Pith Number

pith:23YUK2KL

pith:2012:23YUK2KLVE3NW3JCXWR772AWKJ

not attested not anchored not stored refs pending

NumExp: Numerical epsilon expansion of hypergeometric functions

Jueping Liu, Zhi-Wei Huang

arxiv:1209.3971 v3 · 2012-09-18 · physics.comp-ph · hep-ph · hep-th · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{23YUK2KLVE3NW3JCXWR772AWKJ}

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	2026-05-18T03:25:59.259502Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6f145694ba936db6d22bda3ffe816526d098794213cc84d998d97829928b4f5

Aliases

arxiv: 1209.3971 · arxiv_version: 1209.3971v3 · doi: 10.48550/arxiv.1209.3971 · pith_short_12: 23YUK2KLVE3N · pith_short_16: 23YUK2KLVE3NW3JC · pith_short_8: 23YUK2KL

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/23YUK2KLVE3NW3JCXWR772AWKJ \
  | 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: d6f145694ba936db6d22bda3ffe816526d098794213cc84d998d97829928b4f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a08370b926e814f7ae8623738cedf0522d51bd2adeccb99eb1e67c4d09f63973",
    "cross_cats_sorted": [
      "hep-ph",
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.comp-ph",
    "submitted_at": "2012-09-18T14:12:09Z",
    "title_canon_sha256": "7b3246539ac8e0ecbd0b2b61a6917d16bee4ad75fdc0ba8ffa368039b1b4123a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.3971",
    "kind": "arxiv",
    "version": 3
  }
}