Pith Number

pith:TS55FUBC

pith:2013:TS55FUBC4SBIITPDZI6LDVJ5RQ

not attested not anchored not stored refs pending

Approximate Controllability of Fractional Nonlocal Delay Semilinear Systems in Hilbert Spaces

Amar Debbouche, Delfim F. M. Torres

arxiv:1304.0082 v1 · 2013-03-30 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TS55FUBC4SBIITPDZI6LDVJ5RQ}

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	2026-05-18T03:06:22.122118Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9cbbd2d022e482844de3ca3cb1d53d8c28c85f8dae9f8ee57fbeb08a0f025d6c

Aliases

arxiv: 1304.0082 · arxiv_version: 1304.0082v1 · doi: 10.48550/arxiv.1304.0082 · pith_short_12: TS55FUBC4SBI · pith_short_16: TS55FUBC4SBIITPD · pith_short_8: TS55FUBC

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/TS55FUBC4SBIITPDZI6LDVJ5RQ \
  | 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: 9cbbd2d022e482844de3ca3cb1d53d8c28c85f8dae9f8ee57fbeb08a0f025d6c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c50ba3962d7f1e92fe48519ea8784b9af59b76743b55694887a8e300f9deff24",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2013-03-30T10:11:40Z",
    "title_canon_sha256": "069bc29c0f6a20e178ccac85f7651f6c2a4b5eac87f1ea7a91d116cc3a5a4c3a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.0082",
    "kind": "arxiv",
    "version": 1
  }
}