Pith Number

pith:SI5UJD45

pith:2026:SI5UJD45NVDYR77QCIZ6GL6GF5

not attested not anchored not stored refs pending

Treewidth of the $n \times n$ toroidal grid

Hiraku Morimoto, Tatsuya Gima, Yota Otachi, Yuto Okada

arxiv:2605.21015 v1 · 2026-05-20 · math.CO · cs.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SI5UJD45NVDYR77QCIZ6GL6GF5}

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	2026-05-21T01:05:32.409635Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

923b448f9d6d4788fff01233e32fc62f55ae682cef5442d3e4b191b1b0b772c7

Aliases

arxiv: 2605.21015 · arxiv_version: 2605.21015v1 · doi: 10.48550/arxiv.2605.21015 · pith_short_12: SI5UJD45NVDY · pith_short_16: SI5UJD45NVDYR77Q · pith_short_8: SI5UJD45

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/SI5UJD45NVDYR77QCIZ6GL6GF5 \
  | 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: 923b448f9d6d4788fff01233e32fc62f55ae682cef5442d3e4b191b1b0b772c7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "60f91b913787cce2c27e5ae35771c444a29f14df1f7d23b4cd0f4805626373d5",
    "cross_cats_sorted": [
      "cs.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-20T10:50:16Z",
    "title_canon_sha256": "f68afcbf5fccf1a8e0304b6aedec6ad508e0d63f99ad4820b8e705e82a54e78a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.21015",
    "kind": "arxiv",
    "version": 1
  }
}