Pith Number

pith:PV33TJ4J

pith:2011:PV33TJ4J3N7WA2HWP4MEJAH4GS

not attested not anchored not stored refs pending

Rellich inequalities with weights

Paolo Caldiroli, Roberta Musina

arxiv:1103.6184 v1 · 2011-03-31 · math.FA · 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{PV33TJ4J3N7WA2HWP4MEJAH4GS}

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	2026-05-18T04:25:13.789452Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d77b9a789db7f6068f67f184480fc348390d3928a5e14ba795045cb771cce73

Aliases

arxiv: 1103.6184 · arxiv_version: 1103.6184v1 · doi: 10.48550/arxiv.1103.6184 · pith_short_12: PV33TJ4J3N7W · pith_short_16: PV33TJ4J3N7WA2HW · pith_short_8: PV33TJ4J

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/PV33TJ4J3N7WA2HWP4MEJAH4GS \
  | 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: 7d77b9a789db7f6068f67f184480fc348390d3928a5e14ba795045cb771cce73

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a817e6bac34c0712912d723c6985804ec079935c0455f4dae8ee8ddc76fe7606",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-03-31T13:57:21Z",
    "title_canon_sha256": "114f3719f45cf911cc12b506303e315f7b543a6491e3c5db4c6c5396e16df3a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.6184",
    "kind": "arxiv",
    "version": 1
  }
}