Pith Number

pith:KWE24BAD

pith:2016:KWE24BADKUMTYQQLTEWVYQ26WU

not attested not anchored not stored refs pending

Kleitman's conjecture about families of given size minimizing the number of $k$-chains

Adam Zsolt Wagner, Jozsef Balogh

arxiv:1609.02262 v2 · 2016-09-08 · 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{KWE24BADKUMTYQQLTEWVYQ26WU}

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	2026-05-18T01:03:42.491124Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5589ae040355193c420b992d5c435eb518ea6dec906f9dd76ce6aeb8104ec344

Aliases

arxiv: 1609.02262 · arxiv_version: 1609.02262v2 · doi: 10.48550/arxiv.1609.02262 · pith_short_12: KWE24BADKUMT · pith_short_16: KWE24BADKUMTYQQL · pith_short_8: KWE24BAD

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/KWE24BADKUMTYQQLTEWVYQ26WU \
  | 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: 5589ae040355193c420b992d5c435eb518ea6dec906f9dd76ce6aeb8104ec344

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa81ebe203010ea1b34b7967a64bf4a72f2be08b55e60e26a010bcf380ba1bfb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-09-08T04:20:46Z",
    "title_canon_sha256": "4e306bafca9fbdf6da8b735a3088dab756b4fa05ec3009145fc1d335b8a14963"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.02262",
    "kind": "arxiv",
    "version": 2
  }
}