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oai:figshare.com:article/34018266 2026-09-28T19:11:56Z category_30154 item_type_12 month_year_09_2026

Bilateral Registration, Adaptive Holonomy Selection, and the Irreducible Response Susceptibility in Registration Theory: A Three-Registration ACRF Construction, Parameter-Elimination Audit, and the Remaining First-Principles Bridge EUGENE CATRAMBONE (24756637) Classical physics not elsewhere classified Registration Theory Registration Theory (Physical Foundations) ACRF-4 bilateral registration compact phase U(1) loop holonomy participant-relative contextuality three-registration dynamics equivariant bifurcation S3 symmetry adaptive networks retained history adaptive coupling parameter elimination response susceptibility g_R fine-structure bridge mathematical physics This timestamped research note records a bounded three-registration extension of Registration Theory (Physical Foundations) and an internal parameter-elimination audit of adaptive loop-holonomy selection. The contribution is not a new holonomy formalism, bifurcation theorem, or adaptive-network mechanism. Those mathematical structures are established in gauge theory, equivariant bifurcation theory, and adaptive-network dynamics. The Registration Theory contribution is the application of those tools to an independently developed bilateral-registration architecture and the isolation of exactly where the remaining magnitude-setting freedom enters the RT/ACRF model. Starting from the published bilateral circle invariant and unoriented compact phase structure of canonical ACRF-4, the paper derives a three-registration contextual-defect expression for triangle holonomy. A minimal inherited ACRF successor is then analyzed. Its circulation mode is linearly contractive with multiplier 0.90, while its distortion sector is expansive with multiplier 1.05, ruling out a direct S3-to-C3 chiral pitchfork in this minimal extension. Cubic nonlinearities nevertheless allow relational distortion to source circulation. Restoring the canonical adaptive retained-coupling update produces six symmetry-related, locally attracting S3-to-S2 fixed points carrying a persistent nonzero loop-holonomy magnitude. For the inherited canonical numerical parameters, the selected model value is |Theta*| approximately 0.91602417; the paper explicitly does not identify this value with a physical constant. The parameter audit then reduces the apparent adaptive freedom. The triangular retained-edge budget is fixed to B=3 by symmetric unit-edge normalization. The relaxation parameter rho controls convergence rate but cancels exactly from persistent fixed points. The leading local effects of eta and kappa_0 collapse into one logarithmic adaptive-response susceptibility, g_R = [d/ds log A(s)] at s=0 = eta/(1+kappa_0). For canonical ACRF-4, this equals 40/23, the same coefficient already present in the previously derived quadratic retained-history expansion because both descend from the same canonical adaptive law. No current Registration Theory theorem derives g_R from primitive registration principles. The surviving first-principles problem is therefore isolated sharply: derive, or prove underdetermined, the normalized adaptive-response susceptibility g_R without inserting a phenomenological response law A(s). This paper does not claim a derivation of electromagnetism, electric charge, Maxwell dynamics, quantum electrodynamics, or the physical fine-structure constant. Its timestamped contribution is the reduction of a diffuse coupling-selection problem to one named auditable response susceptibility within the RT/ACRF architecture. 2026-09-28T19:11:56Z Text Preprint 10.6084/m9.figshare.34018266.v1 https://figshare.com/articles/preprint/Bilateral_Registration_Adaptive_Holonomy_Selection_and_the_Irreducible_Response_Susceptibility_in_Registration_Theory_A_Three-Registration_ACRF_Construction_Parameter-Elimination_Audit_and_the_Remaining_First-Principles_Bridge/34018266 CC BY 4.0