Pith Number

pith:4EE46XA2

pith:2009:4EE46XA2PENWS2ZE6G34QENMDY

not attested not anchored not stored refs pending

On the symmetry of extremals for the Caffarelli-Kohn-Nirenberg inequalities

Gabriella Tarantello, Jean Dolbeault (CEREMADE), Maria J. Esteban (CEREMADE), Michael Loss

arxiv:0907.1405 v2 · 2009-07-08 · 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{4EE46XA2PENWS2ZE6G34QENMDY}

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	2026-05-18T03:37:53.572963Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e109cf5c1a791b696b24f1b7c811ac1e3431105d988680556eff88790fb2d5a2

Aliases

arxiv: 0907.1405 · arxiv_version: 0907.1405v2 · doi: 10.48550/arxiv.0907.1405 · pith_short_12: 4EE46XA2PENW · pith_short_16: 4EE46XA2PENWS2ZE · pith_short_8: 4EE46XA2

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/4EE46XA2PENWS2ZE6G34QENMDY \
  | 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: e109cf5c1a791b696b24f1b7c811ac1e3431105d988680556eff88790fb2d5a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8927a4098f8175de2c87312c65da79318ce28cd8261e2df4509817c5b1abe356",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2009-07-08T14:53:56Z",
    "title_canon_sha256": "73506a7f82302281bfe6f28a6a302d40034a0b94f83c75e3e3ca6f2c41780050"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.1405",
    "kind": "arxiv",
    "version": 2
  }
}