Pith Number

pith:TN3MYTBJ

pith:2022:TN3MYTBJYP75QACTPDRSGY65AO

not attested not anchored not stored refs pending

Variational Convexity of Functions and Variational Sufficiency in Optimization

Boris S. Mordukhovich, Pham Duy Khanh, Vo Thanh Phat

arxiv:2208.14399 v2 · 2022-08-30 · 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{TN3MYTBJYP75QACTPDRSGY65AO}

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	2026-07-05T05:36:18.253184Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b76cc4c29c3ffd8005378e32363dd03af3a12aa3e75f653f6bdbf39f76bdab1

Aliases

arxiv: 2208.14399 · arxiv_version: 2208.14399v2 · doi: 10.48550/arxiv.2208.14399 · pith_short_12: TN3MYTBJYP75 · pith_short_16: TN3MYTBJYP75QACT · pith_short_8: TN3MYTBJ

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/TN3MYTBJYP75QACTPDRSGY65AO \
  | 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: 9b76cc4c29c3ffd8005378e32363dd03af3a12aa3e75f653f6bdbf39f76bdab1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7f724d271c28e1ab2b6b83004d25e01c44ae70c76c1a1e518d78f325266c563a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2022-08-30T17:12:40Z",
    "title_canon_sha256": "9c663897cb3a0fd3a5789384cbd05df9e46f8428d4357c81c2d06760db31d758"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2208.14399",
    "kind": "arxiv",
    "version": 2
  }
}