Pith Number

pith:BCZIEROE

pith:2026:BCZIEROEQF2IWZ66LKTZHWZGCF

not attested not anchored not stored refs pending

Clifford semigroups and the monoidal Grothendieck construction

Elena Caviglia, Graham Manuell, Luca Mesiti, Peter F. Faul

arxiv:2607.12944 v1 · 2026-07-14 · math.CT · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BCZIEROEQF2IWZ66LKTZHWZGCF}

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	2026-07-15T01:22:26.613297Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

08b28245c481748b67de5aa793db26115c087e2ac5a69047b5c3f64f42d2f2c9

Aliases

arxiv: 2607.12944 · arxiv_version: 2607.12944v1 · doi: 10.48550/arxiv.2607.12944 · pith_short_12: BCZIEROEQF2I · pith_short_16: BCZIEROEQF2IWZ66 · pith_short_8: BCZIEROE

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/BCZIEROEQF2IWZ66LKTZHWZGCF \
  | 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: 08b28245c481748b67de5aa793db26115c087e2ac5a69047b5c3f64f42d2f2c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5581fcc561ba1f4ddeb01d3fb508b4184a73bfde5036ac00c6ecd5d128cbb4b",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2026-07-14T16:24:14Z",
    "title_canon_sha256": "6f1d0165c649212fd68fb3024ad4031bd22cc89f96d9ec548b0830b55823131b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.12944",
    "kind": "arxiv",
    "version": 1
  }
}