IndisputableMonolith.Foundation.CausalPropagationOrdering
The CausalPropagationOrdering module defines activation steps and hop ordering for causal signals on finite lattices at discrete ticks. It models blended propagation with rate η to enforce temporal sequence in R-hat fixed-point systems. Researchers analyzing discrete causality in Recognition Science cite these objects when building propagation chains from the forcing sequence. The module supplies definitions and short preservation statements that chain from the imported constants and contraction theory.
claimActivation of a node at tick $t$ is the blended state $(1 - η) ψ + η · prop$, where $ψ$ is the local field and $prop$ the incoming signal. This induces a preserved ordering on causal hops across successive ticks $τ_0 = 1$.
background
The module operates on finite lattices equipped with the R-hat fixed-point theory, where R-hat denotes a J-cost contraction whose attractors encode the fixed-point vocabulary of the system. Constants supply the fundamental time quantum $τ_0 = 1$ tick. The supplied doc-comment states that activation at tick $t$ models one step of the linear blend $(1-η)·my_ψ + η·prop$ under incoming propagation.
proof idea
This is a definition module, no proofs. It introduces the core objects blend_step, chain_activation, hop_ordering_preserved, activation_at_tick_2 and general_hop_ordering directly from the imported Constants and RHatFixedPoint modules.
why it matters in Recognition Science
The module supplies the causal ordering primitives required by the unified forcing chain (T0-T8) and the R-hat fixed-point construction. It ensures propagation respects the eight-tick octave and supports downstream determination of spatial dimension D=3 by enforcing ordered hops on the lattice.
scope and limits
- Does not treat infinite lattices or continuous-time limits.
- Does not compute explicit numerical activation values.
- Does not address bidirectional signal destruction of ordering.
- Does not derive the numerical value of the blend rate η.
depends on (2)
declarations in this module (15)
-
def
blend_step -
def
chain_activation -
theorem
hop_ordering_preserved -
theorem
distance_2_zero_at_tick_1 -
theorem
activation_at_tick_2 -
theorem
general_hop_ordering -
structure
ShortcutGraph -
theorem
shortcut_simultaneous_activation -
theorem
bidirectional_destroys_ordering -
def
peak_activation -
theorem
peak_decreases -
theorem
practical_reach_bound -
theorem
phi_blend_5_hop_weak -
theorem
octave_sufficient_for_4_hop -
theorem
diagnostic_q1_q2