Pith Number

pith:5D4A4MGZ

pith:2016:5D4A4MGZ47MM5SIYMONAXVAC3P

not attested not anchored not stored refs pending

Quantum symmetry groups of noncommutative tori

Marcin Marciniak, Michal Banacki

arxiv:1606.06233 v3 · 2016-06-20 · math.OA · math-ph · math.MP · math.QA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5D4A4MGZ47MM5SIYMONAXVAC3P}

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	2026-05-18T00:13:38.161170Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e8f80e30d9e7d8cec918639a0bd402dbc82d80fc1c6f4410d270534d20deff12

Aliases

arxiv: 1606.06233 · arxiv_version: 1606.06233v3 · doi: 10.48550/arxiv.1606.06233 · pith_short_12: 5D4A4MGZ47MM · pith_short_16: 5D4A4MGZ47MM5SIY · pith_short_8: 5D4A4MGZ

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/5D4A4MGZ47MM5SIYMONAXVAC3P \
  | 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: e8f80e30d9e7d8cec918639a0bd402dbc82d80fc1c6f4410d270534d20deff12

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d2442a863d153e48e77ef0d44ec707b17ea0179ed9e28a2a00bc820eb0f0c8e",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2016-06-20T18:20:49Z",
    "title_canon_sha256": "19b4c5e8436a4b6960c0294a6b5abe3eaf768f8687cc7d8bfcb66c9cfb1351bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.06233",
    "kind": "arxiv",
    "version": 3
  }
}