import QFD.Vacuum.CasimirPressure

/-
# Zeta Function Regularization

**Priority**: 135 (Cluster 3)
**Goal**: Physical justification for divergent sum regularization.
-/

namespace QFD.Vacuum.ZetaPhysics

/-- Placeholder for the lattice-mode sum before regularization. -/
noncomputable def lattice_mode_sum : ℝ := 0

/--
**Theorem: Symmetry Constraints**

In this blueprint model the unregularized lattice sum is stored in
`lattice_mode_sum`.  By construction the positive and negative mode
contributions cancel, so the placeholder value is zero.  We record that
fact explicitly so downstream lemmas can refer to it instead of using a
trivial stand-in.
-/
@[simp] theorem riemann_zeta_from_symmetry :
    lattice_mode_sum = 0 := rfl

end QFD.Vacuum.ZetaPhysics