Pith Number

pith:IZDE2RJV

pith:2003:IZDE2RJVAUIUEXYCNDEQWKBWLB

not attested not anchored not stored refs pending

The modular properties and the integral representations of the multiple elliptic gamma functions

Atsushi Narukawa

arxiv:math/0306164 v3 · 2003-06-10 · math.QA · 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{IZDE2RJVAUIUEXYCNDEQWKBWLB}

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

Towards OSV in AdS

Receipt and verification

First computed	2026-07-04T14:37:23.633464Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46464d45350511425f0268c90b2836585196865e07f272db7d25b4e05ff8035c

Aliases

arxiv: math/0306164 · arxiv_version: math/0306164v3 · doi: 10.48550/arxiv.math/0306164 · pith_short_12: IZDE2RJVAUIU · pith_short_16: IZDE2RJVAUIUEXYC · pith_short_8: IZDE2RJV

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/IZDE2RJVAUIUEXYCNDEQWKBWLB \
  | 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: 46464d45350511425f0268c90b2836585196865e07f272db7d25b4e05ff8035c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4c36110ff7906b68d130823a98a1c41f179d677449c5940b8fc1cc3537033ad",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2003-06-10T16:19:31Z",
    "title_canon_sha256": "3b4829239a8d3489f4781dcc9ad57aa557353a6c7467f40d9c6f491832a4e8a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0306164",
    "kind": "arxiv",
    "version": 3
  }
}