Pith Number

pith:KHU7TT5V

pith:2011:KHU7TT5VOI3I2QUTACFSB6MUBL

not attested not anchored not stored refs pending

Generalized $d$-Koszul modules

Ning Bian, Pu Zhang, Yu Ye

arxiv:1109.1765 v1 · 2011-09-08 · math.RA · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KHU7TT5VOI3I2QUTACFSB6MUBL}

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	2026-05-18T04:13:48.093592Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

51e9f9cfb572368d4293008b20f9940ae3b7bb4a8c8604d5442ae719ee55bf89

Aliases

arxiv: 1109.1765 · arxiv_version: 1109.1765v1 · doi: 10.48550/arxiv.1109.1765 · pith_short_12: KHU7TT5VOI3I · pith_short_16: KHU7TT5VOI3I2QUT · pith_short_8: KHU7TT5V

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/KHU7TT5VOI3I2QUTACFSB6MUBL \
  | 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: 51e9f9cfb572368d4293008b20f9940ae3b7bb4a8c8604d5442ae719ee55bf89

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6a230f2609f77018ceabbecf4f7cd383709e5aeb216b38b32e05f87298017d1a",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2011-09-08T16:39:23Z",
    "title_canon_sha256": "0856d40d3ff40708f16539f825b7c554f4c03f8cd105fdfb5f5d2537cd45b7e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.1765",
    "kind": "arxiv",
    "version": 1
  }
}