Pith Number

pith:3EHAKO74

pith:2016:3EHAKO745JABKTV2MAE4QRWZAQ

not attested not anchored not stored refs pending

Sub-Riemannian curvature and a Gauss-Bonnet theorem in the Heisenberg group

Eugenio Vecchi, Jeremy T. Tyson, Zolt\'an Balogh

arxiv:1604.00180 v1 · 2016-04-01 · 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{3EHAKO745JABKTV2MAE4QRWZAQ}

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	2026-05-18T01:17:54.371356Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d90e053bfcea40154eba6009c846d90423912cd7544a4a56785f83628f6d18ad

Aliases

arxiv: 1604.00180 · arxiv_version: 1604.00180v1 · doi: 10.48550/arxiv.1604.00180 · pith_short_12: 3EHAKO745JAB · pith_short_16: 3EHAKO745JABKTV2 · pith_short_8: 3EHAKO74

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/3EHAKO745JABKTV2MAE4QRWZAQ \
  | 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: d90e053bfcea40154eba6009c846d90423912cd7544a4a56785f83628f6d18ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "caf55eafceb480bf3f2d0f1f0d0ac71f1a4d7cb82a104b3dc369ba8dc7e40b42",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2016-04-01T09:51:10Z",
    "title_canon_sha256": "81fb86d2dcd211c66c5318dbfb5751a7d8bd3a056906915b13edb82372ab36d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.00180",
    "kind": "arxiv",
    "version": 1
  }
}