Pith Number

pith:MN4LGUUK

pith:2013:MN4LGUUKER7FIZYEOEU6MVX7KN

not attested not anchored not stored refs pending

Generalized Zernike polynomials: Operational formulae and generating functions

Allal Ghanmi, Amal El Hamyani, Bouchra Aharmim, Fouzia El Wassouli

arxiv:1312.3628 v2 · 2013-12-12 · math.CA · 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{MN4LGUUKER7FIZYEOEU6MVX7KN}

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	2026-05-18T02:19:43.910490Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6378b3528a247e5467047129e656ff536b8e591302ff4d81618301655e9c8053

Aliases

arxiv: 1312.3628 · arxiv_version: 1312.3628v2 · doi: 10.48550/arxiv.1312.3628 · pith_short_12: MN4LGUUKER7F · pith_short_16: MN4LGUUKER7FIZYE · pith_short_8: MN4LGUUK

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/MN4LGUUKER7FIZYEOEU6MVX7KN \
  | 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: 6378b3528a247e5467047129e656ff536b8e591302ff4d81618301655e9c8053

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a70a0a7214ea5797822287d66fdbb06805b5705d1c7fd6681fa58ef8c30d4915",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-12-12T20:56:26Z",
    "title_canon_sha256": "3487f4886424fbef274d0f4fc5d074a31a2e57711e24f09462895ed9b11b0b21"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.3628",
    "kind": "arxiv",
    "version": 2
  }
}