Pith Number

pith:K6OX5TBB

pith:2026:K6OX5TBBYXDLCWZB6QAD3WWNXN

not attested not anchored not stored refs pending

An $e$-positive classification for complete multipartite graphs

Ariel Y. Sun, David G.L. Wang, Watson Z.Y. Wang

arxiv:2607.19110 v1 · 2026-07-21 · 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{K6OX5TBBYXDLCWZB6QAD3WWNXN}

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	2026-07-22T01:24:09.104769Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

579d7ecc21c5c6b15b21f4003ddacdbb45771203b4deb4d70c2e6116799669bc

Aliases

arxiv: 2607.19110 · arxiv_version: 2607.19110v1 · doi: 10.48550/arxiv.2607.19110 · pith_short_12: K6OX5TBBYXDL · pith_short_16: K6OX5TBBYXDLCWZB · pith_short_8: K6OX5TBB

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/K6OX5TBBYXDLCWZB6QAD3WWNXN \
  | 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: 579d7ecc21c5c6b15b21f4003ddacdbb45771203b4deb4d70c2e6116799669bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db96d41e7086a2a7243ff67a1185fdc7a68480035c68ad652e006cc847f239c0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-21T13:55:16Z",
    "title_canon_sha256": "8f91c75907a8dad89a75dbd3c4d88eb01c6f416868030370c9050337a29ca017"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.19110",
    "kind": "arxiv",
    "version": 1
  }
}