Pith Number

pith:TCJ2X22D

pith:2016:TCJ2X22DWKREF2VQF2YQONXYYC

not attested not anchored not stored refs pending

Multivariate approximation in total variation, II: discrete normal approximation

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

arxiv:1612.07519 v1 · 2016-12-22 · 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{TCJ2X22DWKREF2VQF2YQONXYYC}

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	2026-05-18T00:54:09.869125Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9893abeb43b2a242eab02eb10736f8c09e63454572ff820751ff497dfc672dbe

Aliases

arxiv: 1612.07519 · arxiv_version: 1612.07519v1 · doi: 10.48550/arxiv.1612.07519 · pith_short_12: TCJ2X22DWKRE · pith_short_16: TCJ2X22DWKREF2VQ · pith_short_8: TCJ2X22D

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/TCJ2X22DWKREF2VQF2YQONXYYC \
  | 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: 9893abeb43b2a242eab02eb10736f8c09e63454572ff820751ff497dfc672dbe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d91a763b129cc1200ff640907082e3a478bb71ce2b09ebea2f483ebfd930695",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-12-22T10:12:29Z",
    "title_canon_sha256": "a61c3c497805c4ca3f89fd453b2971305bf3f8b296c5840d68f8224a827606f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.07519",
    "kind": "arxiv",
    "version": 1
  }
}