Vacuum Energy
Vacuum Energy (IV.D572) is the τ-categorical Energy Index of the no-defect ground state, computed as the defect functional (IV.D274) evaluated on the empty bundle. In τ it is finite, sign-fixed, and not subject to the conventional vacuum-energy puzzle — there is no naïve UV mode-sum to regulate.
τ-Definition
Vacuum Energy (IV.D572) is the τ-categorical Energy Index of the no-defect ground state, computed as the defect functional (IV.D274) evaluated on the empty bundle. In τ it is finite, sign-fixed, and not subject to the conventional vacuum-energy puzzle — there is no naïve UV mode-sum to regulate.
Categorical invariant. VacuumEnergy := Defect Functional evaluated on the empty (zero-defect) bundle; an E2 invariant of the τ-kernel.
Primary registry anchor:
IV.D572
τ-Derivation Chain
-
I.K0— Universe Postulate establishes τ -
IV.D21— Energy Index — abstract energy quantity -
IV.D274— Defect functional — variational form for many-body energies -
IV.D572— Vacuum Energy from Defect Functional — evaluation on empty bundle -
IV.D76— Energy as CR-Tension confirms vacuum CR-tension is finite (no UV problem)
Lean modules referenced:
TauLib.BookIV.Physics.DefectFunctional,
TauLib.BookIV.ManyBody.DefectFunctionalExt
SI Translation
Calibration anchor: PG-P01-neutron
Calibration chain:
- m_n (anchor)
- c² via IV.D23
- τ-volume scale via IV.D293
- vacuum energy density evaluated on empty bundle
Manuscript reference: manuscript-sources/book-04/part09-vacuum/ch-vacuum-energy.tex