Pith Number

pith:3A2Q4LLJ

pith:2024:3A2Q4LLJ3PKLSYMU4JOGO3ZNF4

not attested not anchored not stored refs pending

Ducci on $\mathbb{Z}_m^n$ and the Maximum Length for $n$ Odd

Mark L. Lewis, Shannon M. Tefft

arxiv:2403.05319 v2 · 2024-03-08 · math.NT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3A2Q4LLJ3PKLSYMU4JOGO3ZNF4}

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.

Cited by

1 paper in Pith

Values of Ducci Periods for Sequences on $\mathbb{Z}_m^n$

Receipt and verification

First computed	2026-07-05T09:00:36.409837Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d8350e2d69dbd4b96194e25c676f2d2f1ef6331026aa0e0e78fb9c0a705ea853

Aliases

arxiv: 2403.05319 · arxiv_version: 2403.05319v2 · doi: 10.48550/arxiv.2403.05319 · pith_short_12: 3A2Q4LLJ3PKL · pith_short_16: 3A2Q4LLJ3PKLSYMU · pith_short_8: 3A2Q4LLJ

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/3A2Q4LLJ3PKLSYMU4JOGO3ZNF4 \
  | 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: d8350e2d69dbd4b96194e25c676f2d2f1ef6331026aa0e0e78fb9c0a705ea853

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ed7df5e0038299694425313f8ac609eef1cee0337ff5c1c89723d14ed5a072c",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2024-03-08T13:49:42Z",
    "title_canon_sha256": "27bc5f9d7aca8a920b9c94822f547ddce31bede6556a437221a3e156603d10e3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2403.05319",
    "kind": "arxiv",
    "version": 2
  }
}