Pith Number

pith:BRF3KV4W

pith:2010:BRF3KV4W43USPMDEY3FHYZABS6

not attested not anchored not stored refs pending

Projective modules over Frobenius algebras and Hopf comodule algebras

Loretta FitzGerald Tokoly, Martin Lorenz

arxiv:1008.4056 v1 · 2010-08-24 · 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{BRF3KV4W43USPMDEY3FHYZABS6}

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	2026-05-18T04:41:54.245026Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c4bb55796e6e927b064c6ca7c640197bb8248d724807f84bcd0750abd54d014

Aliases

arxiv: 1008.4056 · arxiv_version: 1008.4056v1 · doi: 10.48550/arxiv.1008.4056 · pith_short_12: BRF3KV4W43US · pith_short_16: BRF3KV4W43USPMDE · pith_short_8: BRF3KV4W

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/BRF3KV4W43USPMDEY3FHYZABS6 \
  | 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: 0c4bb55796e6e927b064c6ca7c640197bb8248d724807f84bcd0750abd54d014

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa27fff53f2037866804b1c8fc28eda7a21be77bbb6f41ad0f98a808fe74a99f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2010-08-24T14:38:50Z",
    "title_canon_sha256": "b68b146668d7a7102fe4d34fae322f3fc62c4f2ee4770f3f133d0962f3b9e3bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.4056",
    "kind": "arxiv",
    "version": 1
  }
}