Pith Number

pith:DUZR6PMR

pith:2026:DUZR6PMRKXT5D2Y2FLQVYDXXSR

not attested not anchored not stored refs pending

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

Lihua Deng, Lu Lu, Rongrong Lu, Xucheng Bu

arxiv:2608.06810 v1 · 2026-08-07 · 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{DUZR6PMRKXT5D2Y2FLQVYDXXSR}

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	2026-08-10T01:12:09.793303Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1d331f3d9155e7d1eb1a2ae15c0ef7944c1e1104e271e420c66a2d63ef58e12c

Aliases

arxiv: 2608.06810 · arxiv_version: 2608.06810v1 · doi: 10.48550/arxiv.2608.06810 · pith_short_12: DUZR6PMRKXT5 · pith_short_16: DUZR6PMRKXT5D2Y2 · pith_short_8: DUZR6PMR

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/DUZR6PMRKXT5D2Y2FLQVYDXXSR \
  | 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: 1d331f3d9155e7d1eb1a2ae15c0ef7944c1e1104e271e420c66a2d63ef58e12c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3214de6651862143b15c1972f14ca72069e0717b8c77d0994c494c854e386ed5",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-08-07T05:03:22Z",
    "title_canon_sha256": "310186ba7c2c4c4c693ba04c1660fc74d32a9c810de7deb280b606fcb2e9d264"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.06810",
    "kind": "arxiv",
    "version": 1
  }
}