Pith Number

pith:E4Y3RGWD

pith:2013:E4Y3RGWDAOBLRJYKNYDRXBNZPZ

not attested not anchored not stored refs pending

The Legendre Condition of the Fractional Calculus of Variations

Delfim F. M. Torres, Matheus J. Lazo

arxiv:1312.4714 v1 · 2013-12-17 · 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{E4Y3RGWDAOBLRJYKNYDRXBNZPZ}

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	2026-05-18T02:49:20.150903Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2731b89ac30382b8a70a6e071b85b97e6f565a63944dcebcf9e68a59263964f1

Aliases

arxiv: 1312.4714 · arxiv_version: 1312.4714v1 · doi: 10.48550/arxiv.1312.4714 · pith_short_12: E4Y3RGWDAOBL · pith_short_16: E4Y3RGWDAOBLRJYK · pith_short_8: E4Y3RGWD

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/E4Y3RGWDAOBLRJYKNYDRXBNZPZ \
  | 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: 2731b89ac30382b8a70a6e071b85b97e6f565a63944dcebcf9e68a59263964f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "03adad49763514be3636117a08dddb85bc80e8a93620a9c171c7719c19580649",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2013-12-17T10:50:28Z",
    "title_canon_sha256": "ba12977858ef526bb5ccfed5d5ca3c44b3c942295f0e2d6008f5488ee7c5c5c1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.4714",
    "kind": "arxiv",
    "version": 1
  }
}