pith. sign in
Pith Number

pith:WQF7J5KX

pith:2015:WQF7J5KXTQ5RBGLLEISPV26T3Z
not attested not anchored not stored refs pending

Equivariant Picard groups of $C^*$-algebras with finite dimensional $C^*$-Hopf algebra coactions

Kazunori Kodaka

arxiv:1512.07724 v1 · 2015-12-24 · 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{WQF7J5KXTQ5RBGLLEISPV26T3Z}

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 2026-05-18T01:23:48.043826Z
Builder pith-number-builder-2026-05-17-v1
Signature Pith Ed25519 (pith-v1-2026-05) · public key
Schema pith-number/v1.0

Canonical hash

b40bf4f5579c3b10996b2224faebd3de63c3456db3abe12a6d4124331be90dfa

Aliases

arxiv: 1512.07724 · arxiv_version: 1512.07724v1 · doi: 10.48550/arxiv.1512.07724 · pith_short_12: WQF7J5KXTQ5R · pith_short_16: WQF7J5KXTQ5RBGLL · pith_short_8: WQF7J5KX
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/WQF7J5KXTQ5RBGLLEISPV26T3Z \
  | 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: b40bf4f5579c3b10996b2224faebd3de63c3456db3abe12a6d4124331be90dfa
Canonical record JSON 
{
  "metadata": {
    "abstract_canon_sha256": "b3269e2d7c528777d2b32c5947333db04605700a8233d15033a5b0030c700abc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-12-24T06:13:05Z",
    "title_canon_sha256": "3445549a1961eccd4e6bb0098e93e58ace65b645b34d25e89b848814868daeea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.07724",
    "kind": "arxiv",
    "version": 1
  }
}