Pith Number

pith:A7PBK5OC

pith:2011:A7PBK5OCTI2UJLEINZ5HOSN3KF

not attested not anchored not stored refs pending

Higher Order Fractional Variational Optimal Control Problems with Delayed Arguments

Dumitru Baleanu, Fahd Jarad, Thabet Abdeljawad

arxiv:1105.5148 v1 · 2011-05-25 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{A7PBK5OCTI2UJLEINZ5HOSN3KF}

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	2026-05-18T04:21:13.123979Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

07de1575c29a3544ac886e7a7749bb51456d96e80e4bc429402c91856bb103d8

Aliases

arxiv: 1105.5148 · arxiv_version: 1105.5148v1 · doi: 10.48550/arxiv.1105.5148 · pith_short_12: A7PBK5OCTI2U · pith_short_16: A7PBK5OCTI2UJLEI · pith_short_8: A7PBK5OC

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/A7PBK5OCTI2UJLEINZ5HOSN3KF \
  | 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: 07de1575c29a3544ac886e7a7749bb51456d96e80e4bc429402c91856bb103d8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d249afdc25278a13dd2a8a63e9ad4b574a65cd1d0e48f81df88683105cd82bc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-05-25T20:33:58Z",
    "title_canon_sha256": "ce009ed39d9634149541ee1da5e60ee69d771ab04b8a2d3a777fc34a9a14d32b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.5148",
    "kind": "arxiv",
    "version": 1
  }
}