Pith Number

pith:PJVR45DK

pith:2026:PJVR45DKYVJJJV2IU6JMJ5ZI6X

not attested not anchored not stored refs pending

A gap theorem for non-trivial maximal intersecting families and an exact weighted asymptotic

El'mira Yu. Kalimulina

arxiv:2607.16040 v1 · 2026-07-17 · 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{PJVR45DKYVJJJV2IU6JMJ5ZI6X}

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	2026-07-20T02:19:27.768439Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a6b1e746ac55294d748a792c4f728f5ce0415fb5e15d13588b991c62a49077b

Aliases

arxiv: 2607.16040 · arxiv_version: 2607.16040v1 · doi: 10.48550/arxiv.2607.16040 · pith_short_12: PJVR45DKYVJJ · pith_short_16: PJVR45DKYVJJJV2I · pith_short_8: PJVR45DK

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/PJVR45DKYVJJJV2IU6JMJ5ZI6X \
  | 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: 7a6b1e746ac55294d748a792c4f728f5ce0415fb5e15d13588b991c62a49077b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "03dc93257a3e9756ae62d40b6bd905532950ac4d62a20b5efca5774073474eba",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-17T15:15:13Z",
    "title_canon_sha256": "69e8beb8d3e3d5999d45379a3136b10a10f68fbe3c136f691ff6db8f20aaba29"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.16040",
    "kind": "arxiv",
    "version": 1
  }
}