Pith Number

pith:K2CJZZ6V

pith:2017:K2CJZZ6VOIO7PSUVWPW3Q73JWW

not attested not anchored not stored refs pending

Measured quantum groupoids on a finite basis and equivariant Kasparov theory

Jonathan Crespo

arxiv:1706.08516 v1 · 2017-06-26 · math.OA · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K2CJZZ6VOIO7PSUVWPW3Q73JWW}

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	2026-05-18T00:41:31.770835Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

56849ce7d5721df7ca95b3edb87f69b59a820470cf1973697029039f1f4c2868

Aliases

arxiv: 1706.08516 · arxiv_version: 1706.08516v1 · doi: 10.48550/arxiv.1706.08516 · pith_short_12: K2CJZZ6VOIO7 · pith_short_16: K2CJZZ6VOIO7PSUV · pith_short_8: K2CJZZ6V

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/K2CJZZ6VOIO7PSUVWPW3Q73JWW \
  | 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: 56849ce7d5721df7ca95b3edb87f69b59a820470cf1973697029039f1f4c2868

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e6d38ebebda9b073827812832642f83837284ef502c270f0f100b96acfd1c9cd",
    "cross_cats_sorted": [
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2017-06-26T09:41:34Z",
    "title_canon_sha256": "ce295c77d165e7940f833b86060cc8b6162144a976c65a0c6e21a6a6aee1852f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.08516",
    "kind": "arxiv",
    "version": 1
  }
}