Pith Number

pith:RTZFUJGH

pith:2010:RTZFUJGHECV2O35OYNA6VXSMPF

not attested not anchored not stored refs pending

Extremal functions for Caffarelli-Kohn-Nirenberg and logarithmic Hardy inequalities

Jean Dolbeault (CEREMADE), Maria J. Esteban (CEREMADE)

arxiv:1007.0309 v2 · 2010-07-02 · 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{RTZFUJGHECV2O35OYNA6VXSMPF}

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	2026-05-18T03:39:06.548388Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8cf25a24c720aba76faec341eade4c7978270d3f63fa8197325e8c4255a7adfc

Aliases

arxiv: 1007.0309 · arxiv_version: 1007.0309v2 · doi: 10.48550/arxiv.1007.0309 · pith_short_12: RTZFUJGHECV2 · pith_short_16: RTZFUJGHECV2O35O · pith_short_8: RTZFUJGH

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/RTZFUJGHECV2O35OYNA6VXSMPF \
  | 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: 8cf25a24c720aba76faec341eade4c7978270d3f63fa8197325e8c4255a7adfc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47a7e6a4c8bd7efaee1c597c3c75b585d3f200e450bc61167807a38ef1f06901",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-07-02T07:38:39Z",
    "title_canon_sha256": "25da55da59fe10efb51a97e5c3c9bd4c682ac0c10e89492956a9388a103a44f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.0309",
    "kind": "arxiv",
    "version": 2
  }
}