Pith Number

pith:ZV5PRXMQ

pith:2012:ZV5PRXMQRW2YBYKW42UQZ6MIZK

not attested not anchored not stored refs pending

The DuBois-Reymond Fundamental Lemma of the Fractional Calculus of Variations and an Euler-Lagrange Equation Involving only Derivatives of Caputo

Delfim F. M. Torres, Matheus J. Lazo

arxiv:1210.0705 v1 · 2012-10-02 · math.OC · math-ph · math.DS · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZV5PRXMQRW2YBYKW42UQZ6MIZK}

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	2026-05-18T03:33:47.945327Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd7af8dd908db580e156e6a90cf988caa9c170fd44cae929ced20b2b6736f2f2

Aliases

arxiv: 1210.0705 · arxiv_version: 1210.0705v1 · doi: 10.48550/arxiv.1210.0705 · pith_short_12: ZV5PRXMQRW2Y · pith_short_16: ZV5PRXMQRW2YBYKW · pith_short_8: ZV5PRXMQ

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/ZV5PRXMQRW2YBYKW42UQZ6MIZK \
  | 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: cd7af8dd908db580e156e6a90cf988caa9c170fd44cae929ced20b2b6736f2f2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b7d339a7d9603918adcd3414ac5fdf1ab72796bcf0a3969d01854b8d66de9ae",
    "cross_cats_sorted": [
      "math-ph",
      "math.DS",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2012-10-02T09:18:52Z",
    "title_canon_sha256": "d49810258a3f3c868b92aad6d66263a9da1c4fda363d84b0c30f50a4882e681f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.0705",
    "kind": "arxiv",
    "version": 1
  }
}