Pith Number

pith:VGJXJLWJ

pith:1993:VGJXJLWJPFEEFLN64AD4IVBMHS

not attested not anchored not stored refs pending

On necessary multiplier conditions for Laguerre expansions

George Gasper Jr, Walter Trebels

arxiv:math/9307211 v1 · 1993-07-09 · 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{VGJXJLWJPFEEFLN64AD4IVBMHS}

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	2026-05-18T01:05:52.083806Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a99374aec9794842adbee007c4542c3c9fb276c7455f993aba6959e7df212993

Aliases

arxiv: math/9307211 · arxiv_version: math/9307211v1 · doi: 10.48550/arxiv.math/9307211 · pith_short_12: VGJXJLWJPFEE · pith_short_16: VGJXJLWJPFEEFLN6 · pith_short_8: VGJXJLWJ

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/VGJXJLWJPFEEFLN64AD4IVBMHS \
  | 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: a99374aec9794842adbee007c4542c3c9fb276c7455f993aba6959e7df212993

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea3631bef60925e7e780414fda169a63ad318eba3d8624006db5e4cac884ab68",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CA",
    "submitted_at": "1993-07-09T00:00:00Z",
    "title_canon_sha256": "9806b6d66f57280c55a99850a5846b580d495ef224d2340f921324f0eb269323"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9307211",
    "kind": "arxiv",
    "version": 1
  }
}