Pith Number

pith:S7H7WR6D

pith:2010:S7H7WR6DCUJNMCFXKDYXVDWXQF

not attested not anchored not stored refs pending

Abelian JSJ decomposition of graphs of free abelian groups

Benjamin Beeker

arxiv:1012.1311 v1 · 2010-12-06 · 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{S7H7WR6DCUJNMCFXKDYXVDWXQF}

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	2026-05-18T04:34:01.607939Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

97cffb47c31512d608b750f17a8ed7814b23c077a58fb3a760c75954aea678d2

Aliases

arxiv: 1012.1311 · arxiv_version: 1012.1311v1 · doi: 10.48550/arxiv.1012.1311 · pith_short_12: S7H7WR6DCUJN · pith_short_16: S7H7WR6DCUJNMCFX · pith_short_8: S7H7WR6D

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/S7H7WR6DCUJNMCFXKDYXVDWXQF \
  | 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: 97cffb47c31512d608b750f17a8ed7814b23c077a58fb3a760c75954aea678d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63451cd93ca69a412714303bebe59013173df13a9594ed5f03e14669ca25ddd3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-12-06T20:57:03Z",
    "title_canon_sha256": "9193326e9ae983e5eaae09b79bd548751ec3d5c89945db7ff7bcb94a4d3d6a3f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.1311",
    "kind": "arxiv",
    "version": 1
  }
}