What question did this study set out to answer?

Establish a rigorous mathematical foundation to determine when a theorem corpus is independently reconstructible from declared proof routes, verified imports, and a trusted base.

August 14, 2026Open Access

Mechanizing the Identity-Persistence Forcing Architecture: From Declared Regimes to Independently Reconstructible Verdict Theorems

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Establish a rigorous mathematical foundation to determine when a theorem corpus is independently reconstructible from declared proof routes, verified imports, and a trusted base.
Formulated a base-relative monotone closure operator to compute the least fixed point of reconstructible theorems on finite acyclic dependency graphs.
Developed a symbolic provenance calculus using semiring-style Boolean expressions to induce dual certificate families of minimal completion sets and blocking cuts.
Evaluated computational complexity bounds and performed reductions from weighted hitting set to analyze the Minimum Verification Cost problem.
Demonstrated that fixed-set replay and reconstructibility closure evaluation scale linearly with the size of the proof route directed acyclic graph.
Proved that finding a minimum-cost set of unresolved obligations to reconstruct a target theorem is NP-hard in unrestricted architectures, while admitting a linear-time decision procedure for read-once structures.
Established exact blocker duality enabling bidirectional recovery between minimal completion sets and minimal blocking cuts via hypergraph transversals.

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Implication

Formal theoretical analysis develops a symbolic provenance framework for theorem reconstruction in acyclic proof architectures, highlighting computational limits in verification cost optimization.

Cite This Study

Devin Bostick (2026) studied this question.

synapsesocial.com/papers/6a7ec7bab70b84ec8b914477 https://doi.org/10.5281/zenodo.21898137

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Implication

Formal theoretical analysis develops a symbolic provenance framework for theorem reconstruction in acyclic proof architectures, highlighting computational limits in verification cost optimization.

Mechanizing the Identity-Persistence Forcing Architecture: From Declared Regimes to Independently Reconstructible Verdict Theorems

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Implication

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Mechanizing the Identity-Persistence Forcing Architecture: From Declared Regimes to Independently Reconstructible Verdict Theorems

Key Points

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Implication

Cite This Study

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