Pith Number

pith:JNTZXHWK

pith:2026:JNTZXHWK3YAP2UPFG3Y5FEKNBK

not attested not anchored not stored refs pending

Isolation subdivision number of a graph

Magda Dettlaff, Magdalena Lema\'nska, Merce Mora, Pawe{\l} \.Zyli\'nski, Rados{\l}aw Ziemann

arxiv:2606.21190 v1 · 2026-06-19 · 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{JNTZXHWK3YAP2UPFG3Y5FEKNBK}

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	2026-06-23T01:12:32.914982Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b679b9ecade00fd51e536f1d2914d0ab5079d8f50b446492b6abff63775b9ec

Aliases

arxiv: 2606.21190 · arxiv_version: 2606.21190v1 · doi: 10.48550/arxiv.2606.21190 · pith_short_12: JNTZXHWK3YAP · pith_short_16: JNTZXHWK3YAP2UPF · pith_short_8: JNTZXHWK

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/JNTZXHWK3YAP2UPFG3Y5FEKNBK \
  | 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: 4b679b9ecade00fd51e536f1d2914d0ab5079d8f50b446492b6abff63775b9ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa64e30706fff89620fbf20643ab30a489a9700253e5431f7747a521c3eeea3a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-19T07:59:58Z",
    "title_canon_sha256": "050af4076fd7b8417713115231a48df3c02d8e081a6746757d8852b4de5a5b28"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.21190",
    "kind": "arxiv",
    "version": 1
  }
}