Pith Number

pith:QLT5SFOW

pith:2009:QLT5SFOWTNXZNP42IGUM746U2Y

not attested not anchored not stored refs pending

M\"obius inversion formula for monoids with zero

Christophe Tollu (LIPN), G\'erard Duchamp (LIPN), Laurent Poinsot (LIPN)

arxiv:0911.4821 v2 · 2009-11-25 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QLT5SFOWTNXZNP42IGUM746U2Y}

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	2026-05-18T04:40:09.480724Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82e7d915d69b6f96bf9a41a8cff3d4d626e84f73202fcd9a4c339c50bb790cbb

Aliases

arxiv: 0911.4821 · arxiv_version: 0911.4821v2 · doi: 10.48550/arxiv.0911.4821 · pith_short_12: QLT5SFOWTNXZ · pith_short_16: QLT5SFOWTNXZNP42 · pith_short_8: QLT5SFOW

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/QLT5SFOWTNXZNP42IGUM746U2Y \
  | 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: 82e7d915d69b6f96bf9a41a8cff3d4d626e84f73202fcd9a4c339c50bb790cbb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2967b90d776d8831394f9c9b5f7a06c81a0d5e3ed143a2a3c095a0112531eec6",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-11-25T11:31:38Z",
    "title_canon_sha256": "ae52bfa9128a326c6fa3b4872aa1e2c5908e3e75510ea57d17aa3431be0dbd3a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.4821",
    "kind": "arxiv",
    "version": 2
  }
}