Pith Number

pith:NW7PUNIB

pith:2005:NW7PUNIBAWWOUWOKBP6P4QRUM5

not attested not anchored not stored refs pending

Coherence of Associativity in Categories with Multiplication

Matthew G. Brin

arxiv:math/0501086 v1 · 2005-01-06 · math.CT · 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{NW7PUNIBAWWOUWOKBP6P4QRUM5}

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	2026-05-18T03:14:17.990996Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6dbefa350105acea59ca0bfcfe423467745815bbd9012f51d7ebb9a1a3f419dd

Aliases

arxiv: math/0501086 · arxiv_version: math/0501086v1 · doi: 10.48550/arxiv.math/0501086 · pith_short_12: NW7PUNIBAWWO · pith_short_16: NW7PUNIBAWWOUWOK · pith_short_8: NW7PUNIB

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/NW7PUNIBAWWOUWOKBP6P4QRUM5 \
  | 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: 6dbefa350105acea59ca0bfcfe423467745815bbd9012f51d7ebb9a1a3f419dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f46c1ff420355e0ee8bfa15ac17dee85fb35ebeb894d1c104e3735145f327d9",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.CT",
    "submitted_at": "2005-01-06T16:47:39Z",
    "title_canon_sha256": "84bfdb23a14c4046743fecda1cc16a2220bb5ab14bccdf622298b568655e8698"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0501086",
    "kind": "arxiv",
    "version": 1
  }
}