Pith Number

pith:W7FAJSVK

pith:2009:W7FAJSVKQIIYBBXWPGHM2GX46H

not attested not anchored not stored refs pending

Uniquely presented finitely generated commutative monoids

Ignacio Ojeda, Pedro A. Garcia-Sanchez

arxiv:0907.4241 v2 · 2009-07-24 · math.AC · 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{W7FAJSVKQIIYBBXWPGHM2GX46H}

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	2026-05-18T04:39:19.649398Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7ca04caaa82118086f6798ecd1afcf1c9b3bd47d0039a8ac8cab821adc15d0b

Aliases

arxiv: 0907.4241 · arxiv_version: 0907.4241v2 · doi: 10.48550/arxiv.0907.4241 · pith_short_12: W7FAJSVKQIIY · pith_short_16: W7FAJSVKQIIYBBXW · pith_short_8: W7FAJSVK

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/W7FAJSVKQIIYBBXWPGHM2GX46H \
  | 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: b7ca04caaa82118086f6798ecd1afcf1c9b3bd47d0039a8ac8cab821adc15d0b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe2ef744c51380f02b0a1c5446d3e5c849d9ba1183d762005492b30abc9a9351",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2009-07-24T09:28:31Z",
    "title_canon_sha256": "8acecab1eabd9f897a105267bebca075010c268d7a6a61e9e285dcc73aca813a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.4241",
    "kind": "arxiv",
    "version": 2
  }
}