Pith Number

pith:33BWKKLH

pith:2012:33BWKKLHJ6ECSVSLJA2ETSE24Y

not attested not anchored not stored refs pending

The structure of automorphic loops

J. D. Phillips, Ken Kunen, Michael Kinyon, Petr Vojtechovsky

arxiv:1210.1642 v1 · 2012-10-05 · 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{33BWKKLHJ6ECSVSLJA2ETSE24Y}

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	2026-05-18T03:43:53.756707Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dec36529674f8829564b483449c89ae620deecc9371cce1d2b9c9aa94cb5fe00

Aliases

arxiv: 1210.1642 · arxiv_version: 1210.1642v1 · doi: 10.48550/arxiv.1210.1642 · pith_short_12: 33BWKKLHJ6EC · pith_short_16: 33BWKKLHJ6ECSVSL · pith_short_8: 33BWKKLH

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/33BWKKLHJ6ECSVSLJA2ETSE24Y \
  | 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: dec36529674f8829564b483449c89ae620deecc9371cce1d2b9c9aa94cb5fe00

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b22adfeaffe9a88498169ae672ab87ef51f873b74cf5e14adc296ee8473de13",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-10-05T04:07:40Z",
    "title_canon_sha256": "615336ae8c0ea465e6816dc4fd3cc8ac42bc3cf2f06f369ae0291555a37e2246"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.1642",
    "kind": "arxiv",
    "version": 1
  }
}