Pith Number

pith:X4KTGIML

pith:2012:X4KTGIMLOSZC52DKIKYCRYHT7D

not attested not anchored not stored refs pending

Second order conditions for optimality and local controllability of discrete-time systems

B. Jakubczyk, M. Barbero-Li\~n\'an

arxiv:1211.5784 v2 · 2012-11-25 · 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{X4KTGIMLOSZC52DKIKYCRYHT7D}

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	2026-05-18T03:35:13.457642Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf1533218b74b22ee86a42b028e0f3f8e529d43bffaea3c124daced3b9a42c8b

Aliases

arxiv: 1211.5784 · arxiv_version: 1211.5784v2 · doi: 10.48550/arxiv.1211.5784 · pith_short_12: X4KTGIMLOSZC · pith_short_16: X4KTGIMLOSZC52DK · pith_short_8: X4KTGIML

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/X4KTGIMLOSZC52DKIKYCRYHT7D \
  | 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: bf1533218b74b22ee86a42b028e0f3f8e529d43bffaea3c124daced3b9a42c8b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fc80a75131b8884bbb1764be7fd88a0f1b2cf097a380d148bb9a57489e0f1830",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2012-11-25T17:22:14Z",
    "title_canon_sha256": "4e21bd96387df6392ac590f827488e835da800bfe6bdbf00502c3c0a81e5ecfa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.5784",
    "kind": "arxiv",
    "version": 2
  }
}