Pith Number

pith:GGQARUF5

pith:2010:GGQARUF5MCTFPBN7LPDHB3HTQG

not attested not anchored not stored refs pending

Leitmann's direct method of optimization for absolute extrema of certain problems of the calculus of variations on time scales

Agnieszka B. Malinowska, Delfim F. M. Torres

arxiv:1001.1455 v1 · 2010-01-09 · 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{GGQARUF5MCTFPBN7LPDHB3HTQG}

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	2026-05-18T04:40:10.442101Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31a008d0bd60a65785bf5bc670ecf381916b39a1edfd3b0ec7c0bb265aea5e33

Aliases

arxiv: 1001.1455 · arxiv_version: 1001.1455v1 · doi: 10.48550/arxiv.1001.1455 · pith_short_12: GGQARUF5MCTF · pith_short_16: GGQARUF5MCTFPBN7 · pith_short_8: GGQARUF5

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/GGQARUF5MCTFPBN7LPDHB3HTQG \
  | 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: 31a008d0bd60a65785bf5bc670ecf381916b39a1edfd3b0ec7c0bb265aea5e33

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f68e69b81b2c239a1ad833ae9ccb601538221a7f61d5802cb956e9e6dfd4213",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2010-01-09T22:05:50Z",
    "title_canon_sha256": "2e6917d2470e5385055f89c70d46550605810037081cf34ffad346c8dcd28133"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.1455",
    "kind": "arxiv",
    "version": 1
  }
}