IndisputableMonolith.Streams
The Streams module defines Boolean streams as infinite displays to support periodic pattern modeling in Recognition Science. It introduces Stream, Pattern, Cylinder, and extendPeriodic8 for eight-tick structures. Measurement and Core modules cite these primitives to access stream invariants. The module consists of definitions and basic lemmas with no complex proofs.
claimA stream is a map $S: ℕ → {0,1}$ as an infinite Boolean display; a pattern is a finite window; Cylinder denotes agreement on initial segments; extendPeriodic8 produces period-8 extensions.
background
The module sets the stream layer for Recognition Science's eight-tick octave (T7). Stream is the core infinite Boolean display; Pattern and Z_of_window handle local windows and zero counts; Cylinder and extendPeriodic8 manage periodic extensions of period 8. It imports only Mathlib and supplies the discrete display primitives used by downstream measurement scaffolds.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
This module feeds the eight-tick stream invariants into IndisputableMonolith.Core.Streams and IndisputableMonolith.Measurement, where the latter re-exports them for the measurement layer and CQ score. It supplies the stream primitives required for T7 in the unified forcing chain.
scope and limits
- Does not derive constants, masses, or J-cost relations.
- Does not address continuous-time dynamics beyond re-export.
- Does not prove uniqueness or fixed-point properties.
- Does not connect streams to spatial dimensions or alpha band.
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