Pith Number

pith:RQYMAMQS

pith:2010:RQYMAMQSGBQ2Z7BHNE2YVVTVY5

not attested not anchored not stored refs pending

Weighted norm inequalities, Gaussian bounds and sharp spectral multipliers

Adam Sikora, Lixin Yan, Xuan Thinh Duong

arxiv:1003.1831 v3 · 2010-03-09 · 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{RQYMAMQSGBQ2Z7BHNE2YVVTVY5}

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	2026-05-18T04:39:19.510349Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8c30c032123061acfc2769358ad675c750146b5f47b3af60e2e701e7f4fd9b10

Aliases

arxiv: 1003.1831 · arxiv_version: 1003.1831v3 · doi: 10.48550/arxiv.1003.1831 · pith_short_12: RQYMAMQSGBQ2 · pith_short_16: RQYMAMQSGBQ2Z7BH · pith_short_8: RQYMAMQS

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/RQYMAMQSGBQ2Z7BHNE2YVVTVY5 \
  | 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: 8c30c032123061acfc2769358ad675c750146b5f47b3af60e2e701e7f4fd9b10

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d93eec18f7a44cc7b8750b7a68725d38a4fdedbd012345797c35a5a87960c7d",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2010-03-09T08:55:12Z",
    "title_canon_sha256": "2216b62ba395f3842da05e3ce9d704a8c3b9b52ca8ccd8f235e1cee417e73d8f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.1831",
    "kind": "arxiv",
    "version": 3
  }
}