Pith Number

pith:ZKQGIDQO

pith:2018:ZKQGIDQOR2MRB2NDGDH4HQCWEG

not attested not anchored not stored refs pending

Multipliers in Bessel potential spaces. The case of different sign smooth indices

A.A. Belyaev, A.A. Shkalikov

arxiv:1801.01830 v1 · 2018-01-05 · 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{ZKQGIDQOR2MRB2NDGDH4HQCWEG}

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	2026-05-18T00:26:40.848110Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

caa0640e0e8e9910e9a330cfc3c05621aed2a428185aa76c40d6f9c629da4f29

Aliases

arxiv: 1801.01830 · arxiv_version: 1801.01830v1 · doi: 10.48550/arxiv.1801.01830 · pith_short_12: ZKQGIDQOR2MR · pith_short_16: ZKQGIDQOR2MRB2ND · pith_short_8: ZKQGIDQO

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/ZKQGIDQOR2MRB2NDGDH4HQCWEG \
  | 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: caa0640e0e8e9910e9a330cfc3c05621aed2a428185aa76c40d6f9c629da4f29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6deb06060a5e08cbc4d897de429d882baa0682c3819f62b1965ecab0799c7084",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-01-05T16:51:32Z",
    "title_canon_sha256": "8bdaf4467794388c61872747a60173a556f9396e733a778f3ca81a31928ec344"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.01830",
    "kind": "arxiv",
    "version": 1
  }
}