Bilateral Participatory Registration in Canonical ACRF-4: Exact Consequence Factorization, Participant-Exchange Covariance, and a Global Two-Sided Quotient Carrier

Scope

The Bilateral Participatory Registration Principle is a candidate foundational RT refinement. The consequence-factorization theorem is exact conditional mathematics, and the common-carrier, exchange-covariance, generic decomposition, and global reconstruction results are exact within canonical finite ACRF-4. The paper does not identify the ACRF participant-relative records with primitive Trinity conjugates, does not identify block exchange with Trinity conjugation, and does not derive spacetime, Lorentz structure, force, charge, or a universal propagation speed.

Abstract

The paper proposes that an interaction-generated registration is one common relational object with two participant-relative manifestations. Conditional on that proposal, it proves an exact bilateral consequence-factorization theorem. In canonical finite ACRF-4, the same exact quotient is jointly sufficient for both host successor records; the matched receiver-isolation intervention is covariant under participant exchange; the generic nine-dimensional quotient decomposes as a fibered participant-relative pair; and the decomposition extends globally through the invariant orbit record Q=(E,UU^T,VV^T,c^2,cUV^T). The resulting model chain is Q <-> (rho_{S|C}^Q,rho_{C|S}^Q) -> (Delta W_{C->S},Delta W_{S->C}).

Relation to other papers

• Builds on Canonical Foundations of Registration Theory
• Builds on Structural Trinity Conjecture (v2.0)
• Builds on Finite-Amplitude Permutation-Quotient Dynamics
• Builds on Cross-Registration Consequence Networks
• Builds on Persistent Registration and Relative Metric
• Extended by Closure-Induced Complex Structure
• Extended by Canonical Complex Structure Without Canonical Orientation
• Extended by Hosting versus Deriving the Born Rule

Relevant research claims

• InterpretationBilateral Participatory Registration Principle
• Exact TheoremBilateral Consequence Factorization Theorem
• Exact Model ResultGlobal Bilateral Quotient Reconstruction in Canonical ACRF-4
• Exact Model ResultParticipant-Exchange Complex-Orientation No-Go Theorem

Keywords

• Registration Theory
• ACRF-4
• bilateral participatory registration
• participant-relative registration
• consequence factorization
• participant exchange
• exchange covariance
• matched intervention
• quotient dynamics
• permutation symmetry
• invariant quotient
• orbit separation
• stratified quotient
• relational ontology
• pre-geometric physics
• Trinity