Pith Number

pith:CZKU5YU7

pith:2010:CZKU5YU7TMQRCQHPGP2QFFPKFP

not attested not anchored not stored refs pending

On the lack of compactness in the 2D critical Sobolev embedding

Hajer Bahouri, Mohamed Majdoub, Nader Masmoudi

arxiv:1003.2562 v1 · 2010-03-12 · math.AP · math.CA · 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{CZKU5YU7TMQRCQHPGP2QFFPKFP}

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	2026-07-04T17:23:14.696056Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

16554ee29f9b211140ef33f50295ea2be20a1af99acef080c77a012f34ca7b88

Aliases

arxiv: 1003.2562 · arxiv_version: 1003.2562v1 · doi: 10.48550/arxiv.1003.2562 · pith_short_12: CZKU5YU7TMQR · pith_short_16: CZKU5YU7TMQRCQHP · pith_short_8: CZKU5YU7

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/CZKU5YU7TMQRCQHPGP2QFFPKFP \
  | 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: 16554ee29f9b211140ef33f50295ea2be20a1af99acef080c77a012f34ca7b88

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f40cd338ec1822479ab86edd399d7f5d2ec91ff8a4f222ff13f66919338abecc",
    "cross_cats_sorted": [
      "math.CA",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-03-12T15:39:18Z",
    "title_canon_sha256": "f9d817a41609ff5edbd4515637667c0f73cc138e967f2e234f7b50a09c12493b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.2562",
    "kind": "arxiv",
    "version": 1
  }
}