Pith Number

pith:WQP3PANB

pith:2012:WQP3PANBN3WAKJUM5MEXVD4OBA

not attested not anchored not stored refs pending

Idempotents, Localizations and Picard groups of A(1)-modules

Robert R. Bruner

arxiv:1211.0213 v2 · 2012-11-01 · math.AT · 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{WQP3PANBN3WAKJUM5MEXVD4OBA}

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	2026-05-18T02:48:17.930027Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b41fb781a16eec05268ceb097a8f8e081eb5344e60b3d7f681112af108e288b6

Aliases

arxiv: 1211.0213 · arxiv_version: 1211.0213v2 · doi: 10.48550/arxiv.1211.0213 · pith_short_12: WQP3PANBN3WA · pith_short_16: WQP3PANBN3WAKJUM · pith_short_8: WQP3PANB

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/WQP3PANBN3WAKJUM5MEXVD4OBA \
  | 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: b41fb781a16eec05268ceb097a8f8e081eb5344e60b3d7f681112af108e288b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ee945bb6a571997533c93aa363cd231078ec2ef3d4de78b52176771bf94ede2",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2012-11-01T16:12:56Z",
    "title_canon_sha256": "bd8559e157428c35366881cbaea20aa1a3a4298c3d5e9511e5d2c469f635c63d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.0213",
    "kind": "arxiv",
    "version": 2
  }
}