Pith Number

pith:U6L2MEKI

pith:2021:U6L2MEKIUSHTAOI7A4MKOIVJEE

not attested not anchored not stored refs pending

Generalized Leibniz rules and Lipschitzian stability for expected-integral mappings

Boris S. Mordukhovich, Pedro P\'erez-Aros

arxiv:2101.06711 v2 · 2021-01-17 · 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{U6L2MEKIUSHTAOI7A4MKOIVJEE}

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	2026-07-05T02:50:28.619261Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a797a61148a48f30391f0718a722a9212328677c4edcc94f653a206e459e152e

Aliases

arxiv: 2101.06711 · arxiv_version: 2101.06711v2 · doi: 10.48550/arxiv.2101.06711 · pith_short_12: U6L2MEKIUSHT · pith_short_16: U6L2MEKIUSHTAOI7 · pith_short_8: U6L2MEKI

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/U6L2MEKIUSHTAOI7A4MKOIVJEE \
  | 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: a797a61148a48f30391f0718a722a9212328677c4edcc94f653a206e459e152e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bffab9db9ea2ca05e34abd05eb2f8a4b897677687de0d03007c61155e09ebd70",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2021-01-17T16:52:14Z",
    "title_canon_sha256": "49052e3aaeac8a702873d707760c6313eb7608a43eaddbb44b5ffab1f268e9c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2101.06711",
    "kind": "arxiv",
    "version": 2
  }
}