IndisputableMonolith.CrossDomain.CognitiveStateSpace
CognitiveStateSpace defines an integrated model combining sense, emotion, and memory into a single cognitive state space. Cross-domain researchers extending Recognition Science to cognitive modeling would cite its surjectivity results on the component projections. The module supplies type definitions for the state space together with direct lemmas establishing that each projection reaches every element of its target domain.
claimLet $S$, $E$, and $M$ denote the sense, emotion, and memory spaces. The cognitive state space is the product $C = S × E × M$ equipped with projection maps $π_S : C → S$, $π_E : C → E$, $π_M : C → M$ that are each surjective.
background
The module operates in the cross-domain extension of Recognition Science, importing only Mathlib for basic set and function constructions. It introduces Sense as the domain of sensory inputs, Emotion as the space of affective states, MemorySystem as the structure for storage and retrieval, and CognitiveState as their composite product. The supplied doc-comment highlights that the sense projection is surjective, with parallel results for the other components ensuring every configuration in each subsystem is attainable.
proof idea
This is a definition module. It declares the component types and the CognitiveState constructor, then establishes the three surjectivity lemmas (senseProj_surj, emotionProj_surj, memoryProj_surj) by direct application of standard Mathlib tactics for existential witnesses in product spaces.
why it matters in Recognition Science
The module supplies the foundational state space that supports downstream results on cognitive non-collapse and state enumeration within the Recognition framework. It extends the core J-cost and phi-ladder structures to mental domains, preparing the ground for applications of the eight-tick octave to periodic cognitive processes.
scope and limits
- Does not specify transition rules or dynamics on the state space.
- Does not link to physical constants or the T0-T8 forcing chain.
- Does not prove uniqueness or minimality of the product representation.
declarations in this module (19)
-
inductive
Sense -
inductive
Emotion -
inductive
MemorySystem -
theorem
senseCount -
theorem
emotionCount -
theorem
memorySystemCount -
abbrev
CognitiveState -
theorem
cognitiveStateCount -
theorem
senseProj_surj -
theorem
emotionProj_surj -
theorem
memoryProj_surj -
theorem
notCollapsedToSense -
theorem
notCollapsedToEmotion -
theorem
notCollapsedToMemory -
theorem
notCollapsedToPair1 -
theorem
notCollapsedToPair2 -
theorem
notCollapsedToPair3 -
structure
CognitiveStateSpaceCert -
def
cognitiveStateSpaceCert