Pith Number

pith:SMOWETUM

pith:2026:SMOWETUMZA2QPVGIGEHOHG234C

not attested not anchored not stored refs pending

Covering a square by congruent squares

Gy\"orgy D\'osa, Zsolt L\'angi, Zsolt Tuza

The largest square coverable by n unit squares has the same size for full covering and boundary covering when n is at most 4, but the sizes differ when n equals 5.

arxiv:2601.16535 v3 · 2026-01-23 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SMOWETUMZA2QPVGIGEHOHG234C}

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.

Claims

C1strongest claim

We show that these two problems are equivalent for n ≤ 4, but not for n=5. For both problems, we also present the solutions for n=5.

C2weakest assumption

That the optimal coverings for n=5 are attained by finite, explicitly describable arrangements of the five unit squares whose side lengths can be computed exactly from the geometry.

C3one line summary

For n=5 the maximum side length of a square coverable by 5 unit squares is found exactly and shown to differ between full-area and boundary-only versions.

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-06-01T01:02:30.131570Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

931d624e8cc83507d4c8310ee39b5be0bf41780177546827cf19554acf025eb7

Aliases

arxiv: 2601.16535 · arxiv_version: 2601.16535v3 · doi: 10.48550/arxiv.2601.16535 · pith_short_12: SMOWETUMZA2Q · pith_short_16: SMOWETUMZA2QPVGI · pith_short_8: SMOWETUM

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/SMOWETUMZA2QPVGIGEHOHG234C \
  | 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: 931d624e8cc83507d4c8310ee39b5be0bf41780177546827cf19554acf025eb7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a056980cfeda69eeaa3309b5b68d8e7eec767dc1511e1beb702cdb80460b3419",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2026-01-23T08:11:17Z",
    "title_canon_sha256": "388db6f832ef155f9e8ead88c91c88d9176b3dd153505a65155227b64e6f3369"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.16535",
    "kind": "arxiv",
    "version": 3
  }
}