Pith Number

pith:U7YYJTKO

pith:2012:U7YYJTKO3OWPUERIG4ETG2YCEB

not attested not anchored not stored refs pending

Hopf monoids from class functions on unitriangular matrices

Marcelo Aguiar, Nantel Bergeron, Nathaniel Thiem

arxiv:1203.1572 v2 · 2012-03-07 · math.CO · math.GR · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U7YYJTKO3OWPUERIG4ETG2YCEB}

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	2026-05-18T03:10:26.949542Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7f184cd4edbacfa12283709336b022056367511412064b56755047f63e41cf2

Aliases

arxiv: 1203.1572 · arxiv_version: 1203.1572v2 · doi: 10.48550/arxiv.1203.1572 · pith_short_12: U7YYJTKO3OWP · pith_short_16: U7YYJTKO3OWPUERI · pith_short_8: U7YYJTKO

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/U7YYJTKO3OWPUERIG4ETG2YCEB \
  | 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: a7f184cd4edbacfa12283709336b022056367511412064b56755047f63e41cf2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "305a45d762d6ba40886f777901d9dad6a912e22d473b999dc18a7edf03bea7e8",
    "cross_cats_sorted": [
      "math.GR",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-03-07T19:19:30Z",
    "title_canon_sha256": "9ac63d45c45f48f59e5e47df9eeed6021d4df3804630542d63531a18677b773c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.1572",
    "kind": "arxiv",
    "version": 2
  }
}