Pith Number

pith:G2DBWJHO

pith:2015:G2DBWJHOXA2T5WT65LRRLPIBFX

not attested not anchored not stored refs pending

The ternary operations of groupoids

R. A. R. Monzo

arxiv:1510.07955 v1 · 2015-10-12 · math.GM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{G2DBWJHOXA2T5WT65LRRLPIBFX}

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	2026-05-18T01:28:44.961028Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

36861b24eeb8353eda7eeae315bd012ddb39a85462c8303ff4a5ea32c22764e5

Aliases

arxiv: 1510.07955 · arxiv_version: 1510.07955v1 · doi: 10.48550/arxiv.1510.07955 · pith_short_12: G2DBWJHOXA2T · pith_short_16: G2DBWJHOXA2T5WT6 · pith_short_8: G2DBWJHO

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/G2DBWJHOXA2T5WT65LRRLPIBFX \
  | 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: 36861b24eeb8353eda7eeae315bd012ddb39a85462c8303ff4a5ea32c22764e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0cad88ec952a0bfc867c250ebb5d449a7945fe6fde866ea783c932ed0360c495",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GM",
    "submitted_at": "2015-10-12T15:22:45Z",
    "title_canon_sha256": "0c070e5978cd67692c6e77d7f9e2106fd4aa1cfadeb3e7c80093bae085677850"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.07955",
    "kind": "arxiv",
    "version": 1
  }
}