Pith Number

pith:CKCSGEWR

pith:2013:CKCSGEWRUDQ2L3ZFQSQ6RP4IGO

not attested not anchored not stored refs pending

Symmetry breaking of extremals for the Caffarelli-Kohn-Nirenberg inequalities in a non-Hilbertian setting

Paolo Caldiroli, Roberta Musina

arxiv:1307.2226 v1 · 2013-07-08 · 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{CKCSGEWRUDQ2L3ZFQSQ6RP4IGO}

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	2026-05-18T03:01:10.440698Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12852312d1a0e1a5ef2584a1e8bf8833b6174e3c2827cea41d0d178bc27b6fdf

Aliases

arxiv: 1307.2226 · arxiv_version: 1307.2226v1 · doi: 10.48550/arxiv.1307.2226 · pith_short_12: CKCSGEWRUDQ2 · pith_short_16: CKCSGEWRUDQ2L3ZF · pith_short_8: CKCSGEWR

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/CKCSGEWRUDQ2L3ZFQSQ6RP4IGO \
  | 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: 12852312d1a0e1a5ef2584a1e8bf8833b6174e3c2827cea41d0d178bc27b6fdf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "da0b4dea9d38e6c18ec861d6f2d9c9d5023a1f09c74d16698e74748825985e90",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-07-08T19:58:21Z",
    "title_canon_sha256": "6b670f2130f967fffac5ef9e87e3c6104ef132d05eb7e9a8c9f1f0d96afe8f39"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.2226",
    "kind": "arxiv",
    "version": 1
  }
}