Pith Number

pith:TPPL73YO

pith:2026:TPPL73YOY5NNQXJYM6NFMR2HO2

not attested not anchored not stored refs pending

Bipartite cuts in Ramsey-Tur\'an style

Bernard Lidick\'y, Ce Chen, J\'ozsef Balogh

arxiv:2606.20397 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{TPPL73YOY5NNQXJYM6NFMR2HO2}

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	2026-06-19T16:13:11.538815Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9bdebfef0ec75ad85d38679a56474776bcb7f8d4fe6ed35b06658a2dc9510fcb

Aliases

arxiv: 2606.20397 · arxiv_version: 2606.20397v1 · doi: 10.48550/arxiv.2606.20397 · pith_short_12: TPPL73YOY5NN · pith_short_16: TPPL73YOY5NNQXJY · pith_short_8: TPPL73YO

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/TPPL73YOY5NNQXJYM6NFMR2HO2 \
  | 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: 9bdebfef0ec75ad85d38679a56474776bcb7f8d4fe6ed35b06658a2dc9510fcb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a2957dc353355d59a51c61c4b65a8efcfe4a00c19482e68bf68abe5682a5e77",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-18T15:52:25Z",
    "title_canon_sha256": "ac2d542aa0b104566435a100408cd200d122109623ff7cbef47423f55508171b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.20397",
    "kind": "arxiv",
    "version": 1
  }
}