Pith Number

pith:RETKEN4U

pith:2010:RETKEN4UBDHBM5SHIVFVB5ECMX

not attested not anchored not stored refs pending

Necessary Optimality Conditions for Fractional Difference Problems of the Calculus of Variations

Delfim F. M. Torres, Nuno R. O. Bastos, Rui A. C. Ferreira

arxiv:1007.0594 v1 · 2010-07-04 · 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{RETKEN4UBDHBM5SHIVFVB5ECMX}

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	2026-05-18T04:38:16.834277Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8926a2379408ce167647454b50f48265f7334a320dfe8059f8919c8567fedc0f

Aliases

arxiv: 1007.0594 · arxiv_version: 1007.0594v1 · doi: 10.48550/arxiv.1007.0594 · pith_short_12: RETKEN4UBDHB · pith_short_16: RETKEN4UBDHBM5SH · pith_short_8: RETKEN4U

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/RETKEN4UBDHBM5SHIVFVB5ECMX \
  | 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: 8926a2379408ce167647454b50f48265f7334a320dfe8059f8919c8567fedc0f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "276acb85a4faacdafddac69b5a119679b52394e989a8687f203981b771535291",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2010-07-04T22:35:42Z",
    "title_canon_sha256": "ec54453e9051c4c8979e442dadc8146c02004614fb9400bbf2451fe46f0189c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.0594",
    "kind": "arxiv",
    "version": 1
  }
}