Pith Number

pith:SDF4GIQT

pith:2011:SDF4GIQTJRJVQCVS4V4D3WP6RI

not attested not anchored not stored refs pending

On the Sobolev embedding theorem for variable exponent spaces in the critical range

Analia Silva, Julian Fernandez Bonder, Nicolas Saintier

arxiv:1111.6952 v1 · 2011-11-29 · math.AP · 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{SDF4GIQTJRJVQCVS4V4D3WP6RI}

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	2026-05-18T03:41:32.242598Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

90cbc322134c53580ab2e5783dd9fe8a219bd0474c4a759ae007164d81b95cda

Aliases

arxiv: 1111.6952 · arxiv_version: 1111.6952v1 · doi: 10.48550/arxiv.1111.6952 · pith_short_12: SDF4GIQTJRJV · pith_short_16: SDF4GIQTJRJVQCVS · pith_short_8: SDF4GIQT

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/SDF4GIQTJRJVQCVS4V4D3WP6RI \
  | 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: 90cbc322134c53580ab2e5783dd9fe8a219bd0474c4a759ae007164d81b95cda

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd2808a285855e9631450d2f65e8db218eb945d2815f79407c764625cd46a9a5",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-11-29T20:02:46Z",
    "title_canon_sha256": "f621b1f18a528a8324ec9e19c045405fe51dd0ec59e3b57f32a7dd442d4f70a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.6952",
    "kind": "arxiv",
    "version": 1
  }
}