Pith Number

pith:YFC42OQO

pith:2013:YFC42OQO475KY7HH2UQ6QKJHGT

not attested not anchored not stored refs pending

On the Sobolev trace Theorem for variable exponent spaces in the critical range

Analia Silva, Julian Fernandez Bonder, Nicolas Saintier

arxiv:1301.2961 v1 · 2013-01-14 · 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{YFC42OQO475KY7HH2UQ6QKJHGT}

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	2026-05-18T03:36:27.721477Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c145cd3a0ee7faac7ce7d521e8292734e5da945a48fe23c18e98909cc5094493

Aliases

arxiv: 1301.2961 · arxiv_version: 1301.2961v1 · doi: 10.48550/arxiv.1301.2961 · pith_short_12: YFC42OQO475K · pith_short_16: YFC42OQO475KY7HH · pith_short_8: YFC42OQO

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/YFC42OQO475KY7HH2UQ6QKJHGT \
  | 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: c145cd3a0ee7faac7ce7d521e8292734e5da945a48fe23c18e98909cc5094493

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c1b8654109f0a2ff49e9dc17b1b4651ae0747bfd0e20a12bb48cbea45f2a395",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-01-14T13:00:41Z",
    "title_canon_sha256": "a5c6931c25acdfbd244873ac2032b07fa5eeefb9a79735292b494ecf54028d5f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.2961",
    "kind": "arxiv",
    "version": 1
  }
}