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, while zero-point energies cut off at the Planck scale give a density near 10⁻² in the same units, more than 10¹²⁰ times too large. We ask what the recognition ledger's lattice path sum says about this. Its action, the Lorentzian Regge action, has no volume term and is homogeneous of degree one, and 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 phase of the regulated one-loop vacuum is a count of signs, π/4 per mode and of order one per cell, and because the action is homogeneous it does not change when the lattice is rescaled, for the graviton and for 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 in Planck units, and nothing in the ledger yet cancels them. A fixed vacuum phase per cell drops out of every expectation if the number of cells is the same in every history, and acts as a volume term if it varies. 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 creation rate per record is de Sitter expansion, about 5 × 10⁻⁶¹ new records per record per tick for the measured constant, and with whole-number counts Friedmann's equation holds 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, and the measured value enters only as the number a derivation must reach.