Pith Number

pith:CRWYOUPR

pith:2004:CRWYOUPR2XDUKZCWR6VIEY55I7

not attested not anchored not stored refs pending

Associativity in multary quasigroups: The way of biased expansions

Thomas Zaslavsky

arxiv:math/0411268 v2 · 2004-11-11 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CRWYOUPR2XDUKZCWR6VIEY55I7}

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	2026-05-18T01:02:05.577125Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

146d8751f1d5c74564568faa8263bd47d0206c58bc60f4f2c2e7c56141ac3f03

Aliases

arxiv: math/0411268 · arxiv_version: math/0411268v2 · doi: 10.48550/arxiv.math/0411268 · pith_short_12: CRWYOUPR2XDU · pith_short_16: CRWYOUPR2XDUKZCW · pith_short_8: CRWYOUPR

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/CRWYOUPR2XDUKZCWR6VIEY55I7 \
  | 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: 146d8751f1d5c74564568faa8263bd47d0206c58bc60f4f2c2e7c56141ac3f03

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a07dc9b82506cb0a9afd76f3eaf0f653dd1d7400d73fe18faf200888163dac8",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2004-11-11T20:39:05Z",
    "title_canon_sha256": "f9a2b8eb4d6550e9e9fd09828df07637a5c2536435fda8bf89eea23ed7b4a261"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0411268",
    "kind": "arxiv",
    "version": 2
  }
}