Exact Finite-Amplitude Permutation-Quotient Cross-Host Consequence Dynamics in Canonical ACRF-4: Orbit Completeness, Stratified Host-Boundary State, and a Nine-Dimensional Generic Quotient

Scope

Establishes exact finite-amplitude quotient dynamics for the two-host partition S={1,2}, C={3,4} inside canonical finite ACRF-4. The internal relabeling group S2 x S2 is quotiented exactly; equality of quotient states implies equality of every finite-horizon permutation-invariant host consequence. The exact quotient has generic dimension nine and admits a generic 3+3+3 decomposition into two three-coordinate host records and a three-coordinate relational boundary. Globally the quotient is stratified. The result is model-specific and does not derive a universal RT cross-registration law or physical propagation structure.

Relation to other papers

• Builds on Reciprocal Current–Retention Conjugacy in ACRF-4
• Builds on Densification and Node-Block Nonautonomy in ACRF-4
• Builds on Six-Mode Host Consequence Structure
• Builds on Retained History as a Determinant of Boundary Action
• Builds on Closed-Event Consequence Completeness
• Builds on Consequential Closure Diagnostic
• Extended by Persistent Registration and Relative Metric
• Extended by Invariant Registration Closure
• Extended by Particle–Field Trinity Conjugacy
• Extended by Cross-Registration Consequence Networks
• Extended by Bilateral Participatory Registration in ACRF-4
• Extended by Canonical Complex Structure Without Canonical Orientation

Relevant research claims

• Exact Model ResultFinite-Amplitude Permutation-Quotient Host Sufficiency in Canonical ACRF-4
• Exact Model ResultReceiver Odd-Sector Linear Silence and Quadratic Re-Entry
• Exact Model ResultMinimal Homogeneous Odd-Sector Polynomial Invariant Generators
• Exact Model ResultNine-Dimensional Generic Orbit Quotient and Stratified Host-Boundary Structure
• Computational ResultTwo-Step Quotient Observability Rank Nine
• Exact Model ResultCanonical ACRF-4 Two-Channel Boundary-Consequence Field
• Exact Model ResultGlobal Bilateral Quotient Reconstruction in Canonical ACRF-4
• Exact Model ResultParticipant-Exchange Complex-Orientation No-Go Theorem

Keywords

• Registration Theory
• ACRF-4
• permutation quotient
• invariant theory
• adaptive closed registration
• retained boundary
• cross-host consequence
• finite-amplitude dynamics
• orbit completeness
• stratified quotient
• consequence sufficiency
• relational alignment