Pith Number

pith:QART4VIO

pith:2011:QART4VIOHFC3XC6QV7AUHZ6CJP

not attested not anchored not stored refs pending

The Smallest Enclosing Ball Problem and the Smallest Intersecting Ball Problem: Existence and Uniqueness of Solutions

Boris S. Mordukhovich, Cristina Villalobos, Nguyen Mau Nam

arxiv:1111.1280 v2 · 2011-11-05 · 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{QART4VIOHFC3XC6QV7AUHZ6CJP}

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	2026-05-18T04:05:26.852557Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80233e550e3945bb8bd0afc143e7c24bc341327ba1e67dd02fc7316694888ba6

Aliases

arxiv: 1111.1280 · arxiv_version: 1111.1280v2 · doi: 10.48550/arxiv.1111.1280 · pith_short_12: QART4VIOHFC3 · pith_short_16: QART4VIOHFC3XC6Q · pith_short_8: QART4VIO

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/QART4VIOHFC3XC6QV7AUHZ6CJP \
  | 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: 80233e550e3945bb8bd0afc143e7c24bc341327ba1e67dd02fc7316694888ba6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f1f86457d978fb1d6c3e0c9d53d40e3c41172dbd3e4935681ebec47bd27dc1c7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2011-11-05T03:01:27Z",
    "title_canon_sha256": "bd3fe3694fdc3458202d7c3d09b301c68cf0c16ce4bdf3162914439f91ca323e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.1280",
    "kind": "arxiv",
    "version": 2
  }
}