Pith Number

pith:U6FVC5FI

pith:2013:U6FVC5FICTATR6E7VERDNA7Y7N

not attested not anchored not stored refs pending

Congruences of the fork extensions. II. The congruence gamma

George Gr\"atzer

arxiv:1307.6126 v4 · 2013-07-23 · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U6FVC5FICTATR6E7VERDNA7Y7N}

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	2026-05-18T03:13:57.779571Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a78b5174a814c138f89fa9223683f8fb43f49a3372c128390db52a28bf0e55df

Aliases

arxiv: 1307.6126 · arxiv_version: 1307.6126v4 · doi: 10.48550/arxiv.1307.6126 · pith_short_12: U6FVC5FICTAT · pith_short_16: U6FVC5FICTATR6E7 · pith_short_8: U6FVC5FI

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/U6FVC5FICTATR6E7VERDNA7Y7N \
  | 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: a78b5174a814c138f89fa9223683f8fb43f49a3372c128390db52a28bf0e55df

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c41fecb2922b01de2d0dc04b6bae011f4572543ffb82305095bec736f32374b7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2013-07-23T15:39:19Z",
    "title_canon_sha256": "c80980dcc8f30f0be5aec350d988af961a5e033acaf1ecbf31e36452600b0d09"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.6126",
    "kind": "arxiv",
    "version": 4
  }
}