Pith Number

pith:IOTAICZA

pith:2010:IOTAICZA7TX53ULZWFYEJ2TNFC

not attested not anchored not stored refs pending

Hormander class of pseudo-differential operators on compact Lie groups and global hypoellipticity

Jens Wirth, Michael Ruzhansky, Ville Turunen

arxiv:1004.4396 v1 · 2010-04-26 · math.FA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IOTAICZA7TX53ULZWFYEJ2TNFC}

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	2026-05-18T02:44:23.797836Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

43a6040b20fcefddd179b17044ea6d28b94fee0eda522821164e28ef4b057ba2

Aliases

arxiv: 1004.4396 · arxiv_version: 1004.4396v1 · doi: 10.48550/arxiv.1004.4396 · pith_short_12: IOTAICZA7TX5 · pith_short_16: IOTAICZA7TX53ULZ · pith_short_8: IOTAICZA

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/IOTAICZA7TX53ULZWFYEJ2TNFC \
  | 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: 43a6040b20fcefddd179b17044ea6d28b94fee0eda522821164e28ef4b057ba2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5616087100710ccb446969a365600cdd1cc9f8f48b63139ad64dc46586b5267d",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2010-04-26T01:27:14Z",
    "title_canon_sha256": "0cc387eb470ee2f1b8045f4511938a5c0e3f9f55845af08837d82cf87ecb0162"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.4396",
    "kind": "arxiv",
    "version": 1
  }
}