Pith Number

pith:MCA6PYI5

pith:2013:MCA6PYI54TNDDS2DX5HCIQHIDT

not attested not anchored not stored refs pending

Which finitely generated Abelian groups admit equal growth functions?

Clara Loeh, Matthias Mann

arxiv:1309.3381 v1 · 2013-09-13 · 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{MCA6PYI54TNDDS2DX5HCIQHIDT}

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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	2026-05-18T03:13:22.769418Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6081e7e11de4da31cb43bf4e2440e81cf2ff17c846a451e0c6d3dc513abf69b2

Aliases

arxiv: 1309.3381 · arxiv_version: 1309.3381v1 · doi: 10.48550/arxiv.1309.3381 · pith_short_12: MCA6PYI54TND · pith_short_16: MCA6PYI54TNDDS2D · pith_short_8: MCA6PYI5

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/MCA6PYI54TNDDS2DX5HCIQHIDT \
  | 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: 6081e7e11de4da31cb43bf4e2440e81cf2ff17c846a451e0c6d3dc513abf69b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e636f37d925c8f91190daf8e6b4fbadffb4425d2837093b7ecd1e05547179bab",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-09-13T07:06:44Z",
    "title_canon_sha256": "b0141861a8d4f50dbc5dbddc646f535fe728bce310fea870345e44f9e299b019"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.3381",
    "kind": "arxiv",
    "version": 1
  }
}