Pith Number

pith:7CKW3BFC

pith:2012:7CKW3BFCLNX5PH4NGEWNLCATVU

not attested not anchored not stored refs pending

Notions of M\"obius inversion

Tom Leinster

arxiv:1201.0413 v4 · 2012-01-02 · math.CT · 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{7CKW3BFCLNX5PH4NGEWNLCATVU}

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	2026-05-18T03:31:30.897677Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f8956d84a25b6fd79f8d312cd58813ad255e70fd0317f4ffdebfbf14acc9fa94

Aliases

arxiv: 1201.0413 · arxiv_version: 1201.0413v4 · doi: 10.48550/arxiv.1201.0413 · pith_short_12: 7CKW3BFCLNX5 · pith_short_16: 7CKW3BFCLNX5PH4N · pith_short_8: 7CKW3BFC

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/7CKW3BFCLNX5PH4NGEWNLCATVU \
  | 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: f8956d84a25b6fd79f8d312cd58813ad255e70fd0317f4ffdebfbf14acc9fa94

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f29163ff59b9f8f7b865e880f51d0e87e0fa9f4f5879f89a9d8fa42e7b9740c4",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2012-01-02T01:49:45Z",
    "title_canon_sha256": "5dc90e2e7da6a3f598abfcce2354a473d8cebe2301695f6628b938531b879a17"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.0413",
    "kind": "arxiv",
    "version": 4
  }
}