← Numerical Information Object Theory / NIOT-07 · Bidirectional structural localization and responsibility closure

Numerical Information Object Theory NIOT-07 · Bidirectional structural localization and responsibility closure Neo.K (as signed)

Bidirectional Structural Localization and Responsibility Closure: A Generalized Information-Theoretic Form of BCODR

Recasts BCODR as 'bidirectional structural localization': opposing fields, atomic overlap cells, a responsibility graph, a surviving spine, and a task-relative closure certificate, while keeping the BCODR-LUC cautions — container overlap ≠ point alignment ≠ structural alignment ≠ solution. This site's Lebesgue BCODR page expands the same acronym as 'Bidirectional Circular Overlap Decomposition and Recomposition'; this paper's re-reading is a different gloss, and the difference is explained on this case's hub page.

BCODR's cautions (overlap is not alignment; missing data cannot establish alignment) can be written as general responsibility-closure rules. This is a proposal with no worked example. The claimed reach of 'BCODR is no longer only for geometric proofs' (proof search, debugging, latent AI mechanisms, scientific hypothesis spaces) rests on sketches of two to four lines with no worked example; 'Theorems A–E' are explicitly only candidates. This site's own BCODR page states that BCODR v0.1 has not been shown to converge for arbitrary search problems.

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PreviousNIOT-06 · Floating-point projection, completion and cross-domain bridges · Floating-Point Projection, Completion, and Cross-Domain Bridges: Bidirectional Semantics from Finite Machine Representations to Numerical Information Objects

NextNIOT-08 · Nine-layer canonical architecture · Canonical Numerical Architecture: From Numeral Interpretation and Numerical Information Ontology to Authoritative Projection and Responsibility Closure

This is a full-text translation of the Chinese source, which remains authoritative for its research claims. Translation is not independent mathematical verification and does not upgrade the original evidence level.

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