Pith Number

pith:CKZKXJYD

pith:2012:CKZKXJYDO6HEX7I7PR5KN2IEMT

not attested not anchored not stored refs pending

Practical Explicitly Invertible Approximation to 4 Decimals of Normal Cumulative Distribution Function Modifying Winitzki's Approximation of erf

Alessandro Soranzo, Emanuela Epure

arxiv:1211.6403 v1 · 2012-11-27 · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CKZKXJYDO6HEX7I7PR5KN2IEMT}

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	2026-05-18T03:39:51.895758Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12b2aba703778e4bfd1f7c7aa6e90464e3f37e470a4232e914cf5796d55e4b0b

Aliases

arxiv: 1211.6403 · arxiv_version: 1211.6403v1 · doi: 10.48550/arxiv.1211.6403 · pith_short_12: CKZKXJYDO6HE · pith_short_16: CKZKXJYDO6HEX7I7 · pith_short_8: CKZKXJYD

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/CKZKXJYDO6HEX7I7PR5KN2IEMT \
  | 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: 12b2aba703778e4bfd1f7c7aa6e90464e3f37e470a4232e914cf5796d55e4b0b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a504581513e1ad8a94c5d8ebda27a7c9e85e733b79293625cd291fda370a535",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/publicdomain/",
    "primary_cat": "math.ST",
    "submitted_at": "2012-11-27T19:53:21Z",
    "title_canon_sha256": "15b6cb217861d030c43f592ad1b71779bda3381300c96869d366dffea10913ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.6403",
    "kind": "arxiv",
    "version": 1
  }
}