Pith Number

pith:ZQCN7VDR

pith:2026:ZQCN7VDR4THIM2X2LQH3IENOJM

not attested not anchored not stored refs pending

On the generalized Tur\'an number of complete bipartite graphs

Liana Yepremyan, Oliver Janzer, Sean Longbrake

arxiv:2606.09801 v1 · 2026-06-08 · math.CO · 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{ZQCN7VDR4THIM2X2LQH3IENOJM}

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	2026-06-09T02:09:10.594362Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc04dfd471e4ce866afa5c0fb411ae4b1676ceb9a2e03c7081d8d2c94e59ebb8

Aliases

arxiv: 2606.09801 · arxiv_version: 2606.09801v1 · doi: 10.48550/arxiv.2606.09801 · pith_short_12: ZQCN7VDR4THI · pith_short_16: ZQCN7VDR4THIM2X2 · pith_short_8: ZQCN7VDR

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/ZQCN7VDR4THIM2X2LQH3IENOJM \
  | 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: cc04dfd471e4ce866afa5c0fb411ae4b1676ceb9a2e03c7081d8d2c94e59ebb8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4082da0b3408dfce2db433ec3a74257dfe4f123962a3b0fce438facaa9099e19",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-08T17:53:07Z",
    "title_canon_sha256": "7108c969af300ef88e49e848d61347949fd8db247fd198c358425b5925c72a69"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.09801",
    "kind": "arxiv",
    "version": 1
  }
}