SupportingRegistration Geometry

Canonical Emergence of a Local Complex Structure in Registration Theory: A Five-Step Derivation of Anticommuting Closure Involutions at a Persistent ACRF-4 Registration

Derives from the exact persistent closed ACRF-4 sector a native retained/current parity involution and a normalized reciprocal exchange involution; at the nonzero persistent closed registration the two anticommute, giving J_cl^2 = -I.

2026-09-15v1.0DOI: 10.6084/m9.figshare.33823234 View publication

Scope

Exact normalized local tangent result at the nonzero persistent closed ACRF-4 registration. A global finite-amplitude complex structure and physical phase-succession bridge remain open.

Relation to other papers

Builds on Closure-Induced Complex Structure
Builds on Compact Closure and Noncompact Conjugate Escape
Builds on Reciprocal Current–Retention Conjugacy in ACRF-4
Extended by Canonical Complex Structure Without Canonical Orientation

Relevant research claims

Exact Model ResultCanonical Local Complex Structure at a Persistent ACRF-4 Registration
Exact Model ResultParticipant-Exchange Complex-Orientation No-Go Theorem

Keywords

Registration Theory
Registration Theory (Physical Foundations)
Eugene Catrambone
ACRF-4
persistent registration closure
local tangent dynamics
current-retention conjugacy
conjugate involution
closure parity
anticommuting involutions
complex structure
J squared equals minus I
emergent phase structure