Pith Number

pith:M6RM7DLY

pith:2013:M6RM7DLYUJIWB2XFIIISCPKSGL

not attested not anchored not stored refs pending

Uniform approximation of fractional derivatives and integrals with application to fractional differential equations

Delfim F. M. Torres, Hassan Khosravian-Arab

arxiv:1308.0451 v1 · 2013-08-02 · math.CA · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M6RM7DLYUJIWB2XFIIISCPKSGL}

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	2026-05-18T03:04:37.426924Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67a2cf8d78a25160eae54211213d5232f7206f4b1096889f48a0f2e2416f3e5f

Aliases

arxiv: 1308.0451 · arxiv_version: 1308.0451v1 · doi: 10.48550/arxiv.1308.0451 · pith_short_12: M6RM7DLYUJIW · pith_short_16: M6RM7DLYUJIWB2XF · pith_short_8: M6RM7DLY

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/M6RM7DLYUJIWB2XFIIISCPKSGL \
  | 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: 67a2cf8d78a25160eae54211213d5232f7206f4b1096889f48a0f2e2416f3e5f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "035995456aded13e0a0d61fa4ee2485955a4a25b3d9576b1aa007073c53ee950",
    "cross_cats_sorted": [
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-08-02T10:07:43Z",
    "title_canon_sha256": "2e0f17d2840b6bc6326e7ece8e51a1d318d515c4f88edcd607709c941d8131a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.0451",
    "kind": "arxiv",
    "version": 1
  }
}