Pith Number

pith:I4GWVRYT

pith:2026:I4GWVRYTEDJYJB5SIDVUGB7FR5

not attested not anchored not stored refs pending

Shadows of Uniform Hypergraphs under a Minimum Degree Condition

Haorui Liu, Mei Lu, Yi Zhang

For vertex sets larger than a quadratic bound in t, any extremal k-uniform hypergraph with minimum degree binom(t, k-1) contains an isolated copy of K^k_{t+1}.

arxiv:2605.02610 v2 · 2026-05-04 · math.CO

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\usepackage{pith}
\pithnumber{I4GWVRYTEDJYJB5SIDVUGB7FR5}

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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.

Claims

C1strongest claim

By developing a hypergraph transformation that combines shifting operations with antilexicographic compression, we prove that there exists an extremal hypergraph containing an isolated copy of K^k_{t+1} whenever |X| > (1/4)(t+1)^2 binom(t-1, ℓ-2) + 2t.

C2weakest assumption

The new shifting-plus-antilexicographic-compression transformation preserves both the minimum-degree condition and the extremal property for arbitrary k > ℓ ≥ 2.

C3one line summary

For k-uniform hypergraphs with δ(F) ≥ binom(t, k-1), the minimum |∂_ℓ F| is achieved by one containing an isolated K_{t+1}^k when |X| > (1/4)(t+1)^2 binom(t-1, ℓ-2) + 2t.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-07-08T01:18:29.498954Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

470d6ac71320d38487b240eb4307e58f7f6b2159e8e5d5c543257dc818766469

Aliases

arxiv: 2605.02610 · arxiv_version: 2605.02610v2 · doi: 10.48550/arxiv.2605.02610 · pith_short_12: I4GWVRYTEDJY · pith_short_16: I4GWVRYTEDJYJB5S · pith_short_8: I4GWVRYT

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/I4GWVRYTEDJYJB5SIDVUGB7FR5 \
  | 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: 470d6ac71320d38487b240eb4307e58f7f6b2159e8e5d5c543257dc818766469

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5d9c3c9ead731433733fe5a588e371fba8228c2d6a4ce1ae101a7c2ee71fdb3c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-04T13:58:17Z",
    "title_canon_sha256": "786d4c3b040e5a6fb865d6b43cbd1637886385623d4c9b1a15a563429c8ca737"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.02610",
    "kind": "arxiv",
    "version": 2
  }
}