Pith Number

pith:JPZIGS4Q

pith:2010:JPZIGS4QIKANXDIRFOVPVK2RPZ

not attested not anchored not stored refs pending

Matrix factorizations via Koszul duality

Junwu Tu

arxiv:1009.4151 v2 · 2010-09-21 · math.AG · math.KT · math.QA · 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{JPZIGS4QIKANXDIRFOVPVK2RPZ}

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	2026-05-17T23:53:36.878745Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4bf2834b904280db8d112baafaab517e78ea1b46d4b884df2fb2bc1a381c2fd1

Aliases

arxiv: 1009.4151 · arxiv_version: 1009.4151v2 · doi: 10.48550/arxiv.1009.4151 · pith_short_12: JPZIGS4QIKAN · pith_short_16: JPZIGS4QIKANXDIR · pith_short_8: JPZIGS4Q

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/JPZIGS4QIKANXDIRFOVPVK2RPZ \
  | 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: 4bf2834b904280db8d112baafaab517e78ea1b46d4b884df2fb2bc1a381c2fd1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f6ec87bf39366e67d2ebbc72c7fb97e5954a0f93732844c58f40658bfcf2c8b0",
    "cross_cats_sorted": [
      "math.KT",
      "math.QA",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-09-21T17:31:05Z",
    "title_canon_sha256": "c25a5f2cac980c5ac5ca70cf6576a9c5f47d9839daf402ed0f7e2f42fc825b19"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.4151",
    "kind": "arxiv",
    "version": 2
  }
}