Pith Number

pith:N4AHWGXU

pith:2026:N4AHWGXULVXNXLRA55AFQY6M2V

not attested not anchored not stored refs pending

Supersaturation in union-closed families of sets

Christopher Bouchard

arxiv:2607.26425 v1 · 2026-07-29 · 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{N4AHWGXULVXNXLRA55AFQY6M2V}

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	2026-07-30T01:18:23.492080Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

6f007b1af45d6edbae20ef405863ccd56e8427fa18349f3c04e5bed9ea8d57f9

Aliases

arxiv: 2607.26425 · arxiv_version: 2607.26425v1 · doi: 10.48550/arxiv.2607.26425 · pith_short_12: N4AHWGXULVXN · pith_short_16: N4AHWGXULVXNXLRA · pith_short_8: N4AHWGXU

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/N4AHWGXULVXNXLRA55AFQY6M2V \
  | 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: 6f007b1af45d6edbae20ef405863ccd56e8427fa18349f3c04e5bed9ea8d57f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "009936b245ca4addee5f195b920cdfaa21a88397d2944ef60c8311837efe4eaa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-29T03:09:45Z",
    "title_canon_sha256": "79d65791ef597801f06cab401266401b5ac68dcdb28ca8fccc6e3b05b3d43fab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.26425",
    "kind": "arxiv",
    "version": 1
  }
}