Pith Number

pith:5FT22QAC

pith:2019:5FT22QAC7Y5FJ6CP67JPANQHRF

not attested not anchored not stored refs pending

Embeddings of homogeneous Sobolev spaces on the entire space

Zden\v{e}k Mihula

arxiv:1908.03384 v2 · 2019-08-09 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5FT22QAC7Y5FJ6CP67JPANQHRF}

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	2026-07-05T02:08:16.433132Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e967ad4002fe3a54f84ff7d2f03607895d48a977b9511e55b02fed2a8daa955e

Aliases

arxiv: 1908.03384 · arxiv_version: 1908.03384v2 · doi: 10.48550/arxiv.1908.03384 · pith_short_12: 5FT22QAC7Y5F · pith_short_16: 5FT22QAC7Y5FJ6CP · pith_short_8: 5FT22QAC

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/5FT22QAC7Y5FJ6CP67JPANQHRF \
  | 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: e967ad4002fe3a54f84ff7d2f03607895d48a977b9511e55b02fed2a8daa955e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d7d5ac39f01a02ef63d2f6e9e4c89f0a119f396c83ba0670caff2f91805d544",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2019-08-09T09:33:48Z",
    "title_canon_sha256": "437fdc7ddab1a5c7e7c808502bcbba75bced7e3b08e9d44065dcdce3f7e4cc35"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.03384",
    "kind": "arxiv",
    "version": 2
  }
}