Pith Number

pith:MJD4OZRY

pith:2025:MJD4OZRYWBKH3WNHJYVQNHHU7M

not attested not anchored not stored refs pending

On second-order weak sharp minima of general nonconvex set-constrained optimization problems

Binbin Zhang, Jane Ye, Wei Ouyang, Xiaoxiao Ma

arxiv:2507.12682 v1 · 2025-07-16 · 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{MJD4OZRYWBKH3WNHJYVQNHHU7M}

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	2026-07-05T11:38:37.236495Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6247c76638b0547dd9a74e2b069cf4fb3e15366dd1ac6df297f0a611070c55db

Aliases

arxiv: 2507.12682 · arxiv_version: 2507.12682v1 · doi: 10.48550/arxiv.2507.12682 · pith_short_12: MJD4OZRYWBKH · pith_short_16: MJD4OZRYWBKH3WNH · pith_short_8: MJD4OZRY

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/MJD4OZRYWBKH3WNHJYVQNHHU7M \
  | 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: 6247c76638b0547dd9a74e2b069cf4fb3e15366dd1ac6df297f0a611070c55db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6de2dd02c8933f1389d4581db546f510230b3556cf4956bc0de4136a99bd13c4",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-07-16T23:33:47Z",
    "title_canon_sha256": "6f4b3d80cf0c24e4bb4936f868af92fc37946299da7a47035058728430310efb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.12682",
    "kind": "arxiv",
    "version": 1
  }
}