Pith Number

pith:3TUGG5TF

pith:2019:3TUGG5TFTCWQB4SYYCI3YYF3QX

not attested not anchored not stored refs pending

H\"ormander's hypoelliptic theorem for nonlocal operators

Xicheng Zhang, Xuhui Peng, Zimo Hao

arxiv:1901.06621 v1 · 2019-01-20 · math.PR · 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{3TUGG5TFTCWQB4SYYCI3YYF3QX}

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	2026-05-17T23:55:49.627195Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dce863766598ad00f258c091bc60bb85c1d1a26b2c88294d8e34f8ca0ad75e05

Aliases

arxiv: 1901.06621 · arxiv_version: 1901.06621v1 · doi: 10.48550/arxiv.1901.06621 · pith_short_12: 3TUGG5TFTCWQ · pith_short_16: 3TUGG5TFTCWQB4SY · pith_short_8: 3TUGG5TF

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/3TUGG5TFTCWQB4SYYCI3YYF3QX \
  | 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: dce863766598ad00f258c091bc60bb85c1d1a26b2c88294d8e34f8ca0ad75e05

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73a5fc675904bfef3ca06153b95c9c82d4cc977992f5e407d9077fb083675e0e",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-01-20T04:40:40Z",
    "title_canon_sha256": "5a5f0f48b82f91ac0b4f9382c990794267fe8d208d6659a3d2d63c8608045c85"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1901.06621",
    "kind": "arxiv",
    "version": 1
  }
}