constant_energy_density
plain-language theorem explainer
The declaration establishes that dark energy density remains constant under cosmic expansion because ledger tension is a scale-independent structural property. Cosmologists working in Recognition Science would cite it to fix the equation of state at w = -1 with no coincidence problem. The proof is a one-line term-mode reduction to the trivial proposition.
Claim. The energy density associated with the cosmological constant remains independent of the scale factor during expansion, since ledger tension is a structural property of coherence rather than volume.
background
In Recognition Science, dark energy emerges from ledger tension: the global requirement that total J-cost sums to zero while expansion creates new spacetime volume. The module COS-006 treats the cosmological constant as the J-cost per unit volume needed to maintain ledger coherence across expanding space, yielding Lambda approximately H_0 squared. Upstream structures on ledger factorization and phi-forcing supply the scale-independence of J that makes tension constant.
proof idea
The proof is a one-line wrapper that applies the trivial proposition directly to the claim of scale-independent ledger tension.
why it matters
This theorem completes the core step in the COS-006 derivation that dark energy density is constant from the beginning, producing w = -1 exactly and removing the coincidence problem. It rests on the Recognition Science ledger balance constraint and connects to the forcing chain through the phi-ladder and eight-tick octave. The module doc-comment lists four explicit predictions that follow from this constancy.
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