Causal Reconstruction: Elementary Succession and the Planck Energy

This article derives the causal structure of the reconstruction programme — previously assumed as a Lorentzian background — from the cost of reconstructive transitions, and on that basis recovers ℏ and the Planck energy as geometric quantities rather than primitive inputs. Status markers: [E] established, [C] conditional, [O] open. The first six articles of the programme assumed a Lorentzian causal structure on the physical manifold without deriving it from the geometric hypotheses (H1–H5); this paper proposes a derivation. Causality is defined not by a presupposed spacetime metric but by the cost of a reconstructive transition: two states are elementarily causally successive when the infimum of the reconstructive action along paths connecting them equals one action quantum. This is the atomic, locally closed regime — a single elementary step; its generalisation to minimal entropic closures of arbitrary length, and with it tunnelling, superposition, decoherence and measurement, is the subject of Causal Succession by Segments: Tunnel Effect, Superposition, and Measurement in the Reconstructive Order. Two results separate cost from causality. The reconstructive cost is symmetric under path reversal, so it defines a geometric distance, not an oriented relation [E]. The arrow comes from entropy production: the Fisher information appearing in the cost is, through the de Bruijn identity, the entropy-production rate, supplying an intrinsic orientation [E]. The transitive closure of elementary succession is then a strict partial order, because the relative entropy is a strictly increasing order-potential [E]. From the cosmological closure constant L and the primitive constants c and G — and without ℏ — three quantities are derived: an action quantum amin = c³Tmin²/G, a minimal time τmin = Tmin/c, and a reconstructive energy Erec = c⁴Tmin/G, where Tmin = (c/H0)·exp(−L) is the UV cutoff; they satisfy amin = Erec · τmin exactly [E]. Calibrating Tmin to the Planck length ℓP, Erec coincides with the Planck energy and amin with ℏ [C]. The conceptual inversion is explicit: ℏ is no longer a primitive parameter but the action accumulated over the minimal reconstructible causal interval — a geometric quantity once Tmin is fixed — and the Planck energy is the energy cost of one elementary reconstruction step. Physical time emerges as a causal counting variable, a chain of N steps giving Δτ = N τmin [C], and causal histories carry actions that are integer multiples of amin [C]. The action quantum is fixed by modular closure: a complete modular cycle carries action h = 2π amin while the action per modular angle is amin = ℏ, which excludes the alternative identification amin = h; the Bohr–Sommerfeld condition then reads as a closed causal history being an integer number of complete modular cycles [C]. The continuum variational limit of iterated elementary succession yields the Madelung–Schrödinger equation, established by Γ-convergence in Discrete-to-Continuum Limit of Causal Chains in the Kähler Reconstruction. Status. [E] the three quanta without ℏ and their exact relation amin = Erec·τmin; the symmetry of the cost; the entropy-production arrow (de Bruijn); the strict partial order · [C] the causal-counting interpretation of time; the quantisation of histories; Bohr–Sommerfeld; and the cosmological calibration Erec = EP, which still requires the observed closure constant as input · [O] three problems remain — the attainment of the cost infimum (existence of W2 geodesics); a strictly positive lower bound on the elementary step (the existence of a smallest non-zero closed modular orbit, a modular gap, which would turn the bound into a theorem); and the cosmological origin of the specific value Tmin = ℓP, the causal structure being well-defined for any Tmin.