Pith Number

pith:CFY2IKIQ

pith:2022:CFY2IKIQJV2KFM33Q3QPTC4JTN

not attested not anchored not stored refs pending

A constant lower bound for the union-closed sets conjecture

Justin Gilmer

arxiv:2211.09055 v2 · 2022-11-16 · 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{CFY2IKIQJV2KFM33Q3QPTC4JTN}

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.

Cited by

2 papers in Pith

Redundancy Is All You Need (for CSP Sparsification)

Multiplicative error set system sparsification: A simpler proof via chain length contraction

Receipt and verification

First computed	2026-07-05T05:19:56.117876Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1171a429104d74a2b37b86e0f98b899b7ddcc78233c19efbb1ce6b434da94874

Aliases

arxiv: 2211.09055 · arxiv_version: 2211.09055v2 · doi: 10.48550/arxiv.2211.09055 · pith_short_12: CFY2IKIQJV2K · pith_short_16: CFY2IKIQJV2KFM33 · pith_short_8: CFY2IKIQ

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/CFY2IKIQJV2KFM33Q3QPTC4JTN \
  | 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: 1171a429104d74a2b37b86e0f98b899b7ddcc78233c19efbb1ce6b434da94874

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d9917eec784b192a22e6016b833e152494d85c602e19cb73c7540c6671b21c37",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2022-11-16T17:17:42Z",
    "title_canon_sha256": "37cfec0a080cd456b20d1fff20238aca3d0d097f74dd1a929c0348c649248c76"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2211.09055",
    "kind": "arxiv",
    "version": 2
  }
}