Pith Number

pith:WXQAPRER

pith:2011:WXQAPRER2ZTI242WLFSUW7QVSD

not attested not anchored not stored refs pending

A generalized Koszul theory and its application

Liping Li

arxiv:1109.5760 v3 · 2011-09-27 · math.RT · 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{WXQAPRER2ZTI242WLFSUW7QVSD}

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	2026-05-18T03:07:55.087538Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5e007c491d6668d735659654b7e1590c6d61abf1995ae561fba404722e107e7

Aliases

arxiv: 1109.5760 · arxiv_version: 1109.5760v3 · doi: 10.48550/arxiv.1109.5760 · pith_short_12: WXQAPRER2ZTI · pith_short_16: WXQAPRER2ZTI242W · pith_short_8: WXQAPRER

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/WXQAPRER2ZTI242WLFSUW7QVSD \
  | 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: b5e007c491d6668d735659654b7e1590c6d61abf1995ae561fba404722e107e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5844c50f99b8d0ab88994cd8595af733b9726696358de37b63707182f8f0ef99",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2011-09-27T01:04:45Z",
    "title_canon_sha256": "de7f55d74ccbf530c82b01205318986dc12dfad4f19bd5d94f743b38e952c353"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.5760",
    "kind": "arxiv",
    "version": 3
  }
}