Pith Number

pith:LBM2LFK3

pith:2019:LBM2LFK3BLKPZVHO35OB5C2IHA

not attested not anchored not stored refs pending

Calculus, constrained minimization and Lagrange multipliers: Is the optimal critical point a local minimizer?

Ademir Alves Ribeiro, Jose Renato Ramos Barbosa

arxiv:1904.05222 v1 · 2019-04-10 · math.HO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LBM2LFK3BLKPZVHO35OB5C2IHA}

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	2026-05-17T23:48:53.782591Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5859a5955b0ad4fcd4eedf5c1e8b48381cb30fe5aad33a13e6d5af3b5d862018

Aliases

arxiv: 1904.05222 · arxiv_version: 1904.05222v1 · doi: 10.48550/arxiv.1904.05222 · pith_short_12: LBM2LFK3BLKP · pith_short_16: LBM2LFK3BLKPZVHO · pith_short_8: LBM2LFK3

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/LBM2LFK3BLKPZVHO35OB5C2IHA \
  | 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: 5859a5955b0ad4fcd4eedf5c1e8b48381cb30fe5aad33a13e6d5af3b5d862018

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c68ce4689b8c12abc5642b38465cbf5d513590216b9451a91fa95e451541a0c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.HO",
    "submitted_at": "2019-04-10T14:47:37Z",
    "title_canon_sha256": "130cf792c36d64a141ef6b93fe50b54813e88eae641fbcd1cba842a33be5f26f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.05222",
    "kind": "arxiv",
    "version": 1
  }
}