Pith Number

pith:KITA52Q4

pith:2023:KITA52Q4Z67DEDCZ2D3GJC3Y43

not attested not anchored not stored refs pending

Second-Order Subdifferential Optimality Conditions in Nonsmooth Optimization

Boris S. Mordukhovich, Pham Duy Khanh, Vo Thanh Phat, Vu Vinh Huy Khoa

arxiv:2312.16277 v2 · 2023-12-26 · 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{KITA52Q4Z67DEDCZ2D3GJC3Y43}

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	2026-07-05T09:56:49.077754Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

52260eea1ccfbe320c59d0f6648b78e6ec0142c1c97962ecf34131b88d4b80af

Aliases

arxiv: 2312.16277 · arxiv_version: 2312.16277v2 · doi: 10.48550/arxiv.2312.16277 · pith_short_12: KITA52Q4Z67D · pith_short_16: KITA52Q4Z67DEDCZ · pith_short_8: KITA52Q4

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/KITA52Q4Z67DEDCZ2D3GJC3Y43 \
  | 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: 52260eea1ccfbe320c59d0f6648b78e6ec0142c1c97962ecf34131b88d4b80af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b81ef1267981b77a03acbefb8310fbf92ec60cbc2ae781a71f17d563fac2cff6",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2023-12-26T17:58:53Z",
    "title_canon_sha256": "92445ad31c78ca5a5c7cf4a6ef59a727280e0212b955b7a2ea3c09e978a94863"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2312.16277",
    "kind": "arxiv",
    "version": 2
  }
}