Volume 0 — The Collapse Language
Foundation of Binary Existence and φ-Constrained Language
This volume establishes the fundamental language of collapse, built on binary existence with the golden constraint (no consecutive 11s). From the self-referential origin ψ = ψ(ψ), we develop the complete formal language system that underlies all subsequent mathematics.
Chapter Index
Chapter 000: SelfCollapse
ψ = ψ(ψ) as the Origin of All Structure
The foundational chapter establishing self-referential collapse as the origin of all mathematical structure. Introduces the fundamental equation and its implications.
Chapter 001: BitExistence
Binary Information as Ontological Foundation
Establishes binary {0, 1} as the fundamental unit of existence. Shows how all reality emerges from binary information under constraints.
Chapter 002: PhiAlphabet
Defining Σφ = {00, 01, 10} as the Collapse-Safe Language
Introduces the φ-alphabet by excluding 11 to prevent structural collapse. The foundation of all safe trace construction.
Chapter 003: TraceGrammar
Syntax Trees over φ-Constrained Trace Compositions
Develops the grammatical rules for composing valid traces from the φ-alphabet. Establishes syntax for structural expressions.
Chapter 004: ZForm
Zeckendorf Decomposition as Canonical Collapse Blueprint
Shows how every natural number has a unique representation as sum of non-consecutive Fibonacci numbers, establishing canonical forms.
Chapter 005: HSEncode
Hurt–Sada Differential Encoding of Trace Pathways
Introduces differential encoding schemes that preserve the φ-constraint while enabling efficient trace representation.
Chapter 006: PhiRank
Dimensional Lifting of Collapse Traces into Tensor Fields
Develops the concept of φ-rank, showing how traces lift into higher-dimensional tensor structures.
Chapter 007: TraceMachine
Automata for Collapse-Valid φ-Language Recognition
Constructs finite state machines that recognize and generate valid φ-language expressions.
Chapter 008: CollapseToken
Structural Symbol Generator for φ-Based Parsing
Develops tokenization schemes for parsing collapse expressions into structural components.
Chapter 009: TraceLexicon
Minimal Collapse Vocabulary and Valid Expression Fragments
Establishes the minimal vocabulary needed for expressing all collapse structures.
Chapter 010: NestCollapse
Self-Embedded Trace Folding and Recursive Grammar
Shows how traces can embed within themselves, creating recursive grammatical structures.
Chapter 011: CollapseCompress
Entropy-Bounded φ-Trace Optimization Algorithms
Develops compression algorithms that maintain φ-constraint while minimizing entropy.
Chapter 012: SyntaxTree
Hierarchical Collapse Expression Trees for Tensor Construction
Constructs syntax trees that represent collapse expressions hierarchically.
Chapter 013: AlphabetGen
Procedural Construction of Σφ-Conformant Trace Units
Algorithms for generating valid trace units procedurally while maintaining constraints.
Chapter 014: GrammarClassify
Collapse Grammar Equivalence over Structural Path Spaces
Classification of grammatical structures and their equivalence relations.
Chapter 015: CollapseMetric
Defining Distance and Dissimilarity over Trace Topology
Introduces metric structures for measuring distances between collapse traces.
Key Concepts Introduced
- Self-Referential Foundation: ψ = ψ(ψ) as the origin
- Binary Constraint: No consecutive 11s (φ-constraint)
- Golden Base: Zeckendorf representation
- Trace Grammar: Formal language over Σφ = {00, 01, 10}
- Tensor Lifting: From traces to higher dimensions
- Canonical Forms: Unique representations
Dependencies
This volume has no dependencies - it establishes the foundation for all subsequent volumes.
Next Steps
- Volume 1: Build arithmetic on trace structures
- Volume 2: Develop logic and set theory
- Volume 3: Construct algebraic systems
"In the beginning was ψ, and ψ was with ψ, and ψ was ψ(ψ)."