Pith Number

pith:4T6IIXZV

pith:2023:4T6IIXZVUZLRY6LSH3ZDNQEUEL

not attested not anchored not stored refs pending

Extremal families for the Kruskal--Katona theorem

Llu\'is Vena, Oriol Serra

arxiv:2304.05145 v1 · 2023-04-11 · math.CO · cs.DM

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4T6IIXZVUZLRY6LSH3ZDNQEUEL}

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	2026-07-05T05:59:55.899780Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4fc845f35a6571c79723ef236c09422e92ca9cdcda2ee2ed46f4eb7db6888ce

Aliases

arxiv: 2304.05145 · arxiv_version: 2304.05145v1 · doi: 10.48550/arxiv.2304.05145 · pith_short_12: 4T6IIXZVUZLR · pith_short_16: 4T6IIXZVUZLRY6LS · pith_short_8: 4T6IIXZV

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/4T6IIXZVUZLRY6LSH3ZDNQEUEL \
  | 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: e4fc845f35a6571c79723ef236c09422e92ca9cdcda2ee2ed46f4eb7db6888ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc61f9d038035ce254b651773be1f1d9cdbd0fd20322a8a416238ec7404b6149",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-04-11T11:18:36Z",
    "title_canon_sha256": "21cb142940b76c8b011664c19d2a61bb8612bf79768686803b2d464b89f83d1c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2304.05145",
    "kind": "arxiv",
    "version": 1
  }
}