Pith Number

pith:UJXSI7WA

pith:2015:UJXSI7WA4FURNJRHCAKTUUDZCA

not attested not anchored not stored refs pending

Optimal Solutions to Relaxation in Multiple Control Problems of Sobolev Type with Nonlocal Nonlinear Fractional Differential Equations

Amar Debbouche, Delfim F. M. Torres, Juan J. Nieto

arxiv:1504.05153 v1 · 2015-04-20 · 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{UJXSI7WA4FURNJRHCAKTUUDZCA}

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	2026-05-18T00:39:57.144544Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a26f247ec0e16916a62710153a50791027c286716cbc8ba1cfe05bdbcadcf4aa

Aliases

arxiv: 1504.05153 · arxiv_version: 1504.05153v1 · doi: 10.48550/arxiv.1504.05153 · pith_short_12: UJXSI7WA4FUR · pith_short_16: UJXSI7WA4FURNJRH · pith_short_8: UJXSI7WA

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/UJXSI7WA4FURNJRHCAKTUUDZCA \
  | 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: a26f247ec0e16916a62710153a50791027c286716cbc8ba1cfe05bdbcadcf4aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "44a031d967d4a3f01719c5777ec52c5aa532234ea30bb793fbd320efc29f4dd6",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2015-04-20T18:45:39Z",
    "title_canon_sha256": "516403cb69dd7aa5167fd9d6c37017ae287314b663fbf0a20ea8905babc8e98b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.05153",
    "kind": "arxiv",
    "version": 1
  }
}