Pith Number

pith:4QMPWZQM

pith:2026:4QMPWZQMDCUWGSYYU3I3N42NEJ

not attested not anchored not stored refs pending

A Noetherian Hopf algebra is affine iff its Hopf coradical is affine

Huan Jia, Yinhuo Zhang

arxiv:2606.01646 v1 · 2026-06-01 · math.RA · 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{4QMPWZQMDCUWGSYYU3I3N42NEJ}

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	2026-06-02T02:04:39.049176Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e418fb660c18a9634b18a6d1b6f34d226a61d78b3fcdf7290615bb68fbcad157

Aliases

arxiv: 2606.01646 · arxiv_version: 2606.01646v1 · doi: 10.48550/arxiv.2606.01646 · pith_short_12: 4QMPWZQMDCUW · pith_short_16: 4QMPWZQMDCUWGSYY · pith_short_8: 4QMPWZQM

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/4QMPWZQMDCUWGSYYU3I3N42NEJ \
  | 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: e418fb660c18a9634b18a6d1b6f34d226a61d78b3fcdf7290615bb68fbcad157

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4113d7810d657124fb5baeb81953e2b05e8a4fb3a43404e3a343b197a9adefd",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2026-06-01T03:55:04Z",
    "title_canon_sha256": "d6e1ffc29e4e9451315d92db27f5df31389969915d9766b68f4b42d719e2c870"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.01646",
    "kind": "arxiv",
    "version": 1
  }
}