Pith Number

pith:CBFI35L2

pith:2025:CBFI35L2CC42SP5HWXXAPWER54

not attested not anchored not stored refs pending

The independence and clique cover numbers of the squarefree graph

Boris Alexeev, Dustin G. Mixon, Will Sawin

arxiv:2507.01928 v2 · 2025-07-02 · math.CO · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CBFI35L2CC42SP5HWXXAPWER54}

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	2026-07-05T11:31:29.472762Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

104a8df57a10b9a93fa7b5ee07d891ef1327b6660d1b83aa77b150423c567df6

Aliases

arxiv: 2507.01928 · arxiv_version: 2507.01928v2 · doi: 10.48550/arxiv.2507.01928 · pith_short_12: CBFI35L2CC42 · pith_short_16: CBFI35L2CC42SP5H · pith_short_8: CBFI35L2

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/CBFI35L2CC42SP5HWXXAPWER54 \
  | 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: 104a8df57a10b9a93fa7b5ee07d891ef1327b6660d1b83aa77b150423c567df6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2ae826a1d7f0afde4446126e78a09bbbf054061334cc19eb6abaa073f1cc10c2",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-02T17:39:17Z",
    "title_canon_sha256": "ac830f21ebaf42f08b63f5dfc98e08bece33a87bf819d46692c81c0a0249259a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.01928",
    "kind": "arxiv",
    "version": 2
  }
}