Pith Number

pith:XC2P45L2

pith:2018:XC2P45L2KTXTIJK7VMUJYNANRT

not attested not anchored not stored refs pending

The polar decomposition for adjointable operators on Hilbert $C^*$-modules and centered operators

Na Liu, Qingxiang Xu, Wei Luo

arxiv:1807.01598 v2 · 2018-07-03 · 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{XC2P45L2KTXTIJK7VMUJYNANRT}

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	2026-05-18T00:10:51.595868Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8b4fe757a54ef34255fab289c340d8cfde4933ebd2e92e97fe9d26b41238cee

Aliases

arxiv: 1807.01598 · arxiv_version: 1807.01598v2 · doi: 10.48550/arxiv.1807.01598 · pith_short_12: XC2P45L2KTXT · pith_short_16: XC2P45L2KTXTIJK7 · pith_short_8: XC2P45L2

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/XC2P45L2KTXTIJK7VMUJYNANRT \
  | 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: b8b4fe757a54ef34255fab289c340d8cfde4933ebd2e92e97fe9d26b41238cee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "57d9e85cccbe5a4eb6e97ceb928da84d8c65f9a965b159002d359cb9acd73bd6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2018-07-03T07:50:35Z",
    "title_canon_sha256": "cf6906bbb2dfe83b4a66377fdc31479029af6d20d1e2125230f62365fea7e9e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.01598",
    "kind": "arxiv",
    "version": 2
  }
}