N-Record Theory (NRT): Records, Screens, and the Emergence of Geometry

We formulate N-Record Theory (NRT), a records-first operational framework aimed at clarifying how spacetime geometry can arise as an effective description of stable facts. The primitive notions are persistent records, admissible interventions, and operational influence. No background manifold, metric, or microscopic locality is assumed at the primitive level. The influence relation induces an ordering of record creation acts that defines a notion of record time , with temporal orientation fixed by irreversible record formation. This arrow is defined prior to, and does not rely on, any equilibrium assumption. Local Record Equilibrium is a special near-equilibrium limit of the same irreversible bookkeeping; only in this limit, together with focusing/closure assumptions, does Einstein dynamics emerge at leading order. Records are graded: reversible proto-records need not constitute facts, while locked records are effectively irreversible. We summarize this by a lock strength λ ∈ [0, 1] (defined operationally below), with λ → 1 selecting the stable-record regime in which redundancy-based observables become sharp. For a chosen family of independent witnesses (verifiers of redundant records), a screen Σ is an operational cut separating accessible from inaccessible degrees of freedom. Its channel capacity N _cross (Σ) is the maximal number of mutually independent record-carrying channels that cross Σ. In record-dense regimes, capacity calibrates an intrinsic area A(Σ) = ℓ ² ₀ N _cross (Σ) and bounds the maximal objective record entropy on the screen. For a chosen objectivity convention (m, ϵ), redundancy-saturated screens exhibit a stable encoding plateau η = N _bits /N _cross → η∗(m, ϵ). In the continuum regime, we introduce a Lorentzian effective description calibrated by screen capacities. Under a local equilibrium closure for infinitesimal causal screens and a local capacity-response parameterization, the leading generally covariant two-derivative dynamics takes Einstein form with a record-dependent cosmological term. As an existence proof that the primitives are executable, we also present a discrete implementation. In its dense regime, the scaling N _cross (R) ∝ R ² implies an emergent effective spatial dimension d ≃ 3, while isotropy diagnostics approach N _out /N _cross → 1/2.