Pith Number

pith:6YG5X3NS

pith:2011:6YG5X3NSOYKYWCCSRQ2NEZAT3B

not attested not anchored not stored refs pending

Tangential Extremal Principles for Finite and Infinite Systems of Sets, II: Applications to Semi-infinite and Multiobjective Optimization

Boris S. Mordukhovich, Hung M. Phan

arxiv:1101.4176 v1 · 2011-01-21 · 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{6YG5X3NSOYKYWCCSRQ2NEZAT3B}

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	2026-05-18T04:31:12.592532Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f60ddbedb276158b08528c34d26413d878b3be1b42716ad543818584c48679cd

Aliases

arxiv: 1101.4176 · arxiv_version: 1101.4176v1 · doi: 10.48550/arxiv.1101.4176 · pith_short_12: 6YG5X3NSOYKY · pith_short_16: 6YG5X3NSOYKYWCCS · pith_short_8: 6YG5X3NS

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/6YG5X3NSOYKYWCCSRQ2NEZAT3B \
  | 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: f60ddbedb276158b08528c34d26413d878b3be1b42716ad543818584c48679cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "543db66eb5076222f1088b7c0a541018d455e49a2a06a1742a8fb33e405e4b52",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2011-01-21T16:35:18Z",
    "title_canon_sha256": "916da8a92166301cad43e7f8e5ccc9ab04f3d0abd1c5a2ef5938799358e2cf53"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.4176",
    "kind": "arxiv",
    "version": 1
  }
}