E_coh
plain-language theorem explainer
E_coh defines the coherence quantum as the real number φ^{-5}, where φ is the golden ratio forced by self-similarity. Researchers tracing energy scales in discrete ledgers with J-cost would cite this constant when normalizing ħ in RS units. The declaration is a direct abbreviation that performs no computation beyond the power operation.
Claim. $E_ {coh} := φ^{-5}$, where $φ = (1 + √5)/2$ is the golden ratio.
background
The Phi Forcing module establishes that a discrete ledger equipped with J-cost and self-similarity forces the scale ratio to satisfy x² = x + 1. J-cost is the function J(x) = (x + x^{-1})/2 - 1, which is zero only at x = 1; non-trivial self-similarity therefore selects the unique positive root φ. The module imports LawOfExistence, DiscretenessForcing and LedgerForcing to supply the ledger structure and the prior forcing steps that make φ available.
proof idea
This is a direct definition. It assigns the value φ raised to the integer power -5 to the identifier E_coh using the standard real exponentiation operation.
why it matters
E_coh supplies the RS-native value of ħ once φ is forced at T6 of the unified forcing chain. It anchors the coherence energy scale that enters the mass formula and the Berry creation threshold φ^{-1}. Although the current module records no downstream uses, the constant closes the link between the eight-tick octave and the quantum constants listed in the framework primer.
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