IndisputableMonolith.Information.RecognitionBremermann
This module defines the Bremermann bound in Recognition Science as one resolution per 8-tick cycle. In units with τ₀ = 1 the rate equals 1/8 resolutions per tick. It supplies the core constants and lemmas that tie information processing limits to the eight-tick octave. Researchers modeling computational bounds inside RS cite these objects when deriving energy-per-resolution or n_resolutions_time.
claimThe Bremermann bound is the constant rate $1/8$ resolutions per tick, where the octave period equals eight ticks and τ₀ = 1.
background
The module imports the RS time quantum τ₀ = 1 tick from Constants. It introduces the eight-tick octave (period 2³) and the associated resolution rate. Sibling definitions include bremermannBound (the rate itself), octave_is_eight (the period identity), bound_value, bound_pos, one_resolution_per_8tick, energyPerResolution, and n_resolutions_time.
proof idea
This is a definition module. It states bremermannBound directly from the octave structure, then proves bound_value, bound_pos, energy_pos and related facts by algebraic reduction using the imported time quantum and the T7 octave identity.
why it matters in Recognition Science
The module realizes the T7 eight-tick octave inside the information domain and supplies the bound used by downstream results on resolution counting and energy cost. It connects the forcing chain step T7 to concrete information limits without introducing new hypotheses.
scope and limits
- Does not derive the octave period from the phi-ladder or RCL.
- Does not treat continuous-time or relativistic corrections.
- Does not compute numerical values for specific physical systems.