Pith Number

pith:4OLFRXT6

pith:2026:4OLFRXT62K5C7SJ3PM7WW4JAYK

not attested not anchored not stored refs pending

Treewidth of Products of Graphs with High Treewidth

Raj Kaul

arxiv:2607.16778 v1 · 2026-07-18 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4OLFRXT62K5C7SJ3PM7WW4JAYK}

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	2026-07-21T01:20:58.627060Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e39658de7ed2ba2fc93b7b3f6b7120c28aa66187a1c988a5d4960f27cd1bd039

Aliases

arxiv: 2607.16778 · arxiv_version: 2607.16778v1 · doi: 10.48550/arxiv.2607.16778 · pith_short_12: 4OLFRXT62K5C · pith_short_16: 4OLFRXT62K5C7SJ3 · pith_short_8: 4OLFRXT6

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/4OLFRXT62K5C7SJ3PM7WW4JAYK \
  | 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: e39658de7ed2ba2fc93b7b3f6b7120c28aa66187a1c988a5d4960f27cd1bd039

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d2e76dadb557ab4724c750b1ad0c35513a46867623a6c335d2553eb1f68b867",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-18T11:27:34Z",
    "title_canon_sha256": "b8bb4d4c38f41d48c90fe273ebf66a53df655bb29525af41ec721ebd5dd7ffcf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.16778",
    "kind": "arxiv",
    "version": 1
  }
}