Pith Number

pith:4PKBAS7U

pith:2016:4PKBAS7U6WDACWIQE3VRAVRUTW

not attested not anchored not stored refs pending

Sub-Riemannian curvature of Carnot groups with rank-two distributions

Isidro H. Munive

arxiv:1605.07530 v4 · 2016-05-24 · math.DG · math.MG · 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{4PKBAS7U6WDACWIQE3VRAVRUTW}

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	2026-05-18T00:51:07.278422Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3d4104bf4f58601591026eb1056349dadcb9e2fb7fe430f6539b78e1e75a5dc

Aliases

arxiv: 1605.07530 · arxiv_version: 1605.07530v4 · doi: 10.48550/arxiv.1605.07530 · pith_short_12: 4PKBAS7U6WDA · pith_short_16: 4PKBAS7U6WDACWIQ · pith_short_8: 4PKBAS7U

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/4PKBAS7U6WDACWIQE3VRAVRUTW \
  | 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: e3d4104bf4f58601591026eb1056349dadcb9e2fb7fe430f6539b78e1e75a5dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ba721788d2a7eb5f4ece9a445f5af56ed975f8ac9ab44331c334847815d9427",
    "cross_cats_sorted": [
      "math.MG",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2016-05-24T16:23:50Z",
    "title_canon_sha256": "15ed41431043dc9707fa26c56a52a64fb6f531a3bb42d2082ae78dd9876f755f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.07530",
    "kind": "arxiv",
    "version": 4
  }
}