Consequence Propagation

Temporal asymmetry / Lorentzian signature

A non-circular derivation of a single time-facing sign, not assumed as input.

Related threads: Conjugate / Brokerage Structure, Consequence Propagation

Cross-Registration Successor Kernel

Replace consequence-incidence propagation by a receiver-successor law: derive or control a kernel T_ij^k(delta) for the probability that a consequential source/receiver interaction sends the receiver into successor type k, and determine whether the resulting dynamic operator closes on a natural RT quotient.

Related threads: Consequence Propagation, Host Structure

Sources: Cross-Registration Consequence Networks

Finite-step consequence support under one-step locality

If the native ACRF-4 update couples only primitive neighbors (one-step locality), the n-step full-state tangent propagator has no support beyond registration depth n: d_reg(i,j) > n ⇒ (Jⁿ)ⱼᵢ = 0, so the consequence-front length obeys ℓ_reg(n;i) ≤ n.

Scope: Standard locality mathematics applied to the ACRF-4 update graph, conditional on the one-step locality assumption stated in the source; the result itself is not claimed as novel.

• –Does not by itself derive a physical speed of light.
• –Canonical ACRF-4 itself is not thereby shown to satisfy sparse primitive-neighbor locality: its mean term is globally consequential and its adaptive retained-coupling target gives every pair positive support after one update.
• –The forward-generated shared-event transfer carrier required for physical propagation remains unresolved.

Last reviewed 2026-08-27

Canonical ACRF-4 has exact node-block nonautonomy and strict retained-edge densification

For every nontrivial node partition in finite canonical ACRF-4, the node update is not globally autonomous by block. Every zero cross-cut retained-coupling set is destroyed by one update, and the nonnegative fixed-budget coupling simplex maps into strictly positive edge support with K_ij' > 0.0056771420617977… .

Scope: An exact result for the specified four-node adaptive update and its nonnegative six-edge fixed-budget coupling simplex. It includes the generated 2+2 state with cross couplings 0 → 0.15 and c_S = −0.375 under the existing symmetric-host closure theorem.

• –Strict positive K support is a feature of the written all-pairs adaptive target, not a derivation of sparse primitive-neighbor locality.
• –Does not prove coupling of independently closed hosts, cross-registration consequence sufficiency, or a forward-generated inter-host transfer map T_ji.
• –Does not establish primitive Trinity interaction, physical propagation, physical space or time, Lorentz spacetime, or a universal physical c.

Last reviewed 2026-08-28

Receiver-conditioned ACRF-4 consequence generates a boundary-sensitive effective network operator

Using the intervention-defined receiver consequence from canonical ACRF-4, a declared finite-type projection produces an effective cross-registration reproduction operator whose spectral structure is strongly controlled by RT-internal dynamics. At delta=0.0277128, the full two-channel field gives rho=1.02091 while the difference-only mean-channel ablation gives rho=0.61267; low versus high retained-boundary quartiles give rho=0.53974 versus 1.40048.

Scope: Computational result for 12,000 admissible canonical ACRF-4 states sampled with x_i uniform on [-0.8,0.8] and the six retained edges drawn as 6*Dirichlet(2,...,2), using the coordinate-normalized receiver quotient metric, a transparent eight-bin projection of W=(m,p,|d|), and outward branching number b=2.

• –The multitype spectral-radius threshold and ordinary percolation mathematics are standard; the RT-specific contribution is the construction and control of the effective operator from receiver consequence.
• –A rho=1 crossing under a monotone receiver-resolution sweep is not by itself evidence of new RT criticality; the meaningful result is the displacement produced by RT-specific interventions and retained-boundary organization.
• –The branching rerun bootstraps the same empirical offspring law used to construct the operator and is therefore an implementation-consistency check, not independent physical validation.
• –The current operator propagates pre-interaction receiver types. A complete dynamic propagation theorem requires the receiver successor state, formalized by the Cross-Registration Successor Kernel.
• –The first loopy-network realization does not yet enforce one globally compatible ACRF-4 state across every incident edge at each vertex.

Last reviewed 2026-09-04