Pith Number

pith:BL4W6C2V

pith:2015:BL4W6C2VF5FXKHBZJE63TZBKGF

not attested not anchored not stored refs pending

Duality and Reciprocity for Hypergeometric Series with Gamma Product Formula

Katsunori Iwasaki

arxiv:1504.03140 v3 · 2015-04-13 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BL4W6C2VF5FXKHBZJE63TZBKGF}

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	2026-05-18T00:23:59.349751Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0af96f0b552f4b751c39493db9e42a315c4eba7db74865d5b0ecb9792c80bfa1

Aliases

arxiv: 1504.03140 · arxiv_version: 1504.03140v3 · doi: 10.48550/arxiv.1504.03140 · pith_short_12: BL4W6C2VF5FX · pith_short_16: BL4W6C2VF5FXKHBZ · pith_short_8: BL4W6C2V

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/BL4W6C2VF5FXKHBZJE63TZBKGF \
  | 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: 0af96f0b552f4b751c39493db9e42a315c4eba7db74865d5b0ecb9792c80bfa1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b547664b2307854d0e6521aca83e1efe0ff881c30e7e7359d21718f729931b3e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-04-13T11:38:03Z",
    "title_canon_sha256": "ad492440215c73d55e18241f0c87c8c3d81da1361d5a948746a71776b4612c12"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.03140",
    "kind": "arxiv",
    "version": 3
  }
}