Formal theories reveal structural complexities of certification in computational environments, suggesting deeper implications.
Formal theories often collapse many derivations to a single canonical certified record: the question is whether that collapse exhausts everything structurally significant about the realized routes that produced it. This paper is the internal origin theorem of a larger program: we prove that it does not, on named machine-checked carriers in the Infinity Compression native environment. We prove universal collapse of standard Phase-2 extraction to a unique bare certificate; a reflective split (canonical bare certification alongside nontrivial enriched autonomous mirror structure); strict refinement of the typed forgetful map π_A (existence of distinct enriched reflective splits with equal π_A-image); and a forgetful--fiber layer in which the canonical fiber is nontrivial and role assignme
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Nova Spivack (2026) studied this question.
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