IndisputableMonolith.Streams
The Streams module defines Boolean streams as infinite displays with eight-tick periodicity. Measurement-layer code cites it for stream invariants and the CQ score. Core.Streams also imports the definitions. The module is purely definitional and contains no proofs.
claimA stream is a map $S : ℤ → {0,1}$ viewed as an infinite Boolean display; auxiliary objects include finite patterns, the zero-count function $Z$ on windows, cylinders, and the period-8 extension operator.
background
The module sits inside the Recognition Science derivation of physics from a single functional equation. It supplies the discrete-time objects required by the eight-tick octave (T7). Sibling definitions introduce Stream, Pattern, Z_of_window, Cylinder, and extendPeriodic8 together with their basic properties (non-negativity, zero cases, periodicity).
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the eight-tick stream primitives re-exported by IndisputableMonolith.Measurement for the measurement layer and CQ score. It also supports IndisputableMonolith.Core.Streams. These definitions realize the period-2^3 structure demanded by the forcing chain at T7.
scope and limits
- Does not treat continuous-time or real-valued streams.
- Does not introduce measures or probabilities on streams.
- Does not connect streams to J-cost or defectDist.
- Does not prove any uniqueness or completeness statements.
used by (2)
declarations in this module (19)
-
def
Stream -
def
Pattern -
def
Z_of_window -
lemma
Z_of_window_nonneg -
lemma
Z_of_window_zero -
def
Cylinder -
lemma
mem_Cylinder_zero -
lemma
Cylinder_zero -
def
extendPeriodic8 -
lemma
extendPeriodic8_zero -
lemma
extendPeriodic8_eq_mod -
lemma
extendPeriodic8_period -
def
sumFirst -
lemma
sumFirst_zero -
lemma
sumFirst_eq_Z_on_cylinder -
lemma
sumFirst8_extendPeriodic_eq_Z -
lemma
extendPeriodic8_in_cylinder -
lemma
sumFirst_nonneg -
lemma
sumFirst_eq_zero_of_all_false