Pith Number

pith:LAV2KJF5

pith:2022:LAV2KJF5EWHUN4PZOWDCHS2JTO

not attested not anchored not stored refs pending

An improved lower bound for the union-closed set conjecture

Will Sawin

arxiv:2211.11504 v3 · 2022-11-21 · 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{LAV2KJF5EWHUN4PZOWDCHS2JTO}

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

1 paper in Pith

Redundancy Is All You Need (for CSP Sparsification)

Receipt and verification

First computed	2026-07-05T06:21:55.623581Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

582ba524bd258f46f1f9758623cb499bab7ccb8f78fe7f8586de736a7cf5bbf4

Aliases

arxiv: 2211.11504 · arxiv_version: 2211.11504v3 · doi: 10.48550/arxiv.2211.11504 · pith_short_12: LAV2KJF5EWHU · pith_short_16: LAV2KJF5EWHUN4PZ · pith_short_8: LAV2KJF5

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/LAV2KJF5EWHUN4PZOWDCHS2JTO \
  | 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: 582ba524bd258f46f1f9758623cb499bab7ccb8f78fe7f8586de736a7cf5bbf4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5dd60f128f31857342f8c9125e3f1ea251b7a6866226e81a877ae3ed0f9f6f1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2022-11-21T14:42:37Z",
    "title_canon_sha256": "a00f8d5653a84db6f269702aa90c26f10cc333bf30d21ee4a1f2c995b57c62d5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2211.11504",
    "kind": "arxiv",
    "version": 3
  }
}