Pith Number

pith:L44WFCBP

pith:2011:L44WFCBPGEPDHL7G3UXGW7HAQZ

not attested not anchored not stored refs pending

Properties of parabolic Sobolev and parabolic Besov spaces

Tongkeun Chang

arxiv:1108.0499 v1 · 2011-08-02 · 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{L44WFCBPGEPDHL7G3UXGW7HAQZ}

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	2026-05-18T04:16:30.284650Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f3962882f311e33afe6dd2e6b7ce08670e45dfa8303de13373160383c3ab45e

Aliases

arxiv: 1108.0499 · arxiv_version: 1108.0499v1 · doi: 10.48550/arxiv.1108.0499 · pith_short_12: L44WFCBPGEPD · pith_short_16: L44WFCBPGEPDHL7G · pith_short_8: L44WFCBP

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/L44WFCBPGEPDHL7G3UXGW7HAQZ \
  | 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: 5f3962882f311e33afe6dd2e6b7ce08670e45dfa8303de13373160383c3ab45e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a3c1f8bf064224bb46163ec1be5d1d079b8bee6cc4b41f9c797b1ebb875d3641",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-08-02T07:25:40Z",
    "title_canon_sha256": "745a2ca3ed3481b746ec893ba084acd8ca67338707ddcea2da13fe6c17d679da"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.0499",
    "kind": "arxiv",
    "version": 1
  }
}