ShortcutGraph
plain-language theorem explainer
ShortcutGraph defines a structure with positive real weights on edges A-B and A-C to model a shortcut in addition to a directed chain. Researchers examining SpMV propagation in Recognition Science cite it when testing whether shortcuts equalize activation times at the first tick. The declaration is a plain structure definition with four fields for the weights and their strict positivity.
Claim. A structure consisting of two positive real numbers $w_{AB}>0$ and $w_{AC}>0$ that represent the weights of a direct edge from A to B and a shortcut edge from A to C.
background
The module examines whether sparse matrix-vector multiplication preserves causal ordering on directed chains and whether the eight-tick octave suffices for multi-hop propagation. tick denotes the fundamental RS time quantum with value 1; A denotes the active edge count per tick, fixed at 1. Upstream results supply the blend rate η = 1/φ² and the identification of bidirectional SBERT edges with shortcuts that can flatten activation ordering.
proof idea
Structure definition with four fields; no lemmas or tactics are applied.
why it matters
Supplies the hypothesis type for the theorem shortcut_simultaneous_activation, which shows that when w_AC ≥ w_AB the shortcut node C receives at least as much activation as B at tick 1. This directly supports the module claim that bidirectional edges destroy strict causal ordering and connects to the eight-tick octave limit on practical reach.
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