Pith Number

pith:MG2DR67M

pith:2015:MG2DR67MJ2DAX45HDA56ADHCTW

not attested not anchored not stored refs pending

Second-order variational problems on Lie groupoids and optimal control applications

David Martin de Diego, Leonardo Colombo

arxiv:1506.08580 v1 · 2015-06-29 · math.DS · math-ph · math.MP · math.OC · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MG2DR67MJ2DAX45HDA56ADHCTW}

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	2026-05-18T01:37:43.896630Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61b438fbec4e860bf3a7183be00ce29dabba9981b5758a50f09c9ab2141e76ca

Aliases

arxiv: 1506.08580 · arxiv_version: 1506.08580v1 · doi: 10.48550/arxiv.1506.08580 · pith_short_12: MG2DR67MJ2DA · pith_short_16: MG2DR67MJ2DAX45H · pith_short_8: MG2DR67M

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/MG2DR67MJ2DAX45HDA56ADHCTW \
  | 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: 61b438fbec4e860bf3a7183be00ce29dabba9981b5758a50f09c9ab2141e76ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2bd2494df789c5ff31b9befcf8791b91ba8ccb0fc21a7a1481e714ced7e70850",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.OC",
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-06-29T11:04:24Z",
    "title_canon_sha256": "9c090f9cb37738b3262a3129b82348f54c7809abaf1ee66bdedee9f4dc05aa1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.08580",
    "kind": "arxiv",
    "version": 1
  }
}