Pith Number

pith:VAE2CYKF

pith:2011:VAE2CYKFU6NGGXZGBGQ2N3RIMD

not attested not anchored not stored refs pending

Sharp Trace Hardy-Sobolev-Maz'ya Inequalities and the Fractional Laplacian

Achilles Tertikas, Luisa Moschini, Stathis Filippas

arxiv:1110.3604 v1 · 2011-10-17 · math.AP · math-ph · math.MP · math.SP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VAE2CYKFU6NGGXZGBGQ2N3RIMD}

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	2026-05-18T02:00:11.697227Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a809a16145a79a635f2609a1a6ee2860c7dbd7b2992c5ce5322d47bf10eb133c

Aliases

arxiv: 1110.3604 · arxiv_version: 1110.3604v1 · doi: 10.48550/arxiv.1110.3604 · pith_short_12: VAE2CYKFU6NG · pith_short_16: VAE2CYKFU6NGGXZG · pith_short_8: VAE2CYKF

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/VAE2CYKFU6NGGXZGBGQ2N3RIMD \
  | 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: a809a16145a79a635f2609a1a6ee2860c7dbd7b2992c5ce5322d47bf10eb133c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0bbd1e1e166125a85cc9b35233728781652faa9ec837dee355a034fff7ac0aae",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-10-17T08:35:30Z",
    "title_canon_sha256": "ee24d3f05f3417ba46f4e476b2381d8a08869b4d43c37665d3b4b0e650d2174c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.3604",
    "kind": "arxiv",
    "version": 1
  }
}