Pith Number

pith:7VVNQOG4

pith:2007:7VVNQOG4MZPAPY53LZ64HLYPBK

not attested not anchored not stored refs pending

Multivariate normal approximation in geometric probability

Andrew R. Wade, Mathew D. Penrose

arxiv:0707.3898 v1 · 2007-07-26 · 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{7VVNQOG4MZPAPY53LZ64HLYPBK}

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	2026-05-18T03:34:46.821606Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd6ad838dc665e07e3bb5e7dc3af0f0ab39749d98e05f3cfc9349f0a2c65d992

Aliases

arxiv: 0707.3898 · arxiv_version: 0707.3898v1 · doi: 10.48550/arxiv.0707.3898 · pith_short_12: 7VVNQOG4MZPA · pith_short_16: 7VVNQOG4MZPAPY53 · pith_short_8: 7VVNQOG4

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/7VVNQOG4MZPAPY53LZ64HLYPBK \
  | 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: fd6ad838dc665e07e3bb5e7dc3af0f0ab39749d98e05f3cfc9349f0a2c65d992

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1aa8b7f463d72eb1f2c8982c5fd89f61af310a7340dc8d1772c2efc109df25bc",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2007-07-26T11:10:48Z",
    "title_canon_sha256": "ad9e2d384c5c06ec944d0deb816f17a47a58276d40cf7f42e600c94a5d9e2b32"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0707.3898",
    "kind": "arxiv",
    "version": 1
  }
}