Pith Number

pith:2F6EN44J

pith:2015:2F6EN44J44QUZJ4EB74THSMLOK

not attested not anchored not stored refs pending

Global Hypoellipticity for First-Order Operators on Closed Smooth Manifolds

Alexandre Kirilov, Fernando de \'Avila Silva, Todor Gramchev

arxiv:1507.08880 v2 · 2015-07-31 · 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{2F6EN44J44QUZJ4EB74THSMLOK}

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	2026-05-17T23:53:03.157738Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d17c46f389e7214ca7840ff933c98b72b7aa51f9543b52400b0044e08c3c1fc7

Aliases

arxiv: 1507.08880 · arxiv_version: 1507.08880v2 · doi: 10.48550/arxiv.1507.08880 · pith_short_12: 2F6EN44J44QU · pith_short_16: 2F6EN44J44QUZJ4E · pith_short_8: 2F6EN44J

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/2F6EN44J44QUZJ4EB74THSMLOK \
  | 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: d17c46f389e7214ca7840ff933c98b72b7aa51f9543b52400b0044e08c3c1fc7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "927fe6adac9b6a87a3e8a4c32a10e6cbd665e6fb825a2a999ba262133b6ae668",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-07-31T13:56:17Z",
    "title_canon_sha256": "7a2f393aab43177dd6a42d13c351f81c9e4cfe8c1d25a1f5b61d5024b2c7d8d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.08880",
    "kind": "arxiv",
    "version": 2
  }
}