E_coh_storage
plain-language theorem explainer
Recognition Science fixes the coherence energy quantum at phi to the power of negative five in native units. Engineers and physicists modeling storage limits on the phi-ladder cite this constant when scaling J-cost energies from chemical to nuclear regimes. The declaration is a direct one-line abbreviation that supplies the base scale without invoking lemmas or tactics.
Claim. $E_0 = phi^{-5}$ where $E_0$ is the coherence energy quantum in RS-native units.
background
The EN-004 module derives energy storage limits from the phi-ladder and J-cost structure. Energy takes the form E = J(x) · E_coh with J(x) = ½(x + x^{-1}) - 1, which vanishes at the ground state x = 1 and diverges at the extremes. The module states that E_coh = phi^{-5} eV supplies the fundamental quantum, yielding a chemical limit of one quantum per bond and a nuclear limit at rung k ≈ 45.
proof idea
The declaration is a direct definition that sets E_coh_storage equal to phi raised to the integer power -5. No lemmas from the upstream imports are applied; the abbreviation serves as the constant base for all subsequent energy expressions in the module.
why it matters
This definition anchors the EN-004 hierarchy theorems, including E_coh_storage_pos, jcost_energy, and phi_rung_energy, which establish non-negativity and the phi^45 nuclear-to-chemical ratio. It realizes the Recognition framework prediction that storage efficiency is quantized on the phi-ladder (T6 fixed point, T7 eight-tick octave) and supplies the scale for mass-energy equivalence at the ultimate limit.
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