Pith Number

pith:GD4VW57Z

pith:2017:GD4VW57ZRBRWX6LBSNTNDMJ4FY

not attested not anchored not stored refs pending

Product Hardy, BMO spaces and iterated commutators associated with Bessel Schr\"odinger operators

Brett D. Wick, Dongyong Yang, Ji Li, Jorge J. Betancor, Xuan Thinh Duong

arxiv:1701.05161 v2 · 2017-01-18 · math.CA · math.AP · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GD4VW57ZRBRWX6LBSNTNDMJ4FY}

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	2026-05-18T00:45:32.117088Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30f95b77f988636bf9619366d1b13c2e2c51f800c0ed56c2e19df4e48d41dd39

Aliases

arxiv: 1701.05161 · arxiv_version: 1701.05161v2 · doi: 10.48550/arxiv.1701.05161 · pith_short_12: GD4VW57ZRBRW · pith_short_16: GD4VW57ZRBRWX6LB · pith_short_8: GD4VW57Z

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/GD4VW57ZRBRWX6LBSNTNDMJ4FY \
  | 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: 30f95b77f988636bf9619366d1b13c2e2c51f800c0ed56c2e19df4e48d41dd39

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b92ff5b759ce17344f1f708c25be482a5d08737a18e04e030c74942efbed83b7",
    "cross_cats_sorted": [
      "math.AP",
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2017-01-18T17:38:58Z",
    "title_canon_sha256": "9f1ec8acd2b9dda09163f13259340538a0a8bb0c57d8e201b9d914d37aa94e17"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.05161",
    "kind": "arxiv",
    "version": 2
  }
}