Pith Number

pith:JY52PYMI

pith:2017:JY52PYMIBG2AI55LQUZYPRJCE5

not attested not anchored not stored refs pending

Spectral theory of multiplication operators on Hardy-Sobolev spaces

Guangfu Cao, Kehe Zhu, Li He

arxiv:1709.02047 v1 · 2017-09-07 · 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{JY52PYMIBG2AI55LQUZYPRJCE5}

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	2026-05-18T00:35:50.392731Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4e3ba7e18809b40477ab853387c522274b0ba1d1a8dfa8191455bdc8def98d0b

Aliases

arxiv: 1709.02047 · arxiv_version: 1709.02047v1 · doi: 10.48550/arxiv.1709.02047 · pith_short_12: JY52PYMIBG2A · pith_short_16: JY52PYMIBG2AI55L · pith_short_8: JY52PYMI

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/JY52PYMIBG2AI55LQUZYPRJCE5 \
  | 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: 4e3ba7e18809b40477ab853387c522274b0ba1d1a8dfa8191455bdc8def98d0b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "46bfa54493f2fbff2076bc029d845467c0950b57c48b531b3556a273dba93d12",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2017-09-07T02:11:49Z",
    "title_canon_sha256": "f7ff73db4acbede75c80e68f8da062546c363f4897e4d5daffb8e7ee8cf92d10"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.02047",
    "kind": "arxiv",
    "version": 1
  }
}