Pith Number

pith:BGXKLCWF

pith:2022:BGXKLCWFUFND5EI4WDYNAAEWTE

not attested not anchored not stored refs pending

Better bounds for the union-closed sets conjecture using the entropy approach

Stijn Cambie

arxiv:2212.12500 v2 · 2022-12-23 · 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{BGXKLCWFUFND5EI4WDYNAAEWTE}

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	2026-07-05T10:14:34.886497Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

09aea58ac5a15a3e911cb0f0d00096993bac84745871994502a46c423774311c

Aliases

arxiv: 2212.12500 · arxiv_version: 2212.12500v2 · doi: 10.48550/arxiv.2212.12500 · pith_short_12: BGXKLCWFUFND · pith_short_16: BGXKLCWFUFND5EI4 · pith_short_8: BGXKLCWF

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/BGXKLCWFUFND5EI4WDYNAAEWTE \
  | 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: 09aea58ac5a15a3e911cb0f0d00096993bac84745871994502a46c423774311c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ebe6a43d1cc34cbd2b9d3195b8a83e30ebf31c1107c39d8b946b0492104c6ec1",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2022-12-23T17:48:48Z",
    "title_canon_sha256": "4f873dc5332993e61b1dbc9eeeaa58c858087f2123aaa21fdb0fe0faa35fefd5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2212.12500",
    "kind": "arxiv",
    "version": 2
  }
}