bremermannBound
plain-language theorem explainer
bremermannBound supplies the maximum debt-resolution rate in Recognition Science as the reciprocal of the octave period. Information theorists working in the RS framework cite it when deriving energy or time bounds on recognition processes. The declaration is a direct one-line assignment to 1/octave, which evaluates to 1/8 once the upstream octave definition is unfolded.
Claim. The maximum resolution rate in Recognition Science is defined by $B = 1/8$ resolutions per tick, where the denominator is the octave period of eight fundamental time quanta with $τ_0 = 1$.
background
Recognition Science reinterprets Bremermann's classical computation limit through the eight-tick cycle that forms the minimum period for one complete debt-resolution cycle. The module sets the local theoretical setting as Q7, where the bound is tighter than mass-energy limits because each resolution consumes a φ^5 energy quantum (with ℏ = φ^{-5}). Upstream, Constants defines octave as 8 * tick with tick := 1, and the same constant appears in MusicalScale and UniversalForcing.Strict.Music as the ratio 2 or the period 8τ_0.
proof idea
The declaration is a one-line definition that directly assigns the reciprocal of the octave constant. It depends on the upstream octave definition from Constants (and its siblings in Astrophysics and MusicTheory) without further reduction steps.
why it matters
This definition anchors the information bounds and feeds the parent theorems bound_from_phi (which yields the power bound φ^5/8), bound_pos, one_resolution_per_8tick, and n_resolutions_time. It implements the T7 eight-tick octave from the forcing chain, enforcing the minimum time for an R̂ debt-resolution cycle. The module addresses the open question of how the RS limit relates to classical Bremermann bounds.
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