Pith Number

pith:RW7G5QDW

pith:2026:RW7G5QDWPE4CUPU7A2VHBOZ3GC

not attested not anchored not stored refs pending

On linear $k$-graphs with codegree Tur\'an density arbitrarily close to zero

Xiaona Fang, Yaojun Chen

arxiv:2606.04400 v1 · 2026-06-03 · 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{RW7G5QDWPE4CUPU7A2VHBOZ3GC}

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	2026-06-04T01:09:06.636547Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8dbe6ec07679382a3e9f06aa70bb3b309d326cad7ec390629bb0e64e2b515a56

Aliases

arxiv: 2606.04400 · arxiv_version: 2606.04400v1 · doi: 10.48550/arxiv.2606.04400 · pith_short_12: RW7G5QDWPE4C · pith_short_16: RW7G5QDWPE4CUPU7 · pith_short_8: RW7G5QDW

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/RW7G5QDWPE4CUPU7A2VHBOZ3GC \
  | 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: 8dbe6ec07679382a3e9f06aa70bb3b309d326cad7ec390629bb0e64e2b515a56

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "302d19a18452b63763dad6ea8d3c2fe2f2a66507fde0311b19b9f7d3c73a1b95",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-03T03:28:06Z",
    "title_canon_sha256": "fb97de923ffa3668230911d0c2a17a46fd00c06836a7fa9c6fcb280f0c95cc9a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.04400",
    "kind": "arxiv",
    "version": 1
  }
}