Pith Number

pith:C32MUX54

pith:2011:C32MUX54CLX6FLKCSZZ4LVOY6H

not attested not anchored not stored refs pending

The M\"obius function of generalized subword order

Bruce E. Sagan, Peter R. W. McNamara

arxiv:1107.5070 v2 · 2011-07-25 · math.CO · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{C32MUX54CLX6FLKCSZZ4LVOY6H}

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	2026-05-18T04:02:34.937911Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

16f4ca5fbc12efe2ad429673c5d5d8f1c9ef4bdc9c848606dd8ce6d9c383bc60

Aliases

arxiv: 1107.5070 · arxiv_version: 1107.5070v2 · doi: 10.48550/arxiv.1107.5070 · pith_short_12: C32MUX54CLX6 · pith_short_16: C32MUX54CLX6FLKC · pith_short_8: C32MUX54

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/C32MUX54CLX6FLKCSZZ4LVOY6H \
  | 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: 16f4ca5fbc12efe2ad429673c5d5d8f1c9ef4bdc9c848606dd8ce6d9c383bc60

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fc34ee2df1fad08db13737dbdb0a4f5c9d7ecf032254fa47b0b962dd05bcc12d",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-07-25T20:31:55Z",
    "title_canon_sha256": "e35b93ec7c9f3fa09afe312692a2eb9e970ecea4468c7bd1dd5c83ed3d413255"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.5070",
    "kind": "arxiv",
    "version": 2
  }
}