Pith Number

pith:IJR5TCL7

pith:2019:IJR5TCL7EUSUYZ5KICNI4M7HMS

not attested not anchored not stored refs pending

Can Umbral and $q$-calculus be merged?

B. Germano, G. Dattoli, K. G\'orska, M. R. Martinelli

arxiv:1909.00058 v1 · 2019-08-29 · 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{IJR5TCL7EUSUYZ5KICNI4M7HMS}

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	2026-07-05T00:01:04.842995Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4263d9897f25254c67aa409a8e33e764850f158a3afe0c0a2c234c6979714f52

Aliases

arxiv: 1909.00058 · arxiv_version: 1909.00058v1 · doi: 10.48550/arxiv.1909.00058 · pith_short_12: IJR5TCL7EUSU · pith_short_16: IJR5TCL7EUSUYZ5K · pith_short_8: IJR5TCL7

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/IJR5TCL7EUSUYZ5KICNI4M7HMS \
  | 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: 4263d9897f25254c67aa409a8e33e764850f158a3afe0c0a2c234c6979714f52

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cbd043bf6aaef01bcb4c1753a2d7cb0c2b436b0213c188903ef8b9f48cbd0800",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2019-08-29T13:35:22Z",
    "title_canon_sha256": "afaa8f99ff41d42bcc5aff3f776e403bd3f91b090f503d48841637d7e1c47067"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1909.00058",
    "kind": "arxiv",
    "version": 1
  }
}