Pith Number

pith:G2VS3VUB

pith:2019:G2VS3VUBDQXCEBWIUYPUG4CLGZ

not attested not anchored not stored refs pending

Extension operators on Sobolev spaces with decreasing integrability

Alexander Ukhlov

arxiv:1908.09322 v4 · 2019-08-25 · 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{G2VS3VUBDQXCEBWIUYPUG4CLGZ}

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	2026-07-05T01:43:12.958728Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

36ab2dd6811c2e2206c8a61f43704b36488158ec014d664b029892b2e334d182

Aliases

arxiv: 1908.09322 · arxiv_version: 1908.09322v4 · doi: 10.48550/arxiv.1908.09322 · pith_short_12: G2VS3VUBDQXC · pith_short_16: G2VS3VUBDQXCEBWI · pith_short_8: G2VS3VUB

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/G2VS3VUBDQXCEBWIUYPUG4CLGZ \
  | 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: 36ab2dd6811c2e2206c8a61f43704b36488158ec014d664b029892b2e334d182

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e58642f4bc5b022d3c493f027554817e46bbad6faae8c4dfd2c9fa8a504c6ab",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2019-08-25T13:21:43Z",
    "title_canon_sha256": "48d812e28c06be8d49b589e72d9b1bc816d75d940ec4d4310b8f77a8ab8b95ad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.09322",
    "kind": "arxiv",
    "version": 4
  }
}