Pith Number

pith:K4ZNVHSI

pith:2015:K4ZNVHSIDAKONHBTPNWMAUG7L3

not attested not anchored not stored refs pending

Three versions of categorical crossed-product duality

John Quigg, S. Kaliszewski, Tron Omland

arxiv:1503.00663 v4 · 2015-03-02 · 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{K4ZNVHSIDAKONHBTPNWMAUG7L3}

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	2026-05-18T01:19:06.186063Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5732da9e481814e69c337b6cc050df5ee026d097d886ec541f7c38977cab1bce

Aliases

arxiv: 1503.00663 · arxiv_version: 1503.00663v4 · doi: 10.48550/arxiv.1503.00663 · pith_short_12: K4ZNVHSIDAKO · pith_short_16: K4ZNVHSIDAKONHBT · pith_short_8: K4ZNVHSI

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/K4ZNVHSIDAKONHBTPNWMAUG7L3 \
  | 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: 5732da9e481814e69c337b6cc050df5ee026d097d886ec541f7c38977cab1bce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0719bee9c368813e063dd52153d9a4db2342195249177e9a5cec1d9837a151e0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-03-02T18:58:41Z",
    "title_canon_sha256": "fc0e4fafd1f70313440ab2c64cb8986d2433ece123c9aea8f4baad9cdaa8a9b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.00663",
    "kind": "arxiv",
    "version": 4
  }
}