付録D（Appendix D）
Symbol Index

Mathematical Notation by Emergence Stage

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「記号は意味を運ぶ。意味は段階に縛られる。」
Symbols carry meaning. Meaning is bound to stage.

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D.1 Stage 1: CTS (Chapter 1.0)

Symbol	Name	Meaning
CTS	Collapse Tension Substrate	Pre-spatial permission domain
P	Permission	Logical admissibility of collapse
C	Collapse	Selection of one resolution from many
τ	Tension	Coexistence of incompatible permissions

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D.2 Stage 2: Difference (Chapter 2.0)

Symbol	Name	Meaning
Δ	Difference	Non-equivalence of outcomes
A	Asymmetry	Operational distinguishability
≠	Distinction	Two outcomes are not the same

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D.3 Stage 3: Direction (Chapter 3.0)

Symbol	Name	Meaning
→	Order	Logical dependency sequence
∇Φ	Intent Gradient	Collapse ordering tendency (NOT spatial)
d	Direction	Consistent ordering across collapses

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D.4 Stage 4: Memory (Chapter 4.0)

Symbol	Name	Meaning
M	Memory	Prior outcomes influencing future permissions
∇×F	Curl / Self-Reference	Recursive collapse structure (NOT rotation)
↺	Return	Later states referencing earlier states

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D.5 Stage 5: Locking (Chapter 5.0)

Symbol	Name	Meaning
L	Locking	Self-reinforcing recursive alignment
∇²Φ	Laplacian / Consistency	Recursive equilibrium measure (NOT diffusion)
S	Shell	Stabilized region of locked recursion
∂S	Boundary	Pattern influence limit (NOT surface)

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D.6 Stage 6: Space (Chapter 6.0)

Symbol	Name	Meaning
X	Space	Capacity for coexistence without exclusion
d(a,b)	Distance	Remembered separation cost
gμν	Metric	Record of recursive differentiation
xi	Coordinates	Labels for stabilized separations

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D.7 Usage Warning

⚠️ Spatial interpretation of operators is forbidden before Chapter 6.0

• ∇Φ is NOT a spatial gradient until Stage 6
• ∇×F is NOT rotation until Stage 6
• ∇²Φ is NOT diffusion until Stage 6

Pre-geometric interpretations must be strictly maintained.

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「記号を守れ。意味が守られる。」
Guard the symbols. The meaning will be preserved.

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