Pith Number

pith:4X43E2RZ

pith:2012:4X43E2RZSIE6RJSFIXPUVVR7MB

not attested not anchored not stored refs pending

The Hall module of an exact category with duality

Matthew B. Young

arxiv:1212.0531 v2 · 2012-12-03 · math.RT · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4X43E2RZSIE6RJSFIXPUVVR7MB}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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.

Cited by

1 paper in Pith

Modules and generalizations of Joyce vertex algebras

Receipt and verification

First computed	2026-05-18T02:47:53.162079Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5f9b26a399209e8a64545df4ad63f606539fb87d28f2d06893304a63aa60c20

Aliases

arxiv: 1212.0531 · arxiv_version: 1212.0531v2 · doi: 10.48550/arxiv.1212.0531 · pith_short_12: 4X43E2RZSIE6 · pith_short_16: 4X43E2RZSIE6RJSF · pith_short_8: 4X43E2RZ

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/4X43E2RZSIE6RJSFIXPUVVR7MB \
  | 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: e5f9b26a399209e8a64545df4ad63f606539fb87d28f2d06893304a63aa60c20

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d9844a884bc6c9174bee10a33b2c929dadbde8e1537bc7b87f24c36aa0ed2ac",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2012-12-03T20:38:00Z",
    "title_canon_sha256": "d93fd9277384df25ac659e95f2655c8893290eb5bf9cd6c8705c454160bcd0de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.0531",
    "kind": "arxiv",
    "version": 2
  }
}