Pith Number

pith:ZLA7HDXR

pith:2010:ZLA7HDXRFCTCIVFTXL7E2KVWXZ

not attested not anchored not stored refs pending

A lower bound for the tree-width of planar graphs with vital linkages

Isolde Adler, Philipp Klaus Krause

arxiv:1011.2136 v1 · 2010-11-09 · cs.DS · 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{ZLA7HDXRFCTCIVFTXL7E2KVWXZ}

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	2026-05-18T04:36:42.494137Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cac1f38ef128a62454b3bafe4d2ab6be53fb38a716e4ddf4a3458e461b203fb3

Aliases

arxiv: 1011.2136 · arxiv_version: 1011.2136v1 · doi: 10.48550/arxiv.1011.2136 · pith_short_12: ZLA7HDXRFCTC · pith_short_16: ZLA7HDXRFCTCIVFT · pith_short_8: ZLA7HDXR

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/ZLA7HDXRFCTCIVFTXL7E2KVWXZ \
  | 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: cac1f38ef128a62454b3bafe4d2ab6be53fb38a716e4ddf4a3458e461b203fb3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ea210afc81eac85b967ed40bc8a9b73af05619957c40f48740049bfc31049f4",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2010-11-09T16:29:47Z",
    "title_canon_sha256": "637a50531a202442d9d85fa34d2bc37744d9dac8bcee81b5550ae20e9cecd705"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.2136",
    "kind": "arxiv",
    "version": 1
  }
}