Pith Number

pith:NDWWDLK2

pith:2013:NDWWDLK22FL76IPDTV26IZ7IBS

not attested not anchored not stored refs pending

Anisotropic Fractional Sobolev Norms

Monika Ludwig

arxiv:1304.0703 v1 · 2013-04-02 · math.FA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NDWWDLK22FL76IPDTV26IZ7IBS}

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	2026-05-18T02:39:45.989464Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

68ed61ad5ad157ff21e39d75e467e80c83f7fab09de2d98ddabe96667d336e86

Aliases

arxiv: 1304.0703 · arxiv_version: 1304.0703v1 · doi: 10.48550/arxiv.1304.0703 · pith_short_12: NDWWDLK22FL7 · pith_short_16: NDWWDLK22FL76IPD · pith_short_8: NDWWDLK2

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/NDWWDLK22FL76IPDTV26IZ7IBS \
  | 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: 68ed61ad5ad157ff21e39d75e467e80c83f7fab09de2d98ddabe96667d336e86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e4703b618b352debc22dd85f2b59d9ab14b1660f47ea83b82a678e0e283cf9e",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-04-02T17:22:06Z",
    "title_canon_sha256": "60cc6b4eb98e22bb0e0075ad31ddd47912299e94d5a06600980a7b7125d3a356"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.0703",
    "kind": "arxiv",
    "version": 1
  }
}