Pith Number

pith:ZY7HQS3J

pith:2014:ZY7HQS3JMTJJRWWGROA3ZNZDZ5

not attested not anchored not stored refs pending

Density of smooth functions in variable exponent Sobolev spaces

Nikos Yannakakis, Thanasis Kostopoulos

arxiv:1406.5385 v3 · 2014-06-20 · 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{ZY7HQS3JMTJJRWWGROA3ZNZDZ5}

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	2026-05-18T01:37:02.271608Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce3e784b6964d298dac68b81bcb723cf765ab22904ca14f5d4c0866a03e73964

Aliases

arxiv: 1406.5385 · arxiv_version: 1406.5385v3 · doi: 10.48550/arxiv.1406.5385 · pith_short_12: ZY7HQS3JMTJJ · pith_short_16: ZY7HQS3JMTJJRWWG · pith_short_8: ZY7HQS3J

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/ZY7HQS3JMTJJRWWGROA3ZNZDZ5 \
  | 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: ce3e784b6964d298dac68b81bcb723cf765ab22904ca14f5d4c0866a03e73964

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4de5ac1d05e7bff542742d1ca6fe1bb9cdb578b550fab0d9875eceed64df0da8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2014-06-20T13:45:20Z",
    "title_canon_sha256": "a71dbdd79b37295c111bdbd00132324f8196e77212d1089d22bad6d6e6e007a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1406.5385",
    "kind": "arxiv",
    "version": 3
  }
}