This paper extends the information collapse analytical framework established in The Meaning of Mathematics (Part I), clearly distinguishing between two cognitive directions—grasping outward and deconstructing inward—and conducts a complete structural argumentation analysis of Ramanujan's summation of divergent series. Grasping outward extends along the temporal direction, producing determinate objects; deconstructing inward constructs structural relations, exposing the position of the operation itself within the global structure. In Ramanujan's summation, S₁ = 1/2 marks the beginning of the action, S₂ = 1/4 marks the action itself, S₃ = -1/12 is the marker of the result, and 1/3 is the marker of the action's state. The four markers lie between -1 and 1, while the results of the action extend infinitely in the positive direction—markers are structural positions, results are extension-data, and the two are not of the same dimension. This paper distinguishes two mathematical expressions for action: traditional mathematics describes the rules of action through grasping outward, producing result-data; structural argumentation exposes the structure of action through deconstructing inward, producing process-markers. S₁ = 1/2 shares the same cut-marker with the critical line of the Riemann Hypothesis, and 2S₂ = S₁ shares the same residue reduction structure with the Goldbach Conjecture's "sum of two primes." The Green-Tao Theorem serves as an independent case, demonstrating how deconstructing inward, when facing probabilistic obstacles and self-reference prohibitions, transforms the uncertainty of self-referential products into certainty through external mapping. This paper further distinguishes two forms of self-reference. Operational self-reference causes the subject-object distance to disappear, allowing neither proof nor falsification; assertoric self-reference leaves proof lacking a rigidity beam, but falsification requires only a single counterexample. Through this, it analyzes what mathematics can prove and what it cannot prove. While producing certainty, grasping outward inevitably produces residue. Within a closed system, residue continuously accumulates—this is entropy increase. Ramanujan's summation reveals the cognitive root of entropy increase: the act of grasping outward producing residue is itself irreversible. Mathematics is the pure grammar of information collapse, embodying the principle that the divider exists in structure but not in result.