Pith Number

pith:ERHHSWP5

pith:2010:ERHHSWP5EFSEL5HL67ESBC2YB6

not attested not anchored not stored refs pending

Products of all elements in a loop and a framework for non-associative analogues of the Hall-Paige conjecture

Kyle Pula

arxiv:1008.0699 v1 · 2010-08-04 · math.CO · 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{ERHHSWP5EFSEL5HL67ESBC2YB6}

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	2026-05-18T04:42:35.847527Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

244e7959fd216445f4ebf7c9208b580fa2018eef293b93eb0f5bef58551124bb

Aliases

arxiv: 1008.0699 · arxiv_version: 1008.0699v1 · doi: 10.48550/arxiv.1008.0699 · pith_short_12: ERHHSWP5EFSE · pith_short_16: ERHHSWP5EFSEL5HL · pith_short_8: ERHHSWP5

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/ERHHSWP5EFSEL5HL67ESBC2YB6 \
  | 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: 244e7959fd216445f4ebf7c9208b580fa2018eef293b93eb0f5bef58551124bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c49695d0b668f48a03ab22953a9090a0882b7b00bac2a1573aa4b6767b8faebd",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-08-04T05:17:26Z",
    "title_canon_sha256": "a1418f9425d1c490747073a0b4721b8d2c58abcd7968fe821503e3616a035799"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.0699",
    "kind": "arxiv",
    "version": 1
  }
}