfb5ef04b8543eec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d3419e6358fb5f51c0531b66b94e5c93185db4aea95ce5a7e0d87b51e230902b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-12-23T09:20:29Z",
    "title_canon_sha256": "b817537011743840678ac03e1afb3a2f46fe3802b9f5d91adbf521a8400d3420"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.07400",
    "kind": "arxiv",
    "version": 2
  }
}