Pith Number

pith:HRNPENA7

pith:2018:HRNPENA7BIQXNZJCT2CFIOB6QX

not attested not anchored not stored refs pending

An Optimal Sobolev Embedding for $L^1$

Daniel Spector

arxiv:1806.07588 v2 · 2018-06-20 · 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{HRNPENA7BIQXNZJCT2CFIOB6QX}

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	2026-05-18T00:06:24.697851Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3c5af2341f0a2176e5229e8454383e85fd9c10150eed3729f6edcbbb9c779470

Aliases

arxiv: 1806.07588 · arxiv_version: 1806.07588v2 · doi: 10.48550/arxiv.1806.07588 · pith_short_12: HRNPENA7BIQX · pith_short_16: HRNPENA7BIQXNZJC · pith_short_8: HRNPENA7

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/HRNPENA7BIQXNZJCT2CFIOB6QX \
  | 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: 3c5af2341f0a2176e5229e8454383e85fd9c10150eed3729f6edcbbb9c779470

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0366d4cbe2b028d7703d18aeb411e45d7d5b33d00b502bb10725e073f805faec",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-06-20T07:30:33Z",
    "title_canon_sha256": "28e62e1038d32de081972f353d6ba724214f39d18237b2a754a1366b61d296e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.07588",
    "kind": "arxiv",
    "version": 2
  }
}