Pith Number

pith:4WW3JMMW

pith:2010:4WW3JMMWC2GS2J6TOK5I54OMPF

not attested not anchored not stored refs pending

Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives

Delfim F. M. Torres, Ricardo Almeida

arxiv:1007.2937 v1 · 2010-07-17 · 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{4WW3JMMWC2GS2J6TOK5I54OMPF}

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	2026-05-18T04:39:51.094751Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5adb4b196168d2d27d372ba8ef1cc794d7f4d8f0ccb98055a31c2c99f38b33e

Aliases

arxiv: 1007.2937 · arxiv_version: 1007.2937v1 · doi: 10.48550/arxiv.1007.2937 · pith_short_12: 4WW3JMMWC2GS · pith_short_16: 4WW3JMMWC2GS2J6T · pith_short_8: 4WW3JMMW

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/4WW3JMMWC2GS2J6TOK5I54OMPF \
  | 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: e5adb4b196168d2d27d372ba8ef1cc794d7f4d8f0ccb98055a31c2c99f38b33e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "62504adc1bd4b4b575049927987c1777919e57bb4b1ede9e13ede81d3f2a7899",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2010-07-17T16:05:22Z",
    "title_canon_sha256": "138764fd38812430472b8dd775b3c5497b256d170f97b9064a46a6a73700a8e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.2937",
    "kind": "arxiv",
    "version": 1
  }
}