Pith Number

pith:ECM7CWLQ

pith:2017:ECM7CWLQS4NO357NXBEHOYOCBL

not attested not anchored not stored refs pending

Dual pairs of algebras and finite commutative group schemes

Peter Bruin

arxiv:1709.09847 v1 · 2017-09-28 · math.NT · math.AC · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ECM7CWLQS4NO357NXBEHOYOCBL}

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	2026-05-18T00:34:06.524028Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2099f15970971aedf7edb8487761c20ae3e8631d29191a655a25a3f3529edb03

Aliases

arxiv: 1709.09847 · arxiv_version: 1709.09847v1 · doi: 10.48550/arxiv.1709.09847 · pith_short_12: ECM7CWLQS4NO · pith_short_16: ECM7CWLQS4NO357N · pith_short_8: ECM7CWLQ

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/ECM7CWLQS4NO357NXBEHOYOCBL \
  | 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: 2099f15970971aedf7edb8487761c20ae3e8631d29191a655a25a3f3529edb03

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "626548f041c8f5e5596c90f68580717c0c4a10da2d51f7a7ca76efc436409a89",
    "cross_cats_sorted": [
      "math.AC",
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-09-28T08:40:52Z",
    "title_canon_sha256": "2d7d9f63c075e25adce3b64d257463382f3d7368b334e97369529bd11ffcc096"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.09847",
    "kind": "arxiv",
    "version": 1
  }
}