Pith Number

pith:7XSULJMA

pith:2018:7XSULJMA7CYKNI2XXZRFX4H2DF

not attested not anchored not stored refs pending

Atomic Characterizations of Hardy Spaces Associated to Schr\"{o}dinger Type Operators

Junqiang Zhang, Zongguang Liu

arxiv:1811.12820 v1 · 2018-11-29 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7XSULJMA7CYKNI2XXZRFX4H2DF}

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	2026-05-17T23:59:28.381909Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fde545a580f8b0a6a357be625bf0fa1964e2a24e9ddd64aa6efb304ace6656bf

Aliases

arxiv: 1811.12820 · arxiv_version: 1811.12820v1 · doi: 10.48550/arxiv.1811.12820 · pith_short_12: 7XSULJMA7CYK · pith_short_16: 7XSULJMA7CYKNI2X · pith_short_8: 7XSULJMA

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/7XSULJMA7CYKNI2XXZRFX4H2DF \
  | 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: fde545a580f8b0a6a357be625bf0fa1964e2a24e9ddd64aa6efb304ace6656bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61f645de053285faf9b2f4e4b0294e496a40af54ce3b862a3d0f3109321816b7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2018-11-29T14:18:29Z",
    "title_canon_sha256": "31a60d3a4c0364c53a8432c9980c03f30584bc26202689c8d35026a7918984aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.12820",
    "kind": "arxiv",
    "version": 1
  }
}