Pith Number

pith:6LLQDNJK

pith:2001:6LLQDNJKJBJ7MSDICFFGDAQII2

not attested not anchored not stored refs pending

A shorter, simpler, stronger proof of the Meshalkin-Hochberg-Hirsch bounds on componentwise antichains

Matthias Beck, Thomas Zaslavsky

arxiv:math/0112068 v3 · 2001-12-07 · 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{6LLQDNJKJBJ7MSDICFFGDAQII2}

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	2026-05-18T01:01:34.904153Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f2d701b52a4853f64868114a61820846a9a0e73b716dffd554e71b4759fd84c1

Aliases

arxiv: math/0112068 · arxiv_version: math/0112068v3 · doi: 10.48550/arxiv.math/0112068 · pith_short_12: 6LLQDNJKJBJ7 · pith_short_16: 6LLQDNJKJBJ7MSDI · pith_short_8: 6LLQDNJK

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/6LLQDNJKJBJ7MSDICFFGDAQII2 \
  | 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: f2d701b52a4853f64868114a61820846a9a0e73b716dffd554e71b4759fd84c1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a4eadec4f6db63b2a0e657dbcba09199274622f7b7cd235caed97121e432135",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2001-12-07T02:38:32Z",
    "title_canon_sha256": "68e7492fb6955b8026ac45d862c132c9c87c2b41c02f5a8002f144cfa7329ae8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0112068",
    "kind": "arxiv",
    "version": 3
  }
}