Pith Number

pith:PR7Q6PLJ

pith:2018:PR7Q6PLJRUBVMAOR7N7QGBDZ3E

not attested not anchored not stored refs pending

Maximal Hypoellipticity for Left-Invariant Differential Operators on Lie Groups

Tommaso Bruno

arxiv:1811.05009 v1 · 2018-11-12 · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PR7Q6PLJRUBVMAOR7N7QGBDZ3E}

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	2026-05-18T00:01:01.475517Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c7f0f3d698d035601d1fb7f030479d92cf219664f4be5430da26012c5ae9339

Aliases

arxiv: 1811.05009 · arxiv_version: 1811.05009v1 · doi: 10.48550/arxiv.1811.05009 · pith_short_12: PR7Q6PLJRUBV · pith_short_16: PR7Q6PLJRUBVMAOR · pith_short_8: PR7Q6PLJ

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/PR7Q6PLJRUBVMAOR7N7QGBDZ3E \
  | 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: 7c7f0f3d698d035601d1fb7f030479d92cf219664f4be5430da26012c5ae9339

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "377628e267b88844fa262da9a43f3840c774b0240757f204dfa4bbc8189c6544",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-11-12T21:38:55Z",
    "title_canon_sha256": "88834c753d84e413e7eb2daca2a0ade4e9d91bada993e93b1f1c4b18019cd479"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.05009",
    "kind": "arxiv",
    "version": 1
  }
}