Pith Number

pith:PZX2EPVG

pith:2013:PZX2EPVG34ZX4NHLQX44JBWIYO

not attested not anchored not stored refs pending

Approximate controllability and optimal control of impulsive fractional semilinear delay differential equations with non-local conditions

Lakshman Mahto, Syed Abbas

arxiv:1304.3198 v1 · 2013-04-11 · 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{PZX2EPVG34ZX4NHLQX44JBWIYO}

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	2026-05-18T02:59:48.079427Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e6fa23ea6df337e34eb85f9c486c8c3b97183e51a6bcf6dc829a3a05984e9a6

Aliases

arxiv: 1304.3198 · arxiv_version: 1304.3198v1 · doi: 10.48550/arxiv.1304.3198 · pith_short_12: PZX2EPVG34ZX · pith_short_16: PZX2EPVG34ZX4NHL · pith_short_8: PZX2EPVG

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/PZX2EPVG34ZX4NHLQX44JBWIYO \
  | 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: 7e6fa23ea6df337e34eb85f9c486c8c3b97183e51a6bcf6dc829a3a05984e9a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dad8cff3b336c614321743d6d78ccbb5b12c77d5d483b68313c57e371950b9f8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-04-11T05:25:17Z",
    "title_canon_sha256": "8dedd55f72df96ac7b0501336bd5913b9d0c31f2477b3d1e1283befc400c67c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.3198",
    "kind": "arxiv",
    "version": 1
  }
}