Pith Number

pith:XWQBD7JF

pith:2001:XWQBD7JFUQLZTB7BDXWASF3B7L

not attested not anchored not stored refs pending

Koszul Duality for modules over Lie algebra

Andrzej Weber, Tomasz Maszczyk

arxiv:math/0101180 v2 · 2001-01-22 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XWQBD7JFUQLZTB7BDXWASF3B7L}

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	2026-07-04T14:35:02.296298Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bda011fd25a4179987e11dec091761faf5d166fd57615a1ef7a2a47631e4e5f7

Aliases

arxiv: math/0101180 · arxiv_version: math/0101180v2 · doi: 10.48550/arxiv.math/0101180 · pith_short_12: XWQBD7JFUQLZ · pith_short_16: XWQBD7JFUQLZTB7B · pith_short_8: XWQBD7JF

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/XWQBD7JFUQLZTB7BDXWASF3B7L \
  | 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: bda011fd25a4179987e11dec091761faf5d166fd57615a1ef7a2a47631e4e5f7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e028f9a2c8d866fc81f16b0cfef934a1b8d7faf955bf0d88e8861c435fc955a",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2001-01-22T17:53:32Z",
    "title_canon_sha256": "789471e36304568cdfe308cc2e931fe6ef26eae189f443e33c3f409f5f410e1d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0101180",
    "kind": "arxiv",
    "version": 2
  }
}