IndisputableMonolith.Streams
The Streams module defines boolean streams as infinite displays together with patterns, window-to-Z maps, cylinders, and period-8 extensions. Researchers in the measurement layer cite it for the eight-tick stream invariants. The module consists entirely of definitions with no theorems or proofs.
claimA boolean stream is an infinite sequence $s : ℕ → {0,1}$ serving as a display. The module introduces finite patterns, a window-to-Z map, cylinder sets in the product topology, and the periodic extension operator with period 8.
background
Recognition Science models discrete sequences via the eight-tick octave (T7) of period 8. The module supplies the Stream type as boolean sequences for infinite displays, Pattern for finite segments, a map sending windows to integers Z, Cylinder for basic open sets, and the periodic extension with period 8 to enforce the octave periodicity. These objects are imported only from Mathlib and provide the discrete foundation before any continuous-time scaffold.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the stream definitions re-exported by IndisputableMonolith.Core.Streams and used in IndisputableMonolith.Measurement for eight-tick invariants plus the CQ score. It fills the discrete display structures required by T7 in the forcing chain before measurement-layer applications.
scope and limits
- Does not contain theorems or proofs.
- Does not model continuous-time dynamics.
- Does not define J-cost, defect distance, or the phi-ladder.
- Does not import other Recognition Science modules.
- Does not address mass formulas or coupling constants.
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