Pith Number

pith:OHKE5I4V

pith:2026:OHKE5I4VZRMOWIAMW4XBWRVUPP

not attested not anchored not stored refs pending

Structure and properties of large cross-intersecting families

Andrey Kupavskii, Yang Huang

arxiv:2606.20085 v1 · 2026-06-18 · 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{OHKE5I4VZRMOWIAMW4XBWRVUPP}

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

A sharp product bound for non-trivial cross-intersecting families

Receipt and verification

First computed	2026-06-19T16:13:02.456604Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

71d44ea395cc58eb200cb72e1b46b47bf6616d26cf1d2f2947505314a1b0805e

Aliases

arxiv: 2606.20085 · arxiv_version: 2606.20085v1 · doi: 10.48550/arxiv.2606.20085 · pith_short_12: OHKE5I4VZRMO · pith_short_16: OHKE5I4VZRMOWIAM · pith_short_8: OHKE5I4V

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/OHKE5I4VZRMOWIAMW4XBWRVUPP \
  | 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: 71d44ea395cc58eb200cb72e1b46b47bf6616d26cf1d2f2947505314a1b0805e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b5294d922a1814e61e3a75297e1a299202a0b0a5a81599fe9387abdcc26f52e6",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-18T11:06:11Z",
    "title_canon_sha256": "f1795abf87c600461eabe38d423da5551cadddd2a0d000ef347434b7761e5846"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.20085",
    "kind": "arxiv",
    "version": 1
  }
}