Pith Number

pith:UK45EBI6

pith:2026:UK45EBI6GWLDHH7DNKP7Z3L5FB

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Asymptotically optimal lower bounds on weak saturation numbers for hypergraphs

Nikolai Terekhov

Polymatroids establish asymptotically optimal lower bounds on weak saturation numbers for hypergraphs.

arxiv:2604.07104 v2 · 2026-04-08 · math.CO

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Claims

C1strongest claim

We generalize these bounds to the case of hypergraphs and establish their asymptotic optimality. To prove this, we introduce a lower bound method based on polymatroids.

C2weakest assumption

The polymatroid construction correctly captures the weak saturation process for arbitrary r-uniform H and yields tight asymptotic coefficients without hidden integrality constraints.

C3one line summary

Generalizes asymptotically optimal lower bounds on weak saturation numbers wsat(n,H) from graphs to r-uniform hypergraphs via a polymatroid method that yields non-integer coefficients.

Receipt and verification

First computed	2026-07-07T02:19:50.345239Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2b9d2051e3596339fe36a9ffced7d28691d198a62d4e89c6cf12b509f98bf29

Aliases

arxiv: 2604.07104 · arxiv_version: 2604.07104v2 · doi: 10.48550/arxiv.2604.07104 · pith_short_12: UK45EBI6GWLD · pith_short_16: UK45EBI6GWLDHH7D · pith_short_8: UK45EBI6

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/UK45EBI6GWLDHH7DNKP7Z3L5FB \
  | 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: a2b9d2051e3596339fe36a9ffced7d28691d198a62d4e89c6cf12b509f98bf29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0893d3e7e4968f450914029f3673bec0e213c58d5c4b242383f3586a44d18384",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-04-08T13:56:51Z",
    "title_canon_sha256": "501fe23ff1da25db9c7b1cc535d99fc0d06391332a0463cc9628151dc78fcbf5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.07104",
    "kind": "arxiv",
    "version": 2
  }
}