Pith Number

pith:SL7AOUN6

pith:2012:SL7AOUN6NRPUQAVELZ6MQVP23W

not attested not anchored not stored refs pending

$k$-symplectic Pontryagin's Maximum Principle for some families of PDEs

Mar\'ia Barbero-Li\~n\'an, Miguel C. Mu\~noz-Lecanda

arxiv:1210.6762 v1 · 2012-10-25 · math.OC · math-ph · math.DG · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SL7AOUN6NRPUQAVELZ6MQVP23W}

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	2026-05-18T03:42:23.215109Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

92fe0751be6c5f4802a45e7cc855faddb0fa96d103a739835d17fde70ce8cd27

Aliases

arxiv: 1210.6762 · arxiv_version: 1210.6762v1 · doi: 10.48550/arxiv.1210.6762 · pith_short_12: SL7AOUN6NRPU · pith_short_16: SL7AOUN6NRPUQAVE · pith_short_8: SL7AOUN6

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/SL7AOUN6NRPUQAVELZ6MQVP23W \
  | 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: 92fe0751be6c5f4802a45e7cc855faddb0fa96d103a739835d17fde70ce8cd27

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "84633f48a68bb0818021d01235d6720656dbfe1936f276b6e8e34f0c957e0f4e",
    "cross_cats_sorted": [
      "math-ph",
      "math.DG",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2012-10-25T09:16:00Z",
    "title_canon_sha256": "bbe7ebf33102e039d6d31ecbfc55066125a6a023c20645286d35aa052b0afce0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.6762",
    "kind": "arxiv",
    "version": 1
  }
}