Pith Number

pith:UM3ARBAB

pith:2010:UM3ARBABN2BEXG5WVYLH4HDSHA

not attested not anchored not stored refs pending

Axioms for unary semigroups via division operations

Joao Araujo, Michael Kinyon

arxiv:1004.0007 v1 · 2010-03-31 · 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{UM3ARBABN2BEXG5WVYLH4HDSHA}

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	2026-05-18T03:44:34.144529Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3360884016e824b9bb6ae167e1c72380c9f17bc8a069e2e5ffcb1153233c5de

Aliases

arxiv: 1004.0007 · arxiv_version: 1004.0007v1 · doi: 10.48550/arxiv.1004.0007 · pith_short_12: UM3ARBABN2BE · pith_short_16: UM3ARBABN2BEXG5W · pith_short_8: UM3ARBAB

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/UM3ARBABN2BEXG5WVYLH4HDSHA \
  | 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: a3360884016e824b9bb6ae167e1c72380c9f17bc8a069e2e5ffcb1153233c5de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd6fb1feb4eb11154d1b68bbe9e34169ed20ff35ef1a7007394ccf4eba2033ee",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-03-31T20:12:29Z",
    "title_canon_sha256": "4f59108e72db57760e3c649d7a009d157646df329726b5bae0193af9aa67d636"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.0007",
    "kind": "arxiv",
    "version": 1
  }
}