The Cosmological Constant on the Recognition Lattice: Vacuum Energy, Record Creation and the Expansion of the Universe

The expansion of the universe measures the energy of empty space. The Planck 2018 data give a vacuum energy density of 1.1 × 10⁻¹²³ in Planck units; zero-point energies cut off at the Planck scale give about 10⁻², more than 10¹²⁰ times too much. We ask what the recognition ledger's lattice path sum says. Its action, the Lorentzian Regge action, has no volume term and is homogeneous of degree one; its spacing is near the Planck length. With a volume term the flat lattice is a vacuum only when the constant is zero, so in the native amplitude, which the phase premise makes the ledger's, the bare cosmological constant is zero, not free. On a fixed finite lattice the one-loop vacuum phase tends, as the regulator is removed, to a count of signs over the nonzero modes, π/4 each and of order one per cell; by the action's homogeneity that count is the same at every size, for the graviton and massless fields. That the graviton's one-loop vacuum therefore generates no cosmological constant is a reading of the path sum's phase, measure and effective action, conditional in a theory whose massless graviton and unitary evolution are still open. Massive fields respond to the size, at an estimated order (m/m_P)² , and nothing in the ledger yet cancels them. A fixed vacuum phase per cell drops out if every history has the same number of cells, and is a volume term if not. The homogeneous sector reduces exactly to four equations in record time, whose long-wave quadratic form is Friedmann's minisuperspace action. With null postings and a fixed tick a fixed lattice cannot expand, so under these readings the universe grows by adding records: a constant rate per record, about 5 × 10⁻⁶¹ per tick for the measured constant, is de Sitter expansion, and whole-number counts meet Friedmann's equation only in the limit of many records. How the ledger adds records and what the path sum generates beyond one loop are open; no value of the vacuum energy is derived.