Paper 2 · Section 12Boundary
From a brittle edge to a quantitative boundary analysis
The results connect stable reconstruction diagnostics, executable organization, causal encapsulation and operational identification. They provide explicit tests for the next stage of the localization programme.
12 Conclusion
An exact relational candidate rule can be mathematically determinate and still be fragile under small changes in its underlying instruments. The masked encoder demonstrates that fragility in the published minimal-target projection: a tiny new singleton signal deletes a projected edge while substantial joint information and the contrast of a fixed scheduled return remain. A continuous weight cannot reproduce that exact positive support along the family.
Directed statistical deficiency supplies a different and stable information question. It distinguishes common-conditional padding from genuinely joint coding and gives an exact quantitative repair of the masking diagnostic. Separating that reconstruction question from native execution and resource-relative cut simulation prevents strong information, physical return and simulator obstruction from being treated as synonyms.
A realized relational process can be encapsulated through a strong marked interface when its joint record and successor-class laws close under the admitted interactions. Matching causal contexts then preserve complete finite histories, and controlled approximations incur explicit budgets. Transferring a cut profile demands more than target fidelity: the comparison processes must retain their resource meaning as well.
Finally, exact-law identification reaches only attributes constant on the declared operational-equivalence classes. Functional premises that leave a phenomenal predicate unconstrained do not determine it. SPC-2 already supplies a connecting constitutive premise; the present results audit the functional boundary beneath it rather than pretend that the premise was missing. The outcome is a strengthened and more transparent analysis of localization candidates, not a derived unique psychophysical replacement. It leaves the proposed awareness-first interpretation available for philosophical and empirical assessment while making the mathematical obligations independently inspectable.