Pith Number

pith:NFUZ7P6C

pith:2013:NFUZ7P6CGVSPN5N5CA2WDOEEOO

not attested not anchored not stored refs pending

Morrey-Sobolev Spaces on Metric Measure Spaces

Dachun Yang, Wen Yuan, Yufeng Lu

arxiv:1304.3871 v2 · 2013-04-14 · math.CA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NFUZ7P6CGVSPN5N5CA2WDOEEOO}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T03:05:09.770032Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

69699fbfc23564f6f5bd103561b8847391ab8390e09787ae87f4f12f55ae748b

Aliases

arxiv: 1304.3871 · arxiv_version: 1304.3871v2 · doi: 10.48550/arxiv.1304.3871 · pith_short_12: NFUZ7P6CGVSP · pith_short_16: NFUZ7P6CGVSPN5N5 · pith_short_8: NFUZ7P6C

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/NFUZ7P6CGVSPN5N5CA2WDOEEOO \
  | 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: 69699fbfc23564f6f5bd103561b8847391ab8390e09787ae87f4f12f55ae748b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1854979aa6d928a87053bcb713a877426532ff8aa1393b8b2104e6c2a387adab",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-04-14T02:15:55Z",
    "title_canon_sha256": "412c8d25411bdbf9433d656b5e892a959960258b6dd498f6e90f78200813a04d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.3871",
    "kind": "arxiv",
    "version": 2
  }
}