Finite-time branch-record accumulation in one-dimensional baths: independent baselines, amplification, and nonredundant records

This record contains the preprint, supplemental material, source files, figures, and numerical data archive for the manuscript “Finite-time branch-record accumulation in one-dimensional baths: independent baselines, amplification, and nonredundant records”.

Quantum Darwinism diagnoses objectivity through a redundancy plateau: many small, disjoint environment fragments independently reveal the same branch information. This manuscript studies finite-time branch-record accumulation in one-dimensional baths and separates the magnitude of the environmental record from the normalized shape with which that record is accessed locally.

For weak uniform deposition, matched field-only controls with J_X = 0 remain close to the analytic independent-site accumulation law, while the interacting bath increases the total environmental branch distinguishability. In a five-point matched scan at t = 3.6 and g_X = 0.8, 0.9, 1.0, 1.1, 1.2, the interacting denominator is larger than the corresponding field-only denominator by factors 2.56–3.00. At the critical point, D_E = 0.266513 instead of 0.090818, corresponding to a 2.93-fold increase in trace-distance amplitude and an 8.90-fold increase in the effective per-site signal.

After matching the independent null to the interacting value of D_E, the normalized fragment profile remains close to independent accumulation: bulk windows lie slightly above the homogeneous null while edge-attached windows lie below it. A solvable free-fermion benchmark with a local branch perturbation shows a complementary geometry: the record is locally detectable near the perturbation but is not broadcast to distant small fragments.

The result is not a universal failure of Darwinism and not strong data hiding. It is a finite-time classification of independent accumulation, interaction-driven magnitude amplification, small geometry-dependent shape deviations, and local nonredundant records.