Pith Number

pith:4HKFUVBG

pith:2021:4HKFUVBGHMTMBMV64JSZ3VZXXZ

not attested not anchored not stored refs pending

Uniform intersecting families with large covering number

Andrey Kupavskii, Peter Frankl

arxiv:2106.05344 v3 · 2021-06-09 · 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{4HKFUVBGHMTMBMV64JSZ3VZXXZ}

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	2026-07-05T06:07:28.456132Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1d45a54263b26c0b2bee2659dd737be502d5e57a76718ee0939f22a76cf460e

Aliases

arxiv: 2106.05344 · arxiv_version: 2106.05344v3 · doi: 10.48550/arxiv.2106.05344 · pith_short_12: 4HKFUVBGHMTM · pith_short_16: 4HKFUVBGHMTMBMV6 · pith_short_8: 4HKFUVBG

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/4HKFUVBGHMTMBMV64JSZ3VZXXZ \
  | 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: e1d45a54263b26c0b2bee2659dd737be502d5e57a76718ee0939f22a76cf460e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ae0bf0e8326d104861d077b592131489949d1bca6460db7c636e1e8ac227fdd6",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-06-09T19:21:00Z",
    "title_canon_sha256": "8abc9788ec48c5df7371954659888bf9b32d9a6d390dcf733a784bb9fa52992b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.05344",
    "kind": "arxiv",
    "version": 3
  }
}