Pith Number

pith:A46K6CFX

pith:2016:A46K6CFXXAVVOS3JVWNNMF4JPG

not attested not anchored not stored refs pending

Global hypoellipticity for a class of pseudo-differential operators on the torus

Alexandre Kirilov, Cleber de Medeira, Fernando de \'Avila Silva, Rafael Borro Gonzalez

arxiv:1612.02033 v2 · 2016-12-06 · 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{A46K6CFXXAVVOS3JVWNNMF4JPG}

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	2026-05-17T23:53:03.091322Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

073caf08b7b82b574b69ad9ad61789798fdc4418593278f615e94abbc5f943f7

Aliases

arxiv: 1612.02033 · arxiv_version: 1612.02033v2 · doi: 10.48550/arxiv.1612.02033 · pith_short_12: A46K6CFXXAVV · pith_short_16: A46K6CFXXAVVOS3J · pith_short_8: A46K6CFX

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/A46K6CFXXAVVOS3JVWNNMF4JPG \
  | 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: 073caf08b7b82b574b69ad9ad61789798fdc4418593278f615e94abbc5f943f7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1067e70a4e9d7a7a8733e4ebd8b211a420d95d207a36db749c0ec9009e7b122f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-12-06T21:26:35Z",
    "title_canon_sha256": "88235062d7acaaebab02ee44d60f320fececd519dc714b92664fbddf405c3435"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.02033",
    "kind": "arxiv",
    "version": 2
  }
}