Pith Number

pith:AEOPK3LT

pith:2017:AEOPK3LTC6CW35HTWLSPG5KD7U

not attested not anchored not stored refs pending

Tubular neighborhoods in the sub-Riemannian Heisenberg groups

Manuel Ritor\'e

arxiv:1703.01592 v3 · 2017-03-05 · math.MG · 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{AEOPK3LTC6CW35HTWLSPG5KD7U}

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	2026-05-18T00:30:55.184602Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

011cf56d7317856df4f3b2e4f37543fd123a896198c667b5e5c3ceb2403639e1

Aliases

arxiv: 1703.01592 · arxiv_version: 1703.01592v3 · doi: 10.48550/arxiv.1703.01592 · pith_short_12: AEOPK3LTC6CW · pith_short_16: AEOPK3LTC6CW35HT · pith_short_8: AEOPK3LT

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/AEOPK3LTC6CW35HTWLSPG5KD7U \
  | 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: 011cf56d7317856df4f3b2e4f37543fd123a896198c667b5e5c3ceb2403639e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b39055c6d054807ccc275df3ac2c9406bb8f6b953cffd1e5ba5c54659027777",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2017-03-05T12:39:36Z",
    "title_canon_sha256": "e38b6710dae640efd87adcd5fe2b10fad8b29f6ba499c4e9dbfb7d5049fc73c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1703.01592",
    "kind": "arxiv",
    "version": 3
  }
}