Appendix B: Formal Rules

付録B(Appendix B)
Formal Rules of the Construction

CTS Axioms and Constraints


「法則なくして、導出なし。」
Without rules, no derivation.


B.1 Foundational Axioms

Axiom 1: CTS Existence

There exists a pre-spatial domain (CTS) in which collapse may occur.

Axiom 2: Collapse Produces Difference

Collapse selects one outcome from multiple admissible outcomes, creating asymmetry.

Axiom 3: Collapse is Rule-Based

Collapse follows permission constraints, not random selection.

Axiom 4: Prior Collapse Constrains Future Collapse

Collapse outcomes modify subsequent permission structures (memory).


B.2 Prohibition Rules

Rule P1: No Spatial Concepts Before Derivation

Distance, location, extension, volume, area, and containment may not be used before Chapter 6.0.

Rule P2: No Temporal Concepts Before Derivation

Before, after, during, and simultaneous refer only to logical dependency, not temporal sequence, until time is derived.

Rule P3: No Object Language Before Emergence

Particle, field, wave, and entity may not be used until after locking (Chapter 5.0).


B.3 Emergence Rules

Rule E1: Emergence by Necessity

A concept is derived when its absence creates contradiction and its introduction resolves that contradiction using only prior elements.

Rule E2: Non-Retraction

Once a stage is completed, it cannot be undone or questioned in subsequent chapters.

Rule E3: Minimal Introduction

Introduce only the minimum structure required to resolve the current contradiction.


B.4 Operator Correspondence

StageOperatorPre-Geometric Meaning
Direction∇ΦOrdered collapse tendency
Memory∇×FSelf-referential collapse structure
Locking∇²ΦRecursive consistency equilibrium

「形式は自由ではない。束縛である。」
Formalism is not freedom. It is discipline.


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