A Point on the Helix of Time: The Universe Read Through the Euler Lens

The Euler lens spends a low-entropy boundary condition forward: the arrow of time is the monotonic expenditure of the low-entropy beginning named the dawn — the ordered initial condition the beginning possessed and the dynamics do not produce. This paper locates that dawn exactly, shows that every device built to remove it (singularity, bounce, phase-space-growing cycle, beginningless asymptote) relocates it rather than dissolving it, and establishes that the residue is underdetermined by all possible observation, not merely unexplained. It then does what the earlier papers had no occasion to: it takes a position. Among the completions consistent with every measurement, one holds the dawn to be given — supplied, not reducible to dynamics — and this paper adopts it, on the record, as a commitment rather than a result. It shows the paper standing entirely clear of the four cosmological falsifications (it asserts no distance law) and overcoming outright the two technical objections that genuinely threaten a nonsingular winding: the singularity, dissolved by a bounce; and Tolman's cyclic entropy bloat, dissolved by phase-space growth. The felt necessity of a giver is diagnosed as structure in the perceiver, not leverage on the dawn. Everything numerical is imported; the contribution is the arrangement and the marked commitment; the contributed number is none. This is a companion paper in the Euler Universe series. The parent cosmology — cosmological redshift as phase drift on a static background — is falsified by four independent observational tests and is not revived here; the logarithmic spiral e^(λ+i)θ is retained only as an interpretive lens, never as a cosmological claim