Pith Number

pith:T2GZRMW3

pith:2011:T2GZRMW3GQZSL3WY2L6OZWES5Y

not attested not anchored not stored refs pending

HYPERDIRE: HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions pFq, F1,F2,F3,F4

Bernd A.Kniehl (Hamburg U., Dubna, Inst. Theor. Phys. II, Inst. Theor. Phys. II), JINR), Mikhail Yu. Kalmykov (Hamburg U., Vladimir V. Bytev (Dubna

arxiv:1105.3565 v3 · 2011-05-18 · math-ph · cs.SC · hep-ph · hep-th · math.CA · 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{T2GZRMW3GQZSL3WY2L6OZWES5Y}

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	2026-05-18T03:14:07.128878Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e8d98b2db343325eed8d2fcecd892ee2e8e7d1540b6993a462f059bdbcc46fa

Aliases

arxiv: 1105.3565 · arxiv_version: 1105.3565v3 · doi: 10.48550/arxiv.1105.3565 · pith_short_12: T2GZRMW3GQZS · pith_short_16: T2GZRMW3GQZSL3WY · pith_short_8: T2GZRMW3

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/T2GZRMW3GQZSL3WY2L6OZWES5Y \
  | 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: 9e8d98b2db343325eed8d2fcecd892ee2e8e7d1540b6993a462f059bdbcc46fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dabef411808d5ebc2bc62fa4b9dfa92ac574241e78bc86c6db5278f9556ef8a9",
    "cross_cats_sorted": [
      "cs.SC",
      "hep-ph",
      "hep-th",
      "math.CA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-05-18T09:06:44Z",
    "title_canon_sha256": "9ef500eeee777343f9f8aa7928a1ee337715c62a7c9bd4cf23c90a241cd5b024"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.3565",
    "kind": "arxiv",
    "version": 3
  }
}