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WikipediaCombinatorics

Pebbling number conjecture

The pebbling number conjecture: the pebbling number of a Cartesian product of connected graphs is at most equal to the product of the pebbling numbers of the factors. See Asplund, Hurlbert, and Kenter.

Mathematical statement

The pebbling number conjecture: the pebbling number of a Cartesian product of connected graphs is at most equal to the product of the pebbling numbers of the factors. See Asplund, Hurlbert, and Kenter.

Statement source: Wikipedia statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

pebbling_number_conjecture

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem pebbling_number_conjecture {W : Type} [Fintype V] [Fintype W] [DecidableEq W]    (G : SimpleGraph V) (H : SimpleGraph W) (hG : G.Connected) (hH : H.Connected) :    PebblingNumber (G □ H)  PebblingNumber G * PebblingNumber H := by  sorry
Statement source
Formal Conjectures
Lean version
v4.27.0
Placeholder
Present; no proof artifact
Source evidence
Pinned source index
Fidelity review
Community formulation

References