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Title: Quadratic Reciprocity and the Group Orders of Particle States

The construction of inverse states in a finite field F{sub P{sub P{alpha}}} enables the organization of the mass scale by associating particle states with residue class designations. With the assumption of perfect flatness ({Omega}total = 1.0), this approach leads to the derivation of a cosmic seesaw congruence which unifies the concepts of space and mass. The law of quadratic reciprocity profoundly constrains the subgroup structure of the multiplicative group of units F{sub P{sub {alpha}}}* defined by the field. Four specific outcomes of this organization are (1) a reduction in the computational complexity of the mass state distribution by a factor of {approximately}10{sup 30}, (2) the extension of the genetic divisor concept to the classification of subgroup orders, (3) the derivation of a simple numerical test for any prospective mass number based on the order of the integer, and (4) the identification of direct biological analogies to taxonomy and regulatory networks characteristic of cellular metabolism, tumor suppression, immunology, and evolution. It is generally concluded that the organizing principle legislated by the alliance of quadratic reciprocity with the cosmic seesaw creates a universal optimized structure that functions in the regulation of a broad range of complex phenomena.
Authors:
; ; ; ;
Publication Date:
OSTI Identifier:
782710
Report Number(s):
SAND2001-1534
TRN: AH200126%%190
DOE Contract Number:
AC04-94AL85000
Resource Type:
Technical Report
Resource Relation:
Other Information: PBD: 1 Jun 2001
Research Org:
Sandia National Labs., Albuquerque, NM (US); Sandia National Labs., Livermore, CA (US)
Sponsoring Org:
US Department of Energy (US)
Country of Publication:
United States
Language:
English
Subject:
59 BASIC BIOLOGICAL SCIENCES; CONSTRUCTION; DISTRIBUTION; GENETICS; IMMUNOLOGY; MASS NUMBER; METABOLISM; NEOPLASMS; ORGANIZING; RESIDUES; TAXONOMY