A Planck-Based Unified Framework for Dark Energy and Dark Matter

Dark matter and dark energy are the two largest explanatory domains of modern cosmology: galaxies rotate faster than expected in their outskirts, clusters produce lensing too strong to be accounted for by the observed matter, and the expansion accelerates at late times. ΛCDM parameterizes this picture successfully; the question of what the two dark components are remains open. This paper ties the dark sector to a single identity within the ΨD (Dimensional Flow Cosmology) framework: the entire energy budget consists of four states of the same planckon ledger — E(d) = (d+1)εP, U(d) = (3−d)εP. Dark energy is the closed reserve of d0 nodes that have never formed a bond; dark matter is the d1 chain frozen at its first bond; radiation is the d2 mode; visible matter is the d3 closure. The mapping is not left as a hypothesis: given the observational defining properties of the budget items, its uniqueness is proven (Proposition 2). Darkness is derived: d1 has no closed loop (it cannot radiate), d0 has no position (it cannot cluster). Five main results are established. (i) The cosmic coincidence is not an accident: ΩDE/ΩDM = 3·(Nd0/Nd1) is a ledger identity; the closed solution of the freeze kinetics (the three-axis binomial), with a single dynamical input — the zero-parameter stopping scale Af/Ac = 1.46 — yields Nd0/Nd1 = 0.861, within 0.3% of observation (Propositions 14–15). (ii) The smallness of 10⁻¹²² ρP is not fine-tuning but a counter reading: 10⁻¹²² = N⁻², N ≈ 10⁶¹. (iii) Expansion is not a push but fold release: each d0→d1 phase change expends εP of work and releases one fold; from this w = −1 + Γ/3H is derived, the phantom ban w(a) ≥ −1 is a theorem, and the singleanchor solution gives w₀ = −0.85. The observationally locked set (w₀ = −0.844, wa = −0.219) yields χ² = 8.86 in the DESI DR2 BAO test (ΛCDM: 10.56; 13-component vector, within-tracer correlated covariance). (iv) Dark matter is born in the freeze that follows the flash; dark energy initiates acceleration at z ≈ 0.66 and dominates the budget at z ≈ 0.35. (v) The visible-to-dark matter ratio is predicted by path counting to be 5 (observed 5.36). The linear layer is built from the event clock (Propositions 17–18): a ≈ 2.3% suppression in σ₈ and ΔNeff = 0 are two directly testable records. Every numerical claim is presented with its class — derivation, anchor, or input — stated explicitly; the inventory is in Table 3.