Complex Phase Cosmology 2nd Part 1: tan(πθ) = 𝓕(i,π,e)·T/V — Converting Phase from an Input Value into a Produced Output; Existence and the Production of Phase — Phase Grammar and the Method of Measurement

The First Series established a phase language across five parts. Part 1 redefined i as a quarter-turn phase operator and Euler's formula as the language of phase transitions. Part 2 extended this into dynamics with θ(z) and the Phase Tension γ(z). Part 3 defined the intrinsic phase θ_EM = 0.25 as the 50:50 symmetry point of light. Part 4 extended the global function to a local phase field θ(x,z). Part 5 designed six axes for observational verification. Throughout all five parts, however, θ remained an input value arranged on the observational coordinate, and the core phenomenological function inherited the very problem the series set out to reduce — the lineage of its parameters already depends on comparison with observation. This study opens the Second Series and addresses that internal limitation directly. It adds no new concepts. It traces backward, from the problem the First Series left behind, why each definition is needed, and assembles the minimum grammar required for θ to be produced rather than given. The Juridical Structuring Methodology — used by name throughout the First Series but never defined — is formally defined here: examination of the requirements of premises, demarcation of boundaries, design of a falsification structure, and the subsumption principle by which standard physics is not negated but absorbed as a special solution under specific conditions. Building on Part 1 (DOI: 10.5281/zenodo.19158235), Part 2 (DOI: 10.5281/zenodo.19332436), Part 3 (DOI: 10.5281/zenodo.19332612), Part 4 (DOI: 10.5281/zenodo.19412396), and Part 5 (DOI: 10.5281/zenodo.19445570), this study moves from a grammar that describes phase to a grammar that produces it. Core results established in this study: Measurement equation tan(πθ) = 𝓕(i,π,e)·T/V, with inverse θ = (1/π)·arctan(𝓕T/V) — θ converted from input to output T as local Phase Tension: the global γ alone cannot produce why black holes, voids, and filaments at different locations hold different local phase states; the bridge axiom between γ and T is not yet derived V as rate-of-change stability, and 𝓕 as the Euler-fractal operator carrying a ratio into a complex phase state; its functional form is undetermined |e^(iπθ)|² = 1 restricted to a mathematical identity, with total energy conservation separated as the A5 bridge axiom — energy conservation, information conservation, and reversibility are each independent propositions Fractal recursion F_n = e^(iπ·f(Fn−1)) adopted on the structural isomorphism between e's self-referential property and level-by-level generation, with the direction restricted to one side θ_EM = 0.25 meets the measurement grammar at a single point: tan(π·0.25) = 1, so light's 50:50 symmetry is simultaneously the unit reference where 𝓕T/V = 1 The observational integral (0→z) and the internal growth integral (i→i(x)) separated from the outset, so that observed results are not reused as ontological ground The status of the First Series is re-adjusted in the open. θ(z) is retained as a phenomenological medium for arranging phase states on the observational redshift rather than as a confirmed fundamental equation of motion, and γ₀ ≈ 0.15 together with the structural connection later proposed for it is left as a strong candidate and as not yet derived. Two tasks are stated as the top priority: to determine the rule by which 𝓕 satisfies real, dimensionless, non-negative output in the principal real branch, and to confirm whether the new measurement equation reproduces the First Series' θ(z) as a special solution in the homogeneous limit. Only when both hold are the two series connected within a single complex phase. This research applies Juridical Structuring Methodology to cosmology, crossing traditional academic boundaries to propose a strictly falsifiable scientific framework.