Pith Number

pith:H52EGRHY

pith:2010:H52EGRHYNEL5WVHD4HPEHAIQAR

not attested not anchored not stored refs pending

Asymptotic expansions and extremals for the critical Sobolev and Gagliardo-Nirenberg inequalities on a torus

Jonathan H.B. Deane, Michele V. Bartuccelli, Sergey Zelik

arxiv:1012.2061 v1 · 2010-12-09 · 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{H52EGRHYNEL5WVHD4HPEHAIQAR}

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	2026-05-18T04:33:49.066719Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3f744344f86917db54e3e1de43811004744c6c21896ee7c786732988d79de938

Aliases

arxiv: 1012.2061 · arxiv_version: 1012.2061v1 · doi: 10.48550/arxiv.1012.2061 · pith_short_12: H52EGRHYNEL5 · pith_short_16: H52EGRHYNEL5WVHD · pith_short_8: H52EGRHY

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/H52EGRHYNEL5WVHD4HPEHAIQAR \
  | 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: 3f744344f86917db54e3e1de43811004744c6c21896ee7c786732988d79de938

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ce002311f2ba38e7e0d2fcca55a43e13d8f419706311a70f830b3a8237b936a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2010-12-09T17:53:14Z",
    "title_canon_sha256": "9db056948d512185109f5c5b0430b7cddc5b20794a33d5babfce4c6a951afa33"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2061",
    "kind": "arxiv",
    "version": 1
  }
}