Pith Number

pith:77VKJWY4

pith:2011:77VKJWY4XMPJDKR76LOO2TUHUZ

not attested not anchored not stored refs pending

Morita equivalence of measured quantum groupoids: Application to deformation of measured quantum groupoids by 2-cocycles

Michel Enock

arxiv:1106.1018 v3 · 2011-06-06 · 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{77VKJWY4XMPJDKR76LOO2TUHUZ}

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	2026-05-18T03:45:23.310677Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ffeaa4db1cbb1e91aa3ff2dced4e87a672c04b4ddd73d090aacda078cc63bb1c

Aliases

arxiv: 1106.1018 · arxiv_version: 1106.1018v3 · doi: 10.48550/arxiv.1106.1018 · pith_short_12: 77VKJWY4XMPJ · pith_short_16: 77VKJWY4XMPJDKR7 · pith_short_8: 77VKJWY4

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/77VKJWY4XMPJDKR76LOO2TUHUZ \
  | 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: ffeaa4db1cbb1e91aa3ff2dced4e87a672c04b4ddd73d090aacda078cc63bb1c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ae33a8e5a1916dbfb26d00dab24c2721cdc3d5750efbee0e2c090e63a8ed400f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2011-06-06T11:10:53Z",
    "title_canon_sha256": "1c6f60d63d60fadd8ce44469187e7ea98e383c3028d4a744f4a5b143609fc990"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.1018",
    "kind": "arxiv",
    "version": 3
  }
}