Appendix A: Retrodictive Constraint-Based Simulation Configuration (Supplementary Note) A.1 Simulation Overview A high-resolution, retrodictive simulation was conducted to explore physically and informationally viable histories of Earth prior to approximately 2.0 billion years ago. The simulation employed a constraint-based framework designed to identify which classes of early-Earth histories remain compatible with known long-term survivability conditions, rather than reconstructing a single deterministic trajectory. The simulation was completed successfully and produced a consistent ensemble of viable histories satisfying all imposed constraints. A.2 Retrodictive Framework The model operated in a backward-time (retrodictive) mode spanning approximately 2.5 billion years. Rather than specifying detailed initial conditions, the simulation enforced future-derived survivability constraints, allowing only internally consistent histories to persist. Key retrodictive parameters included: Target epoch: Pre–2.0 billion years ago Backward time span: ~2.5 billion years Solution structure: Constraint cone (multiple simultaneous histories retained) Maximum candidate histories: 2048 Objective: Minimize assumptions while maximizing physical and informational consistency This approach enables elimination of impossible histories without presupposing specific geological or biological pathways. A.3 Enforced Survivability Constraints Candidate histories were required to satisfy the following necessary conditions: Persistent global oceans within bounded surface fractions Long-term crustal and continental stability Continuous maintenance of structured biochemical information Allowance for major transition events (e.g., oxygenation windows) Boundary conditions were conservatively defined, including: Surface temperature range: 240–340 K Atmospheric pressure range: 0.3–20 atm Minimum ocean coverage: 50% Histories violating any constraint were discarded. A.4 Environmental Priors Broad environmental priors were used to avoid parameter overfitting: Reduced early solar luminosity Elevated volcanic activity High impact flux Reducing to mixed ocean chemistry Active mineral surface catalysis Permitted surface types included clay-like, basaltic glass–like, and sulfide-like substrates, consistent with early Earth geological evidence. A.5 Dynamical and Noise Modeling The system evolved under nonequilibrium energy fluxes including thermal gradients, redox gradients, ultraviolet pulses, and hydrothermal contributions. Stochastic perturbations were introduced through: Impact events Large igneous (flood basalt) episodes Global cooling events Perturbation severity followed a heavy-tailed distribution, allowing rare but extreme events. Environmental noise was modeled via continuous coupling with bounded escalation. A.6 Observables and Metrics The simulation tracked multiple observables across the ensemble, including: Fraction of surviving histories over time Persistence of causal network structure Redox trajectory classifications Occurrence of major transition windows Global stability indices Topological variance across histories Only histories satisfying all survivability criteria were retained for analysis. The final analysis focused on the most stable subset of histories. A.7 Summary of Emergent Results Despite a large initial ensemble, the simulation rapidly converged onto a small subset of viable histories. These histories exhibited: Strong convergence toward low-dimensional causal topologies Near-zero topological variance across surviving trajectories Consistent causal density and self-similarity metrics Robust informational persistence under repeated perturbations These outcomes indicate that early Earth survivability was highly constrained and depended on structured causal organization rather than random resilience. A.8 Scope and Disclosure Note This appendix provides a conceptual and methodological record only.It does not disclose implementation specifics, proprietary architectures, or internal execution mechanisms.All results reported here are theoretical and intended solely to support the scientific conclusions of the main text.

The earliest history of Earth remains one of the least constrained intervals in planetary science, limited by sparse geological records and extreme sensitivity to initial conditions. This study introduces a retrodictive, constraint-based simulation framework to explore which classes of early-Earth histories are compatible with the long-term persistence of oceans, crustal stability, and durable biochemical information. Rather than reconstructing a single speculative trajectory, the model evolves backward from known survivability constraints, eliminating histories that violate physical, geochemical, or informational persistence requirements. Across a broad ensemble of candidate histories spanning 2.5 billion years, the results reveal a rapid collapse of possibility space toward a small subset of viable trajectories. These surviving histories converge on stable causal network topologies despite extreme environmental noise, impact flux, and geochemical variability. The findings suggest that early Earth survivability was neither inevitable nor arbitrary, but instead depended on entry into narrow constraint corridors in physical and informational state space. This work provides a complementary perspective to forward simulations and offers a general framework for evaluating deep-time planetary habitability under profound uncertainty.