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 in the squared edge lengths, and its spacing is near the Planck length. At every stationary point of the action with a volume term, the action equals twice the cosmological constant times the volume, so the flat lattice is a vacuum only when the constant is zero: in the native amplitude, which the phase premise makes the ledger's, the bare cosmological constant is zero, not free. The one-loop vacuum is a count of signs, a phase of π/4 per mode and of order one per cell; for the graviton and for massless fields it does not change when the lattice is rescaled, and with null postings the lattice symmetry forbids a smooth response to its shape. Massive fields do respond to the size, with a term estimated at order (m/m_P)² in Planck units, and nothing in the ledger yet cancels it. A fixed vacuum phase per cell gravitates only if the number of cells differs between the histories of the path sum, and cancels if it is the same in every history. The homogeneous sector of the lattice reduces exactly to four equations in record time, whose quadratic long-wave form is Friedmann's minisuperspace action with Newton's constant fixed by the action. With null postings and a fixed tick a fixed lattice cannot expand, so under these readings the universe grows by adding records. Then a cosmological constant can be kinematic: a constant rate of record creation per record is de Sitter expansion, and the measured cosmological constant corresponds to about 5 × 10⁻⁶¹ new records per record per tick. With whole-number counts Friedmann's equation then holds only in the limit of many records: exact agreement at every tick would force a Planck-sized constant. How the ledger adds records, whether their number varies between histories, and what the path sum generates beyond one loop are the open steps. No value of the vacuum energy is derived here; the measured value enters only as the number a derivation must reach. Preprint of the Recognition Physics Institute, 18 pages. Not peer reviewed.