Pith Number

pith:PAQRI33I

pith:2011:PAQRI33ITF7LVG6FG4QPA3TAP4

not attested not anchored not stored refs pending

Decompositions of Gelfand-Shilov kernels into kernels of similar class

Andrei Khrennikov, B\"orje Nilsson, Joachim Toft, Sven Nordebo

arxiv:1112.4314 v3 · 2011-12-19 · math.FA · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PAQRI33ITF7LVG6FG4QPA3TAP4}

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	2026-05-18T03:55:57.362394Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7821146f68997eba9bc53720f06e607f0583c60ec50153c3c3e367548587d973

Aliases

arxiv: 1112.4314 · arxiv_version: 1112.4314v3 · doi: 10.48550/arxiv.1112.4314 · pith_short_12: PAQRI33ITF7L · pith_short_16: PAQRI33ITF7LVG6F · pith_short_8: PAQRI33I

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/PAQRI33ITF7LVG6FG4QPA3TAP4 \
  | 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: 7821146f68997eba9bc53720f06e607f0583c60ec50153c3c3e367548587d973

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0486ba143bcc71ba910f3cb1893450c966feff566ee6d074d523756c2ef52cb",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-12-19T12:18:11Z",
    "title_canon_sha256": "22b5a105234607a89f7b62a8a0d092ab8247614974cff4316192b410383a5f0e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4314",
    "kind": "arxiv",
    "version": 3
  }
}