REIST Tree: A Conditional Reduction Tree for Centered Remainder Sums
Abstract
This corrected conceptual note defines a parallel reduction for a finite list of independently available integer contributions with known centered quotient–remainder pairs. A bounded pairwise merge preserves both the integer sum and the canonical remainder interval. For n inputs, a balanced tree uses O(n) merges and O(log n) parallel stages under a fixed-word-cost model with sufficient resources and no overflow. These bounds do not include discovering dependent corrections or dividing arbitrary unnormalized inputs. No measured speedup or new general division algorithm is claimed.
Context
Definiert einen Reduktionsbaum für unabhängig vorliegende, bereits normalisierte Quotient-Rest-Paare. Zahlenerhaltung und kanonischer Restbereich werden bewiesen; logarithmische Stufenzahl gilt nur unter benannten Ressourcen- und Wortkostenannahmen. Kein allgemeiner neuer Divisionsalgorithmus oder gemessener Speedup.