mapDeltaTime_fromZ
plain-language theorem explainer
The lemma shows that the time delta map applied to the integer-generated unit fromZ δ n returns U.tau0 scaled by n. Researchers converting time intervals over integer subgroups in Recognition Science unit mappings cite this result. The term proof reduces directly to the general mapDelta_fromZ lemma instantiated at timeMap U followed by definition unfolding.
Claim. For nonzero integer $δ$, RS unit structure $U$, and integer $n$, the time component of the delta map satisfies mapDeltaTime($δ$, $U$, fromZ($δ$, $n$)) = $τ_0(U) · n$.
background
The UnitMapping module handles deltas via the subgroup generated by a fixed nonzero integer δ, using integers as abstract placeholders. RSUnits bundles the native units with τ₀ (fundamental tick duration), ℓ₀ (voxel), and c satisfying c τ₀ = ℓ₀. tau0 appears in Constants, Derivation, and Compat as the tick duration, while RSNativeUnits.U sets the gauge with τ₀ = 1 tick. The upstream mapDelta_fromZ from LedgerUnits supplies the general reduction mapDelta δ hδ f (fromZ δ n) for arbitrary f; timeMap U extracts the time component via U.τ₀.
proof idea
The term proof applies mapDelta_fromZ with f instantiated to timeMap U. It then uses simpa to rewrite via the definitions of mapDeltaTime and timeMap together with add_comm.
why it matters
This result guarantees linear scaling of time deltas with integer rung n under the RS unit gauge, consistent with τ₀ as the base tick. It supports the unit-mapping layer that feeds constant derivations (τ₀ from hbar, G, c) in the Recognition Science framework. No downstream uses appear in the used_by edges.
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