Pith Number

pith:PKMQ2BYJ

pith:2012:PKMQ2BYJVDU5DTUZQFNQ2GD7DA

not attested not anchored not stored refs pending

Compatibility JSJ decomposition of graphs of free abelian groups

Benjamin Beeker

arxiv:1212.3125 v2 · 2012-12-13 · 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{PKMQ2BYJVDU5DTUZQFNQ2GD7DA}

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	2026-05-18T03:38:32.507041Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a990d0709a8e9d1ce99815b0d187f181c16a833c9fbbe49f61608177245fcd5

Aliases

arxiv: 1212.3125 · arxiv_version: 1212.3125v2 · doi: 10.48550/arxiv.1212.3125 · pith_short_12: PKMQ2BYJVDU5 · pith_short_16: PKMQ2BYJVDU5DTUZ · pith_short_8: PKMQ2BYJ

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/PKMQ2BYJVDU5DTUZQFNQ2GD7DA \
  | 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: 7a990d0709a8e9d1ce99815b0d187f181c16a833c9fbbe49f61608177245fcd5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f3ab11502fc33343abd36c0731391c65080af094d9be934eddf9dd540b02fa4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-12-13T11:00:23Z",
    "title_canon_sha256": "e3c9c5615e1c8a97679238cf1e171c6bcd4dd3f26b451d659b07d7b66fc5aedd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.3125",
    "kind": "arxiv",
    "version": 2
  }
}