Pith Number

pith:QTWRIVHH

pith:2008:QTWRIVHHESNJ6UFQKEYSCJ5ROA

not attested not anchored not stored refs pending

A limit transition from the Heckman-Opdam hypergeometric functions to the Whittaker functions associated with root systems

Nobukazu shimeno

arxiv:0812.3773 v1 · 2008-12-19 · math.RT · 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{QTWRIVHHESNJ6UFQKEYSCJ5ROA}

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	2026-05-18T00:00:09.723983Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

84ed1454e7249a9f50b051312127b1702664ab03771a7e47a0c2a884e5f37995

Aliases

arxiv: 0812.3773 · arxiv_version: 0812.3773v1 · doi: 10.48550/arxiv.0812.3773 · pith_short_12: QTWRIVHHESNJ · pith_short_16: QTWRIVHHESNJ6UFQ · pith_short_8: QTWRIVHH

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/QTWRIVHHESNJ6UFQKEYSCJ5ROA \
  | 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: 84ed1454e7249a9f50b051312127b1702664ab03771a7e47a0c2a884e5f37995

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ac4e16379f176a100ee7934154ac29ada05cda003e1be1f8308200f8dfa9d18",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2008-12-19T12:47:59Z",
    "title_canon_sha256": "ec5ccdcbaadafa773e762ac05f3884bdd2d9cdaa034b3f840a272fe4812930d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.3773",
    "kind": "arxiv",
    "version": 1
  }
}