gap45
plain-language theorem explainer
Recognition Science attention models set the complexity ceiling at 45. Cross-domain researchers cite the value to bound attentional states at 40 configurations from the product of networks and phases, leaving 5 overflow slots for saturated singletons. The declaration is a direct constant assignment in natural numbers.
Claim. The complexity ceiling is defined as the natural number $45$, leaving exactly five overflow slots after the attentional state space of $5$ networks times $8$ phases equals $40$.
background
The module treats attentional state space as the product of AttentionNetwork and TickPhase. This product is fixed at five times eight, which equals forty. The ceiling is then placed at forty-five so that five slots remain for the singletons that appear under saturation. The local setting is the C5 structural claim for wave-62 cross-domain attention, with zero axioms or sorry markers.
proof idea
The declaration is a direct definition that assigns the natural number 45 to the complexity ceiling.
why it matters
The definition supplies the numerical bound required by the C5 attention-space claim. It feeds downstream statements on overflow slots and network surjectivity. The factor of eight in the state-space product aligns with the eight-tick octave from the forcing chain, while the five overflow slots match the predicted transient plateaus in attentional-blink experiments.
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