Pith Number

pith:LFAH2FNC

pith:2026:LFAH2FNCEIQWEJVCEMQISAGBM6

not attested not anchored not stored refs pending

$K_{2, t+1}$-free graphs containing an optimal number of $K_{t, t}$'s

Vladislav Taranchuk

arxiv:2606.02855 v1 · 2026-06-01 · 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{LFAH2FNCEIQWEJVCEMQISAGBM6}

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	2026-06-03T01:05:24.636460Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

59407d15a222216226a223208900c16796f2cfd9964ea9e07206524b7e16c9bd

Aliases

arxiv: 2606.02855 · arxiv_version: 2606.02855v1 · doi: 10.48550/arxiv.2606.02855 · pith_short_12: LFAH2FNCEIQW · pith_short_16: LFAH2FNCEIQWEJVC · pith_short_8: LFAH2FNC

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/LFAH2FNCEIQWEJVCEMQISAGBM6 \
  | 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: 59407d15a222216226a223208900c16796f2cfd9964ea9e07206524b7e16c9bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0454fb5c03a9e4b3193d6915e078c6bd0368937b5dead95f81196d8b4f57dd2f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-01T20:19:23Z",
    "title_canon_sha256": "f4f8f5aa1bec395d0e8827b18a57cf34c4d92d517bd7fa20ae89c98bd2897074"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.02855",
    "kind": "arxiv",
    "version": 1
  }
}