Pith Number

pith:TOODYODF

pith:2016:TOODYODFSJD5DVFEHYLXG4MTUA

not attested not anchored not stored refs pending

Asymptotic approximation of central binomial coefficients with rigorous error bounds

Richard P. Brent

arxiv:1608.04834 v4 · 2016-08-17 · math.NA · cs.NA · math.CA · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TOODYODFSJD5DVFEHYLXG4MTUA}

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.

Cited by

1 paper in Pith

The mean absolute deviation of the classical discrete distributions: collapse identities, complete asymptotic expansions, and enveloping series

Receipt and verification

First computed	2026-07-05T03:41:55.472538Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b9c3c38659247d1d4a43e17737193a03023bef7ab4d1e22171380fa68dcd87a

Aliases

arxiv: 1608.04834 · arxiv_version: 1608.04834v4 · doi: 10.48550/arxiv.1608.04834 · pith_short_12: TOODYODFSJD5 · pith_short_16: TOODYODFSJD5DVFE · pith_short_8: TOODYODF

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/TOODYODFSJD5DVFEHYLXG4MTUA \
  | 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: 9b9c3c38659247d1d4a43e17737193a03023bef7ab4d1e22171380fa68dcd87a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "33b019b582a8594dfaec3104bf45313ac32dbead8ba1f3e7e15e68205b5691fe",
    "cross_cats_sorted": [
      "cs.NA",
      "math.CA",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2016-08-17T02:12:14Z",
    "title_canon_sha256": "948c3bc467ce950dd8eb073ae1194d806dda4c359b4da7aa011a7c9483f99906"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.04834",
    "kind": "arxiv",
    "version": 4
  }
}