Pith Number

pith:47O3TOKS

pith:2017:47O3TOKSX5CUKBECDNYDX4BQ3Y

not attested not anchored not stored refs pending

Sharp Sobolev type embeddings on the entire Euclidean space

Andrea Cianchi, Angela Alberico, Lenka Slavikova, Lubos Pick

arxiv:1711.11549 v1 · 2017-11-30 · 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{47O3TOKSX5CUKBECDNYDX4BQ3Y}

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	2026-05-18T00:29:11.309418Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7ddb9b952bf454504821b703bf030de0aa9e650f14a0aa17ec584f6e472f4bd

Aliases

arxiv: 1711.11549 · arxiv_version: 1711.11549v1 · doi: 10.48550/arxiv.1711.11549 · pith_short_12: 47O3TOKSX5CU · pith_short_16: 47O3TOKSX5CUKBEC · pith_short_8: 47O3TOKS

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/47O3TOKSX5CUKBECDNYDX4BQ3Y \
  | 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: e7ddb9b952bf454504821b703bf030de0aa9e650f14a0aa17ec584f6e472f4bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f90d0e740ec2114941c8ef8c9f39c6ccc2c5d22f19303bcc3bd33d30569c20c6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2017-11-30T18:12:41Z",
    "title_canon_sha256": "aeaa6baccbbfcbcf5e292d114c3fc831cffd8d0e479028ccf08cc1673e6ef7af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.11549",
    "kind": "arxiv",
    "version": 1
  }
}