Pith Number

pith:FK6M5GJO

pith:2026:FK6M5GJOW7SRLSOYBSAJ4BBJ76

not attested not anchored not stored refs pending

Explicit thresholds in a generalized Tur\'an problem for \(K_{3,t}\)-free graphs

Caiyun Hu, Hezhi Wang, Jianfeng Hou

arxiv:2606.19217 v1 · 2026-06-17 · 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{FK6M5GJOW7SRLSOYBSAJ4BBJ76}

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	2026-06-19T16:12:08.047891Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2abcce992eb7e515c9d80c809e0429ffa779210e90bff7e5f610293811357de3

Aliases

arxiv: 2606.19217 · arxiv_version: 2606.19217v1 · doi: 10.48550/arxiv.2606.19217 · pith_short_12: FK6M5GJOW7SR · pith_short_16: FK6M5GJOW7SRLSOY · pith_short_8: FK6M5GJO

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/FK6M5GJOW7SRLSOYBSAJ4BBJ76 \
  | 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: 2abcce992eb7e515c9d80c809e0429ffa779210e90bff7e5f610293811357de3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "27dfcbcdced29388fa315c8c348d16cf9ea5a55e40df2a10f68380e0b87a4fd2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-17T15:54:48Z",
    "title_canon_sha256": "4988db9cbfda68eb17f255a53fbfcd42370a98862b907faa555a6c385c1193ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.19217",
    "kind": "arxiv",
    "version": 1
  }
}