−1 Is the Proof: Zero as the Shared Condition of Existence, and Its Cross-Civilizational Recognition

This paper argues that zero is not the symbol of nothingness but the symbol of a boundary — the ontological condition that makes −1 and 1 possible. The existence of −1 is sufficient proof: if zero meant "nothing," then −1 would mean "less than nothing," which is incoherent. Zero must be a boundary, not a void. The paper extends the earlier publication "Why Zero Must Exist" (DOI: 10.5281/zenodo.19350709) with three contributions: (1) the −1 proof from common sense; (2) a cross-civilizational survey showing that every sufficiently developed mathematical tradition independently arrived at zero's function before naming it; (3) an analysis of the two great historical paths to zero — the Indian inward path through śūnya, and the European outward path through commerce — as two complementary recognitions of the same structure, mapped onto the Prome/Eagor axis of Meta-Originary Ontology.