Pith Number

pith:IO2OI7U3

pith:2026:IO2OI7U3R7WAYYCHLYUETY6KHK

not attested not anchored not stored refs pending

Tree-independence number of $K_{1,d}$-free graph classes

{\DH}or{\dj}e Vasi\'c, Hidde Koerts, Kenny Be\v{s}ter \v{S}torgel, Mujin Choi

arxiv:2606.20256 v1 · 2026-06-18 · 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{IO2OI7U3R7WAYYCHLYUETY6KHK}

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	2026-06-19T16:13:07.054343Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

43b4e47e9b8fec0c60475e2849e3ca3aa29fbd1b8593bd304f9284b480cee318

Aliases

arxiv: 2606.20256 · arxiv_version: 2606.20256v1 · doi: 10.48550/arxiv.2606.20256 · pith_short_12: IO2OI7U3R7WA · pith_short_16: IO2OI7U3R7WAYYCH · pith_short_8: IO2OI7U3

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/IO2OI7U3R7WAYYCHLYUETY6KHK \
  | 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: 43b4e47e9b8fec0c60475e2849e3ca3aa29fbd1b8593bd304f9284b480cee318

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b01bbc4ecf6425b0232b2e64875b4fc3883805fec08a9eb708c9a1f52335080",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-18T14:05:30Z",
    "title_canon_sha256": "085aa329c89b26e8f91a9717452562b385ace8ea326f52d61453b181920d6f03"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.20256",
    "kind": "arxiv",
    "version": 1
  }
}