Pith Number

pith:CJ7CPBP6

pith:2005:CJ7CPBP63BVEL3FEOEZVUAWBXX

not attested not anchored not stored refs pending

Precompact abelian groups and topological annihilators

G\'abor Luk\'acs

arxiv:math/0502223 v2 · 2005-02-10 · math.GN · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CJ7CPBP63BVEL3FEOEZVUAWBXX}

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	2026-05-18T04:12:19.412741Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

127e2785fed86a45eca471335a02c1bdfc21b2b441daa5916812df39e7858240

Aliases

arxiv: math/0502223 · arxiv_version: math/0502223v2 · doi: 10.48550/arxiv.math/0502223 · pith_short_12: CJ7CPBP63BVE · pith_short_16: CJ7CPBP63BVEL3FE · pith_short_8: CJ7CPBP6

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/CJ7CPBP63BVEL3FEOEZVUAWBXX \
  | 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: 127e2785fed86a45eca471335a02c1bdfc21b2b441daa5916812df39e7858240

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49fb95afbdccb90cbcf031c570cd01ab5cc0c6644f5c26dd6000515dd71a0ef6",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.GN",
    "submitted_at": "2005-02-10T23:37:16Z",
    "title_canon_sha256": "322ba5bc42c2b19b4a26e73c35b1302683505e9db67aaac04da10f6df62b3ceb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0502223",
    "kind": "arxiv",
    "version": 2
  }
}