Pith Number

pith:NF3YBRUW

pith:2013:NF3YBRUWFBUH32N5JWFOQ6CRUU

not attested not anchored not stored refs pending

Reconstructing multisets over commutative groupoids and affine functions over nonassociative semirings

Erkko Lehtonen

arxiv:1302.7109 v2 · 2013-02-28 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NF3YBRUWFBUH32N5JWFOQ6CRUU}

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	2026-05-18T00:57:38.649240Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

697780c69628687de9bd4d8ae87851a5079fd299f99a3c305a163785bc678add

Aliases

arxiv: 1302.7109 · arxiv_version: 1302.7109v2 · doi: 10.48550/arxiv.1302.7109 · pith_short_12: NF3YBRUWFBUH · pith_short_16: NF3YBRUWFBUH32N5 · pith_short_8: NF3YBRUW

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/NF3YBRUWFBUH32N5JWFOQ6CRUU \
  | 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: 697780c69628687de9bd4d8ae87851a5079fd299f99a3c305a163785bc678add

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df8458b015cbbc6085154b79f28354341199edf5a0afbd1eb267e01e02389562",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-02-28T08:34:19Z",
    "title_canon_sha256": "e8779991be65da73bfcb45cfaffc29123cf24c4c4a02c42c1f7d9dc59ed747fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.7109",
    "kind": "arxiv",
    "version": 2
  }
}