Pith Number

pith:IILJP2AV

pith:2025:IILJP2AVMMMAYM74FWNQA2AF3Z

not attested not anchored not stored refs pending

Characterizations of Strong Variational Sufficiency in General Models of Composite Optimization

Boris S. Mordukhovich, Chengjing Wang, Peipei Tang

arxiv:2507.09522 v1 · 2025-07-13 · 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{IILJP2AVMMMAYM74FWNQA2AF3Z}

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.

Cited by

1 paper in Pith

Second-Order Characterizations of Tilt Stability in Composite Optimization

Receipt and verification

First computed	2026-07-05T11:36:10.443389Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

421697e81563180c33fc2d9b006805de6f042c2a10034fbc79fb0cbc74cf706d

Aliases

arxiv: 2507.09522 · arxiv_version: 2507.09522v1 · doi: 10.48550/arxiv.2507.09522 · pith_short_12: IILJP2AVMMMA · pith_short_16: IILJP2AVMMMAYM74 · pith_short_8: IILJP2AV

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/IILJP2AVMMMAYM74FWNQA2AF3Z \
  | 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: 421697e81563180c33fc2d9b006805de6f042c2a10034fbc79fb0cbc74cf706d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "367c63c2e6b8c9fa11cfc106f77c5eeee7ff1e96800a6661f053ea73f6c5b438",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-07-13T07:15:46Z",
    "title_canon_sha256": "70b6102a00dde801bb22739e019b948215981cd6b0072330e34decd5a8731266"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.09522",
    "kind": "arxiv",
    "version": 1
  }
}