Early Earth Was Not Arbitrary: Retrodictive Constraints on Pre-2.0 Ga Planetary Survivability

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.