Pith Number

pith:KCLQWZYC

pith:2026:KCLQWZYCZK2L2YX6MGQIYUBJPQ

not attested not anchored not stored refs pending

Spectral Radius Conditions for 3-Uniform Intersecting Families

An Chang, Guorong Gao, Lusheng Fang

arxiv:2607.08468 v1 · 2026-07-09 · 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{KCLQWZYCZK2L2YX6MGQIYUBJPQ}

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 Spectral Hilton--Milner--Frankl Theorem for $t$-Intersecting Families

Receipt and verification

First computed	2026-07-10T01:19:51.423883Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

50970b6702cab4bd62fe61a08c50297c13cb38d0bc25eaaab9b58e495e700a7e

Aliases

arxiv: 2607.08468 · arxiv_version: 2607.08468v1 · doi: 10.48550/arxiv.2607.08468 · pith_short_12: KCLQWZYCZK2L · pith_short_16: KCLQWZYCZK2L2YX6 · pith_short_8: KCLQWZYC

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/KCLQWZYCZK2L2YX6MGQIYUBJPQ \
  | 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: 50970b6702cab4bd62fe61a08c50297c13cb38d0bc25eaaab9b58e495e700a7e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0a3334eb8d526e4d901fa7f50cf652f79d46a976f9790030fd74e4ad1deedcf",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-09T13:26:46Z",
    "title_canon_sha256": "b860326ba52d7956cba2efda9dab87ae95b371f53b50416d4b1fec9cef8c1e5b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.08468",
    "kind": "arxiv",
    "version": 1
  }
}