Pith Number

pith:KPT7WP6D

pith:2011:KPT7WP6D2ANCBBQVZFKUVPQFQJ

not attested not anchored not stored refs pending

Rationality of the Hilbert series of Hopf-invariants of free algebras

Lucia S. I. Murakami, Vitor O. Ferreira

arxiv:1105.5364 v1 · 2011-05-26 · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KPT7WP6D2ANCBBQVZFKUVPQFQJ}

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	2026-05-18T04:21:12.711559Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53e7fb3fc3d01a208615c9554abe0582689c1610f7d0bb959e5e8cbb39d0c7db

Aliases

arxiv: 1105.5364 · arxiv_version: 1105.5364v1 · doi: 10.48550/arxiv.1105.5364 · pith_short_12: KPT7WP6D2ANC · pith_short_16: KPT7WP6D2ANCBBQV · pith_short_8: KPT7WP6D

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/KPT7WP6D2ANCBBQVZFKUVPQFQJ \
  | 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: 53e7fb3fc3d01a208615c9554abe0582689c1610f7d0bb959e5e8cbb39d0c7db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af7d8268a8a4b6a8a5cf5b60b0f8e8a20e1edd0531905d7c8aa63aea50b50313",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2011-05-26T18:02:27Z",
    "title_canon_sha256": "5bc8746c9a4b0b3dabc56be2fbdaa8b54822c70b2d47f2882d3fa44dfb4406f5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.5364",
    "kind": "arxiv",
    "version": 1
  }
}