Pith Number

pith:PRKZBXIB

pith:2011:PRKZBXIBKOU4JT3TJ7P56XRIOX

not attested not anchored not stored refs pending

Sobolev and Hardy-Littlewood-Sobolev inequalities: duality and fast diffusion

Jean Dolbeault (CEREMADE)

arxiv:1103.1145 v1 · 2011-03-06 · 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{PRKZBXIBKOU4JT3TJ7P56XRIOX}

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	2026-05-18T03:54:06.226978Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c5590dd0153a9c4cf734fdfdf5e2875ddf98b9605fa07b2b4604f6c93221374

Aliases

arxiv: 1103.1145 · arxiv_version: 1103.1145v1 · doi: 10.48550/arxiv.1103.1145 · pith_short_12: PRKZBXIBKOU4 · pith_short_16: PRKZBXIBKOU4JT3T · pith_short_8: PRKZBXIB

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/PRKZBXIBKOU4JT3TJ7P56XRIOX \
  | 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: 7c5590dd0153a9c4cf734fdfdf5e2875ddf98b9605fa07b2b4604f6c93221374

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b6edcf1151df63ae05fe22725b5f4f024be5d2169b7a1a64b5235a65854b662e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-03-06T17:15:59Z",
    "title_canon_sha256": "e375927a919741dc056ccd70c817de21423e26d9d2081d4670e42ab5fd5cbadf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.1145",
    "kind": "arxiv",
    "version": 1
  }
}