Pith Number

pith:4MFBUZSZ

pith:2026:4MFBUZSZRUZKCQCM4L6WSSJWTQ

not attested not anchored not stored refs pending

Counting subsets of integers free of arithmetic configurations

Juanjo Ru\'e, Miquel Ortega, Patrick Morris

arxiv:2607.17746 v1 · 2026-07-20 · 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{4MFBUZSZRUZKCQCM4L6WSSJWTQ}

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	2026-07-21T02:21:57.804314Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e30a1a66598d32a1404ce2fd6949369c36a16bb7818d228cc8d1cb52521061f7

Aliases

arxiv: 2607.17746 · arxiv_version: 2607.17746v1 · doi: 10.48550/arxiv.2607.17746 · pith_short_12: 4MFBUZSZRUZK · pith_short_16: 4MFBUZSZRUZKCQCM · pith_short_8: 4MFBUZSZ

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/4MFBUZSZRUZKCQCM4L6WSSJWTQ \
  | 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: e30a1a66598d32a1404ce2fd6949369c36a16bb7818d228cc8d1cb52521061f7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6f90c521837ccb07e7671d880fdf94cd24e98202b3ceb79ba41468f5058f30f",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-20T09:40:09Z",
    "title_canon_sha256": "99ae74538760458553171d5bf1b2e29da3a96fd3bfb0b70c670b6c9be524a1fc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.17746",
    "kind": "arxiv",
    "version": 1
  }
}