Pith Number

pith:POPD4VKX

pith:2019:POPD4VKXNEVTNJ5FQ26QYPRJIW

not attested not anchored not stored refs pending

Koszul duality and the Hochschild cohomology of Artin-Schelter regular algebras

Leilei Liu

arxiv:1903.00647 v1 · 2019-03-02 · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{POPD4VKXNEVTNJ5FQ26QYPRJIW}

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	2026-05-17T23:52:13.874393Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b9e3e5557692b36a7a586bd0c3e2945aa83cbb1c06fae2e564858d40423e8ff

Aliases

arxiv: 1903.00647 · arxiv_version: 1903.00647v1 · doi: 10.48550/arxiv.1903.00647 · pith_short_12: POPD4VKXNEVT · pith_short_16: POPD4VKXNEVTNJ5F · pith_short_8: POPD4VKX

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/POPD4VKXNEVTNJ5FQ26QYPRJIW \
  | 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: 7b9e3e5557692b36a7a586bd0c3e2945aa83cbb1c06fae2e564858d40423e8ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e51337bab449317d3c9f51da50b371d215ec2a6b757473c72f45cb9830d5fbd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2019-03-02T07:42:46Z",
    "title_canon_sha256": "a2cbdec3b3e3294475c2d166330b4b16c32adca69b8e8a088631ed3b99e14d5d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.00647",
    "kind": "arxiv",
    "version": 1
  }
}