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August 19, 2026Open Access

Closure Fibers and Defect Representation Task Quotients, Compression, Witnesses, and the Structure of Intrafiber Information

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Authors

PLPhilip Lilien

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Implication

Mathematical analysis demonstrates task-relative compression and defect representation within closure fibers, establishing an organizing framework across matroid, deductive, and topological systems.

Key Points

  • To formalize the representation, task-relative compression, and witness structures of intrafiber information preserved within kernel classes of closure operators.
  • Defined task equivalence quotients, pointed defect representations, and factorization criteria for transport under closure-compatible mappings.
  • Introduced witnessed closure systems to formalize admissible certificates for omitted closure consequences.
  • Evaluated the theoretical architecture across three domain realizations: finite matroid closure, deductive logic closure, and topological closure.
  • Formulated an omission–redundancy conservation law and a compression hierarchy ranging from circuit witnesses to scalar metrics in finite matroid closure.
  • Showed that deductive closure preserves closure identity across variations in proof-based coordinate systems.
  • Established topological closure as a negative control where closure fibers persist despite the absence of finite witnesses, minimal generators, or privileged scalar defects.

Cite This Study

Philip Lilien (2026) studied this question.

synapsesocial.com/papers/6a85637603308d306e2d6aaehttps://doi.org/10.5281/zenodo.21982060
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