Pith Number

pith:WK43463I

pith:2012:WK43463I7R5FDIH2UHWZXSEBNQ

not attested not anchored not stored refs pending

Necessary optimality conditions for infinite horizon variational problems on time scales

Delfim F. M. Torres, Monika Dryl

arxiv:1212.0988 v1 · 2012-12-05 · 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{WK43463I7R5FDIH2UHWZXSEBNQ}

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	2026-05-18T03:35:01.592670Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2b9be7b68fc7a51a0faa1ed9bc8816c3401643a96e780188c12ef4587ca45fb

Aliases

arxiv: 1212.0988 · arxiv_version: 1212.0988v1 · doi: 10.48550/arxiv.1212.0988 · pith_short_12: WK43463I7R5F · pith_short_16: WK43463I7R5FDIH2 · pith_short_8: WK43463I

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/WK43463I7R5FDIH2UHWZXSEBNQ \
  | 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: b2b9be7b68fc7a51a0faa1ed9bc8816c3401643a96e780188c12ef4587ca45fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dfcc3b807aef507f7d6f168fc122a972c6134babb7e5b749f7eb5712a00f0850",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2012-12-05T10:37:30Z",
    "title_canon_sha256": "7b15a38f17fe44f75687558e82d5fe172ae40b0c793a29c3ed836ae45585bc0b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.0988",
    "kind": "arxiv",
    "version": 1
  }
}