Pith Number

pith:ZO6TK3K3

pith:2025:ZO6TK3K37QQYHKILOUTZFRPVJW

not attested not anchored not stored refs pending

Layered tree-independence number and clique-based separators

Andrea Munaro, Cl\'ement Dallard, Martin Milani\v{c}, Shizhou Yang

arxiv:2506.12424 v1 · 2025-06-14 · 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{ZO6TK3K37QQYHKILOUTZFRPVJW}

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	2026-07-05T11:21:53.121574Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbbd356d5bfc2183a90b752792c5f54d96f44982d964afe8a379957a7641502d

Aliases

arxiv: 2506.12424 · arxiv_version: 2506.12424v1 · doi: 10.48550/arxiv.2506.12424 · pith_short_12: ZO6TK3K37QQY · pith_short_16: ZO6TK3K37QQYHKIL · pith_short_8: ZO6TK3K3

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/ZO6TK3K37QQYHKILOUTZFRPVJW \
  | 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: cbbd356d5bfc2183a90b752792c5f54d96f44982d964afe8a379957a7641502d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66abe945d498b8977e585adce17a5a5b6576bb6aa1c54b117ad13fade74c0cde",
    "cross_cats_sorted": [
      "cs.CG",
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-06-14T09:50:44Z",
    "title_canon_sha256": "0be255946458f283c3329c49d3f5aeea3ee72942d2e7db9c7cef96d43c5e088e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.12424",
    "kind": "arxiv",
    "version": 1
  }
}