Pith Number

pith:N4NBGP2P

pith:2013:N4NBGP2PRZFPMEASJ4NSA3U7PB

not attested not anchored not stored refs pending

Variations of the Morse-Hedlund Theorem for $k$-Abelian Equivalence

Aleksi Saarela, Juhani Karhum\"aki, Luca. Q. Zamboni

arxiv:1302.3783 v1 · 2013-02-15 · 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{N4NBGP2PRZFPMEASJ4NSA3U7PB}

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	2026-05-18T03:33:35.724781Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f1a133f4f8e4af610124f1b206e9f7840e7dcb3e2f32439c074044314187c81

Aliases

arxiv: 1302.3783 · arxiv_version: 1302.3783v1 · doi: 10.48550/arxiv.1302.3783 · pith_short_12: N4NBGP2PRZFP · pith_short_16: N4NBGP2PRZFPMEAS · pith_short_8: N4NBGP2P

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/N4NBGP2PRZFPMEASJ4NSA3U7PB \
  | 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: 6f1a133f4f8e4af610124f1b206e9f7840e7dcb3e2f32439c074044314187c81

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0efbb31c18a11e7a02540c21e32c346ada280e27a2036f8067cc91648ea6435c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-02-15T15:43:16Z",
    "title_canon_sha256": "2de58a6998a018c4fc07b26afe95894c8ea299a152d310d3a2125ff9ddacadd7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.3783",
    "kind": "arxiv",
    "version": 1
  }
}