Pith Number

pith:KO4WGCT6

pith:2017:KO4WGCT6BFQPXF6IBSTJW4KHE2

not attested not anchored not stored refs pending

Two Stronger Versions of the Union-closed Sets Conjecture

Ze-Chun Hu, Zhen Cui

arxiv:1711.04276 v6 · 2017-11-12 · 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{KO4WGCT6BFQPXF6IBSTJW4KHE2}

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	2026-05-17T23:41:47.015825Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53b9630a7e0960fb97c80ca69b7147269666f2e1f9886e78b0749ac7f1ebed0a

Aliases

arxiv: 1711.04276 · arxiv_version: 1711.04276v6 · doi: 10.48550/arxiv.1711.04276 · pith_short_12: KO4WGCT6BFQP · pith_short_16: KO4WGCT6BFQPXF6I · pith_short_8: KO4WGCT6

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/KO4WGCT6BFQPXF6IBSTJW4KHE2 \
  | 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: 53b9630a7e0960fb97c80ca69b7147269666f2e1f9886e78b0749ac7f1ebed0a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "864e7e713c8c30f4f4d8358ceb039b8001fd9f9813cc16e926a18ef0c6efdd3e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-11-12T11:41:45Z",
    "title_canon_sha256": "30e15760670c5eb20889b9528fcfc4ef87aeff072dfaf166de5ab3bab2151bdc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.04276",
    "kind": "arxiv",
    "version": 6
  }
}