Pith Number

pith:PC64CN5P

pith:2013:PC64CN5PXVPSB3TLKGHHMXSVMB

not attested not anchored not stored refs pending

A necessary and sufficient condition for local controllability around closed orbits

Marek Grochowski

arxiv:1312.4181 v1 · 2013-12-15 · 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{PC64CN5PXVPSB3TLKGHHMXSVMB}

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	2026-05-18T03:04:35.376161Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78bdc137afbd5f20ee6b518e765e5560671792b8c422446531797be5b9ff9083

Aliases

arxiv: 1312.4181 · arxiv_version: 1312.4181v1 · doi: 10.48550/arxiv.1312.4181 · pith_short_12: PC64CN5PXVPS · pith_short_16: PC64CN5PXVPSB3TL · pith_short_8: PC64CN5P

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/PC64CN5PXVPSB3TLKGHHMXSVMB \
  | 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: 78bdc137afbd5f20ee6b518e765e5560671792b8c422446531797be5b9ff9083

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6561883d9ee3686ef3e35cf0f8bb02ca57d3ec8c05a3952204fc6c234ce67440",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2013-12-15T19:13:53Z",
    "title_canon_sha256": "2f4269c0d1bc614e6afff6f95bbcdf66423ac107d7a9c87fd6635d4fd718e01b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.4181",
    "kind": "arxiv",
    "version": 1
  }
}