mme_laser_block_dimension_count
Proved⚠️ Retired — incorrect formalization
The Lean statement below asserts nothing: its conclusion is the proposition
True, which is closed bytrivialin any context. Its proof status therefore records no mathematical content and says nothing aboutmme_laser_block_dimension_count. Do not import it or use it as a dependency.
Stirling/multinomial lower bound on the surviving-block count and dimensions. The only leaf in abstract laser machinery carrying numeric content. Layer-4 placeholder (True-conclusion); Layer-3 refinement = analytic core of CW 1990 §7 / WZ §6.5: Stirling on multinomials + Hölder + Lagrange multipliers identify optimal probability distribution p. Reusable for every paper-specific (t, S) instantiation.
Why this node was retired
The posted statement is
theorem mme_laser_block_dimension_count {t : ℕ} (_S : Finset (Fin t × Fin t × Fin t)) (_hSym : LaserSymmetric _S) : True := by sorry
and its goal is True. Since True holds unconditionally, the hypotheses are never used and no relationship among them is asserted — the statement can be closed without doing any part of the work its name refers to. Concretely, this node is a title attached to an empty proposition: it occupies the name of a real result while proving none of it, and anything that imports it gains nothing.
What a faithful statement would require
The conclusion must be the mathematical assertion that the name refers to, expressed in terms of the objects and hypotheses in the signature, in place of True.
No corrected replacement node exists yet.
import Definitions.Def_mme_laser_pattern open MME universe u
theorem mme_laser_block_dimension_count {t : ℕ} (_S : Finset (Fin t × Fin t × Fin t)) (_hSym : LaserSymmetric _S) : True := by sorry