Spherical Geometric Constraints on Synchronous Civilization Emergence: A Physical Prediction Derived from the Photon Projection Hypothesis

This paper derives a falsifiable geometric prediction for the spatial distribution of synchronously emerging civilizations, using as its sole physical premise the Photon Projection Hypothesis (PPH): that consciousness information is transmitted via photons at velocity c. Combining this premise with the spherical geometry of Earth and the confirmed earliest date of Homo sapiens (approximately 300,000 years BP), we establish that a single unidirectional photon emission event illuminates at most one hemisphere of the Earth's surface. We then prove that the maximum great-circle distance between any two points within the illuminated hemisphere is equal to Earth's half-circumference, approximately 20,015 km. This yields the prediction: civilizations originating from the same projection event must satisfy a pairwise great-circle distance constraint of d ≤ 20,015 km. We test this prediction against the four independently confirmed primary civilizations (Mesopotamia, Egypt, Indus Valley, Yellow River; c. 3500–2000 BCE) and find that all pairwise distances satisfy the constraint, with a maximum observed distance of approximately 8,000 km (Egypt to Yellow River). The later emergence of Mesoamerican civilization (Olmec, c. 1500 BCE) at distances of 13,000–16,000 km from primary Old World sites is consistent with assignment to a subsequent projection event rather than a simultaneous one. We formalize three falsifiability conditions, present the derivation in full, and situate the result within the broader Consciousness Projection Hierarchy (CPH) framework Ai Chen 2026e. The central prediction—maximum inter-civilizational distance of 20,015 km within a single projection event—does not require acceptance of any philosophical premises beyond the PPH, and is directly testable against the archaeological record.