Pith Number

pith:PDNZUFPY

pith:2018:PDNZUFPY3ORVKXKLFABD5CHJIN

not attested not anchored not stored refs pending

Analytic Solution of a Delay Differential Equation Arising in Cost Functionals for Systems with Distributed Delays

Murad Abu-Khalaf, Suat Gumussoy

arxiv:1804.06713 v2 · 2018-04-18 · eess.SY · cs.SY · 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{PDNZUFPY3ORVKXKLFABD5CHJIN}

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	2026-06-04T19:11:48.428661Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78db9a15f8dba3555d4b28023e88e9435430caddb54f17d5b29bc73b87f47e45

Aliases

arxiv: 1804.06713 · arxiv_version: 1804.06713v2 · doi: 10.48550/arxiv.1804.06713 · pith_short_12: PDNZUFPY3ORV · pith_short_16: PDNZUFPY3ORVKXKL · pith_short_8: PDNZUFPY

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/PDNZUFPY3ORVKXKLFABD5CHJIN \
  | 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: 78db9a15f8dba3555d4b28023e88e9435430caddb54f17d5b29bc73b87f47e45

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f8cc4f7eb35b740b950705b31a44b51ae6eb1481f17fefdc047b19e7c4436e7",
    "cross_cats_sorted": [
      "cs.SY",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "eess.SY",
    "submitted_at": "2018-04-18T13:33:33Z",
    "title_canon_sha256": "cde9a95cd0f95dc7f080b33f59f8b25a71d107d9226473ca8d4f80a2a99e5c3c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.06713",
    "kind": "arxiv",
    "version": 2
  }
}