Pith Number

pith:3XX73LYC

pith:2014:3XX73LYCY67NEXCYGVVMEVIL2A

not attested not anchored not stored refs pending

Sub-Riemannian geodesics on the free Carnot group with the growth vector (2,3,5,8)

Yuri Sachkov

arxiv:1404.7752 v1 · 2014-04-30 · 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{3XX73LYCY67NEXCYGVVMEVIL2A}

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	2026-05-18T02:52:50.039453Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ddeffdaf02c7bed25c58356ac2550bd023456db2a0479e800ffcd2ea951a9932

Aliases

arxiv: 1404.7752 · arxiv_version: 1404.7752v1 · doi: 10.48550/arxiv.1404.7752 · pith_short_12: 3XX73LYCY67N · pith_short_16: 3XX73LYCY67NEXCY · pith_short_8: 3XX73LYC

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/3XX73LYCY67NEXCYGVVMEVIL2A \
  | 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: ddeffdaf02c7bed25c58356ac2550bd023456db2a0479e800ffcd2ea951a9932

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0ef10a48909b3de9fbe496f3002a3ce6d22cd5e16e163cc298a57b8b8c520d2",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2014-04-30T14:59:28Z",
    "title_canon_sha256": "03aaadc9477cb0cd4fcfbab8b57c4a4e3dbd529a3bae0c28ca7330f5e7f151f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1404.7752",
    "kind": "arxiv",
    "version": 1
  }
}