Persistent Individuation and the Physical Preconditions of Mathematical Representation: From Maintained Distinction to Stable Comparison
Develops the Persistence–Individuation Principle and Mathematical Individuation Conjecture, arguing that stable operand-sensitive physical comparison requires persistent contextual individuation and identifying retained registration as the Registration-Theoretic physical basis for stable mathematical representation.
Scope
Establishes a formal necessity relation between stable operand-sensitive comparison and persistence-bearing contextual individuation, then proposes retained registration as the RT physical mechanism supporting that requirement. It does not derive number, scalar, vector, tensor, metric, geometry, or abstract mathematics from registration, and it does not establish that Registration Theory is the unique ontology capable of supporting mathematical representation.
Relation to other papers
- Builds on Canonical Foundations of Registration Theory
- Builds on Persistent Registration Lineage Theorem
- Extended by Closure-Induced Complex Structure
Relevant research claims
- InterpretationPersistence–Individuation Principle
- Exact TheoremPersistent Individuation as a Necessary Condition for Stable Comparison
- ConjectureMathematical Individuation Conjecture
Keywords
- Registration Theory
- persistent registration
- persistent individuation
- mathematical representation
- stable comparison
- physical identity
- contextual equivalence
- foundations of mathematics
- foundations of physics
- relational ontology
- scientific representation
- emergent mathematics