Earth's Unrecorded Past: Directed Photon Histories, Causal Stellar Archives, and Late-Time Reconstruction

Can an event on Earth leave a recoverable physical record even when no camera existed to capture it? This research investigates the possibility of reconstructing Earth's physical past through information retained in naturally propagated photon fields. Within the framework of Six-Throat Directed Geometry, it develops a causal and information-theoretic description of how an earlier physical event may imprint a field, propagate through directed optical histories, enter a candidate stellar archive, and become accessible to an instrument constructed only after the event occurred. The study establishes mathematical conditions for recovering historical source information from late-time measurements. Its central results include a recorder-free inversion theorem, causal transport constraints, quantitative reconstruction-error bounds, and identifiability conditions for spatial and temporal information. It also characterizes information loss arising from inaccessible optical modes, intensity-only measurements, uncertain source clocks, and unresolved intermediate histories. A differential archival-clock model examines how historical timing information may be extracted from independently calibrated field-transfer properties. Complementary statistical analysis develops a marginal-likelihood comparison between specified optical-imprint and null-data models. Reproducible numerical experiments demonstrate the reconstruction of synthetic source information from independently generated late-time observations. The work further develops a convergent dual-directional optical architecture, combining two directed receiving paths into a common target geometry. Simulated detector measurements are reconstructed into four directional image branches and two final image fields representing intensity and signed directional contrast. Together, these results establish a mathematical and computational framework for investigating whether the physical history of Earth can be recovered without an instrument having recorded the original event. The accompanying reproducibility package provides executable programs, numerical results, visualizations, and supplementary simulated videos to support independent examination and future experimental development.