Pith Number

pith:BBUGCUB4

pith:2013:BBUGCUB4645H6B5XZW5UFQRDT7

not attested not anchored not stored refs pending

Layered Separators in Minor-Closed Graph Classes with Applications

David R. Wood, Pat Morin, Vida Dujmovi\'c

arxiv:1306.1595 v9 · 2013-06-07 · math.CO · cs.CG · 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{BBUGCUB4645H6B5XZW5UFQRDT7}

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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.

Cited by

2 papers in Pith

Tree decompositions with small width, spread, order and degree

Sparse String Graphs and Region Intersection Graphs over Minor-Closed Classes have Linear Expansion

Receipt and verification

First computed	2026-05-18T00:12:51.080948Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

086861503cf73a7f07b7cdbb42c2239fe21d2944df4d453bd458e73def0360d7

Aliases

arxiv: 1306.1595 · arxiv_version: 1306.1595v9 · doi: 10.48550/arxiv.1306.1595 · pith_short_12: BBUGCUB4645H · pith_short_16: BBUGCUB4645H6B5X · pith_short_8: BBUGCUB4

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/BBUGCUB4645H6B5XZW5UFQRDT7 \
  | 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: 086861503cf73a7f07b7cdbb42c2239fe21d2944df4d453bd458e73def0360d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a069e97a8988b3aca7262b0aa65018afcb3ae204245ade9557e6902492c4bfdd",
    "cross_cats_sorted": [
      "cs.CG",
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-06-07T03:16:39Z",
    "title_canon_sha256": "cdd7fbc176c506fb47fd863e8cea2325bbab633818cda87f7e6e9b0a3f5cae50"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.1595",
    "kind": "arxiv",
    "version": 9
  }
}