Pith Number

pith:WGQCKH7S

pith:2012:WGQCKH7SQ6VKIOENZRCN333N3A

not attested not anchored not stored refs pending

Inverse-Closed Subalgebras of Noncommutative Tori

Karlheinz Gr\"ochenig, Michael Leinert

arxiv:1208.6229 v2 · 2012-08-30 · 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{WGQCKH7SQ6VKIOENZRCN333N3A}

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	2026-05-18T00:42:08.121936Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1a0251ff287aaa4388dcc44ddef6dd8048119f3a03c6c5e6f853c7aa6042f98

Aliases

arxiv: 1208.6229 · arxiv_version: 1208.6229v2 · doi: 10.48550/arxiv.1208.6229 · pith_short_12: WGQCKH7SQ6VK · pith_short_16: WGQCKH7SQ6VKIOEN · pith_short_8: WGQCKH7S

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/WGQCKH7SQ6VKIOENZRCN333N3A \
  | 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: b1a0251ff287aaa4388dcc44ddef6dd8048119f3a03c6c5e6f853c7aa6042f98

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b26a8692c12fa4c5ab6d9ac5f724a5c66878b936dd4c3279276687102a765eae",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2012-08-30T16:33:51Z",
    "title_canon_sha256": "adbbecef9b07ecde32f5b9235f9775c54b352333640915c11e533ffe2a85652d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.6229",
    "kind": "arxiv",
    "version": 2
  }
}