Pith Number

pith:ES3XQJIA

pith:2011:ES3XQJIA2RZ2IXRSGWZYFESDCX

not attested not anchored not stored refs pending

Optimal Control Theory on almost-Lie Algebroids

Michal Jozwikowski

arxiv:1111.1549 v1 · 2011-11-07 · math.OC · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ES3XQJIA2RZ2IXRSGWZYFESDCX}

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	2026-05-18T04:09:25.835270Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

24b7782500d473a45e3235b382924315e6a9add4c8f5e463054f7f1bf346aea3

Aliases

arxiv: 1111.1549 · arxiv_version: 1111.1549v1 · doi: 10.48550/arxiv.1111.1549 · pith_short_12: ES3XQJIA2RZ2 · pith_short_16: ES3XQJIA2RZ2IXRS · pith_short_8: ES3XQJIA

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/ES3XQJIA2RZ2IXRSGWZYFESDCX \
  | 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: 24b7782500d473a45e3235b382924315e6a9add4c8f5e463054f7f1bf346aea3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0664a977146f69958ce32173b81d8bd6d25d5f7a091c1db2ec9e70ee83e4dca2",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2011-11-07T11:42:51Z",
    "title_canon_sha256": "212993574b0caffb07b1fe0ecff9a345a92b4a961007db85e424147c3ca285b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.1549",
    "kind": "arxiv",
    "version": 1
  }
}