Pith Number

pith:2OKX25GH

pith:2016:2OKX25GHRSV472SYXIQ4WBQMRO

not attested not anchored not stored refs pending

Local Hardy and Rellich inequalities for sums of squares of vector fields

Durvudkhan Suragan, Michael Ruzhansky

arxiv:1601.06157 v2 · 2016-01-21 · math.AP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2OKX25GHRSV472SYXIQ4WBQMRO}

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	2026-05-18T01:18:08.319804Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3957d74c78cabcfea58ba21cb060c8b9180640c56e569323297a529f090fb53

Aliases

arxiv: 1601.06157 · arxiv_version: 1601.06157v2 · doi: 10.48550/arxiv.1601.06157 · pith_short_12: 2OKX25GHRSV4 · pith_short_16: 2OKX25GHRSV472SY · pith_short_8: 2OKX25GH

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/2OKX25GHRSV472SYXIQ4WBQMRO \
  | 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: d3957d74c78cabcfea58ba21cb060c8b9180640c56e569323297a529f090fb53

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "38faba94c5d28e2ff42059fda67dbca61683e41677acbe4abed8fbeb43ac577d",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-01-21T21:25:02Z",
    "title_canon_sha256": "5dc8df3e15a5365632793095ae824559e5f8d0f3761aa18e74f0281518b2ba8d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.06157",
    "kind": "arxiv",
    "version": 2
  }
}