Pith Number

pith:VQDOIULQ

pith:2019:VQDOIULQOVGV5APZ2NLGQUDOY4

not attested not anchored not stored refs pending

Global estimates in Sobolev spaces for homogeneous H\"ormander sums of squares

Andrea Bonfiglioli, Marco Bramanti, Stefano Biagi

arxiv:1906.07835 v1 · 2019-06-18 · 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{VQDOIULQOVGV5APZ2NLGQUDOY4}

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	2026-05-17T23:42:57.625682Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac06e45170754d5e81f9d35668506ec7338a60e624264f0ea4a84802ec1098c4

Aliases

arxiv: 1906.07835 · arxiv_version: 1906.07835v1 · doi: 10.48550/arxiv.1906.07835 · pith_short_12: VQDOIULQOVGV · pith_short_16: VQDOIULQOVGV5APZ · pith_short_8: VQDOIULQ

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/VQDOIULQOVGV5APZ2NLGQUDOY4 \
  | 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: ac06e45170754d5e81f9d35668506ec7338a60e624264f0ea4a84802ec1098c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a4e9d3a1961960890c05cdf3a49ffdc462ce50ffbcdbfb4018175a34f9191c1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-06-18T22:43:29Z",
    "title_canon_sha256": "241bab4b2a8ecc830e6a6e41c3714d8dcf41ec54c45b349184bf24188d69d2ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.07835",
    "kind": "arxiv",
    "version": 1
  }
}