← Numerical Information Object Theory / NIOT-06 · Floating-point projection, completion and cross-domain bridges

Numerical Information Object Theory NIOT-06 · Floating-point projection, completion and cross-domain bridges Neo.K (as signed)

Floating-Point Projection, Completion, and Cross-Domain Bridges: Bidirectional Semantics from Finite Machine Representations to Numerical Information Objects

A float is the projection of an object into a finite machine representation, f=π_F(𝔑). Cross-domain bridges (a tuple taken from the author's earlier 'completion projection' paper, plus Addr and Cert) carry fibers, loss, exceptions and certificates; a probe-preserving partial bridge can suffice without converting the whole object. Non-injective rounding has no left inverse, and equal target values do not imply equal sources. The worked examples (1/10 is not exact in binary64; √2∈[1.4142,1.4143]; a sign probe) are correct but toy-sized.

Non-injective floating-point rounding has no global left inverse, so a float cannot uniquely determine the object it came from. This is an elementary fact, written here as a specification of bridge semantics. The most careful paper of the series: its five 'theorems' are elementary statements and only Theorem 1 carries a proof sketch of about five lines; formalization of IEEE 754 is explicitly deferred; no external numerical-analysis literature is cited. §46 of the source has one LaTeX defect.

Connections · Connections

PreviousNIOT-05 · Numerical index geometry (reference page) · Numerical Index Geometry: Addressing, Reindexing, Local Neighborhoods, and Identity Preservation
NextNIOT-07 · Bidirectional structural localization and responsibility closure · Bidirectional Structural Localization and Responsibility Closure: A Generalized Information-Theoretic Form of BCODR

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.

Editor's note: §46 of the source (around lines 1066–1068) has an unclosed \boxed{; that expression will show as raw source on this page. The file's bytes are unchanged.

Loading…