Pith Number

pith:NC2QAZS7

pith:2018:NC2QAZS7RLFS2BPYUD5YXWOPBY

not attested not anchored not stored refs pending

Approximate Controllability of Impulsive Non-local Non-linear Fractional Dynamical Systems and Optimal Control

Amar Debbouche, Delfim F. M. Torres, Sarra Guechi

arxiv:1804.00612 v1 · 2018-04-02 · math.OC · 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{NC2QAZS7RLFS2BPYUD5YXWOPBY}

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	2026-05-18T00:11:17.560224Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

68b500665f8acb2d05f8a0fb8bd9cf0e2954d6e834a6f3610406a6c3e72f2b1a

Aliases

arxiv: 1804.00612 · arxiv_version: 1804.00612v1 · doi: 10.48550/arxiv.1804.00612 · pith_short_12: NC2QAZS7RLFS · pith_short_16: NC2QAZS7RLFS2BPY · pith_short_8: NC2QAZS7

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/NC2QAZS7RLFS2BPYUD5YXWOPBY \
  | 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: 68b500665f8acb2d05f8a0fb8bd9cf0e2954d6e834a6f3610406a6c3e72f2b1a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "35bbd16502b62d37e13924ee8021daf53f256cd320ee4248d59f05a94fa345bb",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2018-04-02T16:21:12Z",
    "title_canon_sha256": "ee2e09da988887366cbf9200f9a14e56d388cc8d04be17964b399315696ddb19"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.00612",
    "kind": "arxiv",
    "version": 1
  }
}