Pith Number

pith:4KOESD5R

pith:2013:4KOESD5RZ5INSNZZ6RYRFS6VNP

not attested not anchored not stored refs pending

The Fermat-Torricelli Problem and Weiszfeld's Algorithm in the Light of Convex Analysis

Boris Mordukhovich, Nguyen Mau Nam

arxiv:1302.5244 v4 · 2013-02-21 · 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{4KOESD5RZ5INSNZZ6RYRFS6VNP}

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	2026-07-05T00:28:05.055551Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e29c490fb1cf50d93739f47112cbd56bc3fbbdc1f3f741c28a585f1172ebd0e1

Aliases

arxiv: 1302.5244 · arxiv_version: 1302.5244v4 · doi: 10.48550/arxiv.1302.5244 · pith_short_12: 4KOESD5RZ5IN · pith_short_16: 4KOESD5RZ5INSNZZ · pith_short_8: 4KOESD5R

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/4KOESD5RZ5INSNZZ6RYRFS6VNP \
  | 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: e29c490fb1cf50d93739f47112cbd56bc3fbbdc1f3f741c28a585f1172ebd0e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b827f4a2d6246c213a3f6d4b40af2040a51e5e360b3f0ff0cac6172dc485cd4a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2013-02-21T10:29:41Z",
    "title_canon_sha256": "ba31891da35f1247fca11fcd0f560592d495362b3d85890043952074f65cfc9c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.5244",
    "kind": "arxiv",
    "version": 4
  }
}