Pith Number

pith:QYLCVLCQ

pith:2012:QYLCVLCQT4OHMGMS5EC2KCAKHI

not attested not anchored not stored refs pending

Fractional Calculus in Wave Propagation Problems

Francesco Mainardi

arxiv:1202.0261 v1 · 2012-02-01 · math-ph · math.MP · nlin.SI

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QYLCVLCQT4OHMGMS5EC2KCAKHI}

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	2026-05-18T04:03:19.794118Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86162aac509f1c761992e905a5080a3a394946705413e5ed22a56519d0d33f53

Aliases

arxiv: 1202.0261 · arxiv_version: 1202.0261v1 · doi: 10.48550/arxiv.1202.0261 · pith_short_12: QYLCVLCQT4OH · pith_short_16: QYLCVLCQT4OHMGMS · pith_short_8: QYLCVLCQ

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/QYLCVLCQT4OHMGMS5EC2KCAKHI \
  | 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: 86162aac509f1c761992e905a5080a3a394946705413e5ed22a56519d0d33f53

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fc1668fa9bca8c262e919d9ddd9349a8ed687c4c9db3aef48d9416e7a930ef88",
    "cross_cats_sorted": [
      "math.MP",
      "nlin.SI"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-02-01T20:18:55Z",
    "title_canon_sha256": "559fe7cc5463ecbef9e4f0881e6eabafc76ff7f00112e49fc9ef10754a2f8495"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.0261",
    "kind": "arxiv",
    "version": 1
  }
}