Pith Number

pith:CTFZ3VUV

pith:2010:CTFZ3VUVBF3OCEHNUQJD5QFHCP

not attested not anchored not stored refs pending

The Second Euler-Lagrange Equation of Variational Calculus on Time Scales

Delfim F. M. Torres, Natalia Martins, Zbigniew Bartosiewicz

arxiv:1003.5826 v1 · 2010-03-30 · math.OC · math.CA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CTFZ3VUVBF3OCEHNUQJD5QFHCP}

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	2026-05-18T04:28:20.337018Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

14cb9dd6950976e110eda4123ec0a713e8b28cec03b2d083091df6002a767a7f

Aliases

arxiv: 1003.5826 · arxiv_version: 1003.5826v1 · doi: 10.48550/arxiv.1003.5826 · pith_short_12: CTFZ3VUVBF3O · pith_short_16: CTFZ3VUVBF3OCEHN · pith_short_8: CTFZ3VUV

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/CTFZ3VUVBF3OCEHNUQJD5QFHCP \
  | 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: 14cb9dd6950976e110eda4123ec0a713e8b28cec03b2d083091df6002a767a7f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "046b812a252cace424e76696f6bb4bdb155335ab5a2122e6206c254b761c95df",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2010-03-30T14:05:19Z",
    "title_canon_sha256": "32ff72d8537034904853dce7b6bf5c079f2e8de7bf84af261353bf6cc7f8200a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.5826",
    "kind": "arxiv",
    "version": 1
  }
}