Pith Number

pith:UYZEZ5CY

pith:2014:UYZEZ5CYVN6ZK3V7XACDTK5FXV

not attested not anchored not stored refs pending

Quantum Heisenberg Manifolds as Twisted Groupoid $C^*$-Algebras

Alex Kumjian, Judith Packer, Sooran Kang

arxiv:1403.5313 v1 · 2014-03-20 · 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{UYZEZ5CYVN6ZK3V7XACDTK5FXV}

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	2026-05-18T02:55:56.706043Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a6324cf458ab7d956ebfb80439aba5bd7b70ac1ca7c3122994fbfa3482586cf1

Aliases

arxiv: 1403.5313 · arxiv_version: 1403.5313v1 · doi: 10.48550/arxiv.1403.5313 · pith_short_12: UYZEZ5CYVN6Z · pith_short_16: UYZEZ5CYVN6ZK3V7 · pith_short_8: UYZEZ5CY

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/UYZEZ5CYVN6ZK3V7XACDTK5FXV \
  | 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: a6324cf458ab7d956ebfb80439aba5bd7b70ac1ca7c3122994fbfa3482586cf1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db7d5ebbaa38beb8c5306b86f6b0725fe8869749d7ba0a4558a98d1087a5645a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2014-03-20T22:08:15Z",
    "title_canon_sha256": "b0571663e2ebb1dc25ed6babed32221a4e535753c82feb3836249c2835eb74d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1403.5313",
    "kind": "arxiv",
    "version": 1
  }
}