Chapter 12 Population Layer: Threshold Determination of Cultural Effective Population Size —The second threshold of the LSED framework

Finding stone tools and fossils at an archaeological site does not mean people continuously lived on that land. For a human group to persist in one place for tens of thousands of years, four constraints must be satisfied simultaneously: enough people, connected, no gaps, sufficient area. If any one fails, the group is eliminated. This paper proposes the “Population Gate”, introduces the cultural effective population size Neff, and uses the formula Neff = ρ × A × fcult × g(⟨k⟩) to quantify a region's capacity to sustain an ancient human population. A calibration point N* = 1000 is set, with a ✓/?/× ternary determination. Among the four constraints, “connected” is the load-bearing one — too few people can be compensated by connectivity; dispersed people can also be compensated by connectivity; but if connectivity breaks, it cannot be compensated. Therefore what matters is the time average, not the peak. Accordingly, a failure-factor typology is established: “failure” is divided into four types plus one suspension (discontinuous, disintegrated, valve-type, capped, suspended), not induced from cases but necessarily derived from the possible ways the four constraints can break. Regional determinations: Africa discontinuous ×, Europe disintegrated ×, West Asia valve-type ×, Southeast Asia capped ×, South Asia suspended; North China and South China serve as undiscontinuous control typologies ✓; the Americas and Oceania serve as framework-external tests. Each regional determination is accompanied by falsification conditions. The product of this paper is not a conclusion, but a failure-factor typology, plus a control typology for “what undiscontinuous looks like”.