Manuscript VIII-C@3 · VIII-C-v3.tex · section · 3b070436

Exact clocks and germ modes

Configurations, clocks, and command domains › Exact clocks and germ modes · lines 629–658

VIII-C@3#eq:clocks, VIII-C@3#eq:s-flow

Finite codes use exact dyadic parameters

s = j 2^{- d}, σ = j_{A} 2^{- d_{A}}, t_{col} = j_{col} 2^{- d_{col}} .

Recorded execution slots satisfy

τ = k Δ τ, Δ τ > 0.

A geometric segment can be parametrized by

s = s_{a} + v_{s} (τ - τ_{a}),

or the analogous law for $σ$ or $t_{col}$ . Only designated endpoint codes need lie on the finite grid.

Incoming and outgoing germs at zero have the same exact parameter but different incidence modes. We write $0^{-}$ and $0^{+}$ for those modes, not for rounded real numbers.

A discrete incidence or source command may consume an execution slot while leaving its slicing parameter fixed. No continuous interpolation of that discrete command is asserted. The execution clock is not identified with proper time or a relational lapse.

Displayed formulas in this passage

VIII-C@3#eq:clocks · line 632
$s = j 2^{- d}, σ = j_{A} 2^{- d_{A}}, t_{col} = j_{col} 2^{- d_{col}} .$
VIII-C@3#eq:s-flow · line 643
$s = s_{a} + v_{s} (τ - τ_{a}),$
unlabeled · line 639
$τ = k Δ τ, Δ τ > 0.$

Exact clocks and germ modes

Displayed formulas in this passage

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