Pith Number

pith:STQUPPLG

pith:2015:STQUPPLGPREQPL7HIOP7IKLFY3

not attested not anchored not stored refs pending

$L^p$-$L^q$ multipliers on locally compact groups

Michael Ruzhansky, Rauan Akylzhanov

arxiv:1510.06321 v3 · 2015-10-19 · math.RT · math.CA · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{STQUPPLGPREQPL7HIOP7IKLFY3}

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	2026-05-18T00:47:29.472641Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

94e147bd667c4907afe7439ff42965c6c12c6166a057b05692f1ab07183fcb13

Aliases

arxiv: 1510.06321 · arxiv_version: 1510.06321v3 · doi: 10.48550/arxiv.1510.06321 · pith_short_12: STQUPPLGPREQ · pith_short_16: STQUPPLGPREQPL7H · pith_short_8: STQUPPLG

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/STQUPPLGPREQPL7HIOP7IKLFY3 \
  | 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: 94e147bd667c4907afe7439ff42965c6c12c6166a057b05692f1ab07183fcb13

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b282b1dca4e75d29525dc55e6d513b65ca9b8e80a77c47a0cce17ed598ddf44",
    "cross_cats_sorted": [
      "math.CA",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2015-10-19T12:28:29Z",
    "title_canon_sha256": "2e6697bf038ceb1d0b05b8a59b94792743b17dfd2c796fc8b6cecee9355bcfbf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.06321",
    "kind": "arxiv",
    "version": 3
  }
}