Pith Number

pith:45X36Z2W

pith:2010:45X36Z2W45DWKAS35QWGK36V5O

not attested not anchored not stored refs pending

Haj\lasz-Sobolev Imbedding and Extension

Yuan Zhou

arxiv:1004.5307 v2 · 2010-04-29 · math.CA · math.AP · 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{45X36Z2W45DWKAS35QWGK36V5O}

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	2026-05-18T02:24:15.034643Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e76fbf6756e74765025bec2c656fd5eba5cfd03494ffa342c767a5c5d8d280a2

Aliases

arxiv: 1004.5307 · arxiv_version: 1004.5307v2 · doi: 10.48550/arxiv.1004.5307 · pith_short_12: 45X36Z2W45DW · pith_short_16: 45X36Z2W45DWKAS3 · pith_short_8: 45X36Z2W

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/45X36Z2W45DWKAS35QWGK36V5O \
  | 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: e76fbf6756e74765025bec2c656fd5eba5cfd03494ffa342c767a5c5d8d280a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "458ba6043f5b9738b0ca0c21c307607a992ec378cafb4d9657a78a8c388ab8bf",
    "cross_cats_sorted": [
      "math.AP",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2010-04-29T14:38:16Z",
    "title_canon_sha256": "a2fab9d40115b8b2155433259b7d3b2a58b911138a489a4efc44e7be24d8582a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.5307",
    "kind": "arxiv",
    "version": 2
  }
}