Pith Number

pith:GEOOUSLQ

pith:2012:GEOOUSLQJ7MTRBQDHVYYAPBLKL

not attested not anchored not stored refs pending

Reconstruction from Koszul homology and applications to module and derived categories

Ryo Takahashi

arxiv:1210.1982 v2 · 2012-10-06 · math.AC · 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{GEOOUSLQJ7MTRBQDHVYYAPBLKL}

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	2026-05-18T01:22:26.186725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

311cea49704fd93886033d71803c2b52c24faeedb544d10396dfb00262b908e1

Aliases

arxiv: 1210.1982 · arxiv_version: 1210.1982v2 · doi: 10.48550/arxiv.1210.1982 · pith_short_12: GEOOUSLQJ7MT · pith_short_16: GEOOUSLQJ7MTRBQD · pith_short_8: GEOOUSLQ

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/GEOOUSLQJ7MTRBQDHVYYAPBLKL \
  | 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: 311cea49704fd93886033d71803c2b52c24faeedb544d10396dfb00262b908e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87c3320dc194e4d594071f2e08099f2b5e2e26832482769760efad2b0d5e22e3",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2012-10-06T18:09:32Z",
    "title_canon_sha256": "be5922533f0f1ada1ff3c5439b187f7b93eac9443ec979998f8859134adc7382"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.1982",
    "kind": "arxiv",
    "version": 2
  }
}