Coherence Cone: Spectral Causal Body of the Binary Views of a Finite Coherence, a Volume-Fixed Candidate Metric with Deformed Light Cones, and Its Closure by Curvature Divergence at the Spectral Boundaries (N = 4, 5) — RCD Program, Technical Note CC-

Technical Note CC (CC-0 to CC-3) of the RCD program (continues I-F0, DOI 10.5281/zenodo.24064727). Question: can a single finite coherence ρ ≥ 0 on ℂ^N, with no prior spacetime, produce a four-dimensional scenario with signature 1+3 and a metric g? This note records a construction that reached an explicit metric and was closed by a pre-registered death condition; it does not claim a derived spacetime. Prior art comes first. A two-report prior-art audit with cross-verification (reports, log and consolidation included) classifies as INHERITED: the cone of 2×2 Hermitian matrices with 4·det as the Lorentz form and SL(2,ℂ) (Baez; Arrighi–Patricot), its physical reading in the qubit — velocity, mass, purity, filtering as Lorentz, concurrence, a pure state being "like a photon" (Chen et al.; Bogdanov et al.; Burns–Greenfield–Dressel; Verstraete et al.; Rungta et al.; Fullwood–Vedral–Guzmán-González) —, the set of compressions (Fan–Pall 1957), the Löwner order as causal order (Mori–Šemrl), the density of compressions as a projection of an orbital measure (Olshanski; Faraut; Baryshnikov), the logic "causal order + volume = metric" (Finkelstein 1969; Hawking–King–McCarthy; Malament; Bombelli–Lee–Meyer–Sorkin) and the program of obtaining 3+1 from binary alternatives (Weizsäcker; Finkelstein; Müller–Masanes; Höhn–Müller; Gil). Three close neighbours (Finkelstein 1969, Brody–Hughston 2005, Gil 2026) are cited as the audit reports them, with a declaration of how each was read. OWN, as far as the two searches reached (medium confidence): (1) reading the views V†ρV of an N-level coherence through framed binary windows V ∈ St(2,N) as events — the spectral causal body 𝒟(ρ) = {2λ_{N−1} ≤ u ≤ 2λ₁, 2λ_N ≤ v ≤ 2λ₂, u ≥ v}, a 4-dimensional region bounded by null surfaces at the eigenvalues of ρ, with the trace as time function; (2) the soldering on the space of windows, e_P(X) = X†B + B†X with B = P⊥ρP: signature (1,3) plus a kernel of dimension 4N − 12 exactly where rank B = 2, and no timelike directions for pure ρ; (3) the coherential variance M̄(a) = E[V†ρ²V | a] − a² in closed form (M̄ = (α − a)(a − β) in the central chamber); (4) a specific metric: the pushed-forward invariant measure of the views as volume (Principle of Coherential Volume) and the cone by pullback of the coherential diffusion tensor (Rule C-0); (5) the computed results. Four postulates are declared, not derived: the governing rule C ⟹ g_μν (thesis of the program, not a result), Gate F (a framed binary cut is physical data), the Principle of Volume and Rule C-0. Results. CC-1 (N = 4): closed-form density of views, constant in the core; the volume metric g = (w/8)^{1/2}η has a flat core, curved outer chambers, R ~ d^{−3/2} at the boundary and undeformed cones; a 200,000-sample check agrees (one badly designed criterion failed, is archived, and was rerun with a corrected, pre-fixed criterion). CC-2 (N = 4): with Rule C-0 the metric is no longer conformally flat — Weyl² ≠ 0 in the four chambers and non-radial null geodesics are deflected — but at the outer spectral boundaries R ~ d⁻¹ and Kretschmann ~ d⁻³. CC-3 (N = 5, new input formulas checked by sampling): same qualitative picture, with R ~ d^{−5/2} and Kretschmann ~ d⁻⁵, i.e. stronger than for N = 4. The three death conditions (isotropic variance everywhere; curvature divergence at the outer boundaries; no deflection of null geodesics) and their operational definitions were written in the script headers and hashed before running; the second one triggered in both computations and the principal ratified both closures. One spectrum per N was computed; N ≥ 6, internal chamber walls and degenerate spectra were not. Not claimed: spacetime, gravity, Einstein's equations, absence of singularities. Scripts, outputs and SHA-256 manifest included; all charges of the adversarial rounds documented. English and Spanish versions; the Spanish text prevails.