Density Mathematics: Numbers as Emergents of Density Clustering — Extension Volume: Dynamics Self-Production (EN)

Extension volume of Density Mathematics: dynamics self-production — the dynamics of density space is derived from the static axioms A1-A4 alone, importing no physical equation. Mass flow: the flow version of A2 uniquely forces the logarithmic potential V=k(m²/2−ln m); the 1/m wall is the analytic expression of A2. Uniqueness theorem for the damping form + a breathing discriminator theorem (inertia selected by the observed existence of breathing). Shape flow: the A4 power-flow generator coincides pointwise with the discrete ⊗-chain (σ²ₙ=σ₀²/2ⁿ). Transport: the A3 mixing limit equals the heat-kernel step exactly (⊕→diffusion). Structural reading: the parent program's unified field PDE is the product-rule expansion of d(mp)/dt — 'why exactly three terms' is answered by the mass×shape decomposition. Confrontation conclusion: the self-produced equations coincide term-by-term with the observation-introduced version — physical observation and mathematical derivation as independent discoveries of the same equations (an in-house instance of Wigner's question). Machine verification 27/27 (companion scripts). Includes the numerical signature of breathing half-cycle asymmetry.