SupportingRegistration Geometry

Densification and Node-Block Nonautonomy in Canonical ACRF-4: An Exact Zero-Cut Destruction Theorem and Generated Cross-Cut Retained Coupling

An exact canonical ACRF-4 theorem package: every zero cross-cut is destroyed in one update, every retained edge becomes strictly positive, and the node update is not globally autonomous across a nontrivial node block.

2026-08-28v1.0DOI: 10.5281/zenodo.22150386 View publication

Scope

Establishes finite-model node-block nonautonomy and strict retained-coupling densification. The exact 2+2 example maps cross couplings 0 → 0.15 and internal couplings 3 → 2.70; at its generated symmetric state c_S = −0.375 gives nonzero first-order exterior-current sensitivity within the prior symmetric-host theorem's scope. It does not derive sparse primitive-neighbor locality, primitive Trinity interaction, physical propagation, spacetime, Lorentz structure, a universal physical c, or an inter-host transfer map.

Relation to other papers

Builds on Reciprocal Current–Retention Conjugacy in ACRF-4
Builds on Persistent Relational Localization (ACRF-4)
Extended by Finite-Amplitude Permutation-Quotient Dynamics

Relevant research claims

Exact Model ResultCanonical ACRF-4 has exact node-block nonautonomy and strict retained-edge densification
Open ProblemReconstruction of physical spacetime from registration dynamics

Keywords

Registration Theory
ACRF-4
node-block nonautonomy
zero-cut destruction
retained coupling
emergent locality