Pith Number

pith:VZFJCNTJ

pith:2025:VZFJCNTJ24YNCX52XPQKSUHCB5

not attested not anchored not stored refs pending

The Euler-Lagrange and Legendre Necessary Conditions for Fractional Calculus of Variations

Elimhan N. Mahmudov, Shakir Sh. Yusubov, Shikhi Sh. Yusubov

arxiv:2506.06736 v1 · 2025-06-07 · 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{VZFJCNTJ24YNCX52XPQKSUHCB5}

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	2026-07-05T11:17:54.895872Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae4a913669d730d15fbabbe0a950e20f6e00d81ec05168229105eb768960ce6e

Aliases

arxiv: 2506.06736 · arxiv_version: 2506.06736v1 · doi: 10.48550/arxiv.2506.06736 · pith_short_12: VZFJCNTJ24YN · pith_short_16: VZFJCNTJ24YNCX52 · pith_short_8: VZFJCNTJ

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/VZFJCNTJ24YNCX52XPQKSUHCB5 \
  | 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: ae4a913669d730d15fbabbe0a950e20f6e00d81ec05168229105eb768960ce6e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df914a0bb5a23bbe3bdda601a8ec98f4847e3f41801abfb7c95ed9fcf741f0d9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-06-07T09:44:37Z",
    "title_canon_sha256": "6d514a9251508c60026f207308acf98eb829b8c3e0cad55170bf28e5c9b41310"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.06736",
    "kind": "arxiv",
    "version": 1
  }
}