The Cosmological Arrow: From Coherent Historical Direction to the Limits of Origin Inference

The existence of a coherent cosmological arrow does not by itself identify the cosmological source of that arrow. This paper treats origin inference as a stratified inverse problem. It separates orientation, thermodynamic resource, record-forming mechanism, witness accessibility, cross-sector coherence, and source selection; then asks which source distinctions survive transport into observables. Seven source families are compared: Past-Hypothesis/low-Weyl boundary, no-boundary, tunneling, Janus/relational two-sided, CPT/global-symmetry, spontaneous-inflation/eternal, and generic symmetric/null-origin constructions. A 21-pair source atlas classifies each comparison as robustly discriminable (A), constructively quotient/non-identifiable (Q), lacking a presently justified source-neutral normalized common arena (N), or blocked by a sharply specified missing physical input (O). The resulting atlas has A=0, Q=2, N=13, O=6. A source-bottleneck theorem shows why descendant records cannot recreate source information lost before record proliferation. The strongest licensed conclusion is therefore neither a favored origin story nor undifferentiated ignorance: it is stratified source identifiability, with constructive no-go results, explicit non-comparability, and named reopening conditions.