Pith Number

pith:SLCEUOLA

pith:2026:SLCEUOLAZXKUAZD7EHUOORGD7X

not attested not anchored not stored refs pending

Entanglement from Expansion: High Rank-Width in Deterministic Graphs

Cyril Gavoille, Simon Martiel, Tristan Cam, Yvan Le Borgne

arxiv:2606.07110 v1 · 2026-06-05 · 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{SLCEUOLAZXKUAZD7EHUOORGD7X}

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	2026-06-08T01:04:46.883594Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

92c44a3960cdd540647f21e8e744c3fdfed32313f4faaa2fb7211773132fabc7

Aliases

arxiv: 2606.07110 · arxiv_version: 2606.07110v1 · doi: 10.48550/arxiv.2606.07110 · pith_short_12: SLCEUOLAZXKU · pith_short_16: SLCEUOLAZXKUAZD7 · pith_short_8: SLCEUOLA

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/SLCEUOLAZXKUAZD7EHUOORGD7X \
  | 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: 92c44a3960cdd540647f21e8e744c3fdfed32313f4faaa2fb7211773132fabc7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4696a81981bc6370d05e0d30480162e4a030984f9d3674a590a731ef72cd11bb",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2026-06-05T10:04:54Z",
    "title_canon_sha256": "91351a055ec3bf19cb6b7e61afdf303fd465dedad491d2cee95f0ac23a7f023b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.07110",
    "kind": "arxiv",
    "version": 1
  }
}