Pith Number

pith:X6HVUY2F

pith:2026:X6HVUY2FNCNANWGAUM2Y5S56FO

not attested not anchored not stored refs pending

On the generalized Tur\'{a}n number of the complete bipartite graph $K_{3,b+1}$

Jing Wang, Junpeng Zhou, Zixuan Yang

arxiv:2607.01680 v1 · 2026-07-02 · 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{X6HVUY2FNCNANWGAUM2Y5S56FO}

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	2026-07-03T01:17:26.595814Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf8f5a6345689a06d8c0a3358ecbbe2b951efbade27228e63671a372df7e4734

Aliases

arxiv: 2607.01680 · arxiv_version: 2607.01680v1 · doi: 10.48550/arxiv.2607.01680 · pith_short_12: X6HVUY2FNCNA · pith_short_16: X6HVUY2FNCNANWGA · pith_short_8: X6HVUY2F

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/X6HVUY2FNCNANWGAUM2Y5S56FO \
  | 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: bf8f5a6345689a06d8c0a3358ecbbe2b951efbade27228e63671a372df7e4734

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "867a7e227c5f79420706e4091c7cb20714cd5d9be44cfcb5f321e746348bee4c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-02T04:12:00Z",
    "title_canon_sha256": "38abe6486861ecd3c3951e97056195a6d169b6cd53a8d60b413ea25295f60281"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.01680",
    "kind": "arxiv",
    "version": 1
  }
}