Pith Number

pith:APXDMFCY

pith:2026:APXDMFCY5RGROX3JVZKW5YQIEK

not attested not anchored not stored refs pending

On $\ell$-weakly cross $t$-intersecting families for sets and vector spaces

Lijun Ji, Shuhui Yu

ℓ-weakly cross t-intersecting subspace families satisfy a product size bound when the ambient dimension meets an explicit threshold.

arxiv:2605.09557 v2 · 2026-05-10 · math.CO

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\usepackage{pith}
\pithnumber{APXDMFCY5RGROX3JVZKW5YQIEK}

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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

If F and G are ℓ-weakly cross t-intersecting subspace families, then |F| · |G| ≤ [n-t choose k-t] [n-t choose k'-t] provided that n ≥ (2k-t+1)(t+1) + (k-t+1)k' + k + 2ℓ - 1.

C2weakest assumption

The ambient dimension n is at least the stated explicit lower bound involving k, t, ℓ and k'; without this the inequality may fail for small n.

C3one line summary

For n large enough, the product of the sizes of two ℓ-weakly cross t-intersecting families of k- and k'-dimensional subspaces is at most the product of two Gaussian binomial coefficients.

Receipt and verification

First computed	2026-05-25T02:02:16.537302Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03ee361458ec4d175f69ae556ee208229484a48a476622e9ecae71a7d81b9b55

Aliases

arxiv: 2605.09557 · arxiv_version: 2605.09557v2 · doi: 10.48550/arxiv.2605.09557 · pith_short_12: APXDMFCY5RGR · pith_short_16: APXDMFCY5RGROX3J · pith_short_8: APXDMFCY

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/APXDMFCY5RGROX3JVZKW5YQIEK \
  | 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: 03ee361458ec4d175f69ae556ee208229484a48a476622e9ecae71a7d81b9b55

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6afdc962c53b34f5de87bbb9fce61d154347bdca8d6a361d8a58c1074e0592a2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-10T14:17:53Z",
    "title_canon_sha256": "d596aaf0ba3c7d3456427157041b0ea5c348c3491309a8592c678aef57bbe90a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.09557",
    "kind": "arxiv",
    "version": 2
  }
}