ConsciousnessHypothesis
plain-language theorem explainer
The ConsciousnessHypothesis structure packages the BarrierCert for the coprimality barrier between 8-tick and 45-fold cycles with a claim that experiential processing is needed to navigate it, as no finite sub-period aligns both. Researchers in Recognition Science foundations cite it to link mathematical barriers to phenomenology. The definition is a direct structure construction embedding the certificate and a falsifier observation.
Claim. A consciousness hypothesis consists of a barrier certificate encoding the coprimality of 8 and 45, the primality of the beat frequency 37, and the insufficiency of any window shorter than 360 ticks, together with the claim that navigation of the 8/45 barrier requires experiential processing because no finite sub-period resolves both constraints simultaneously, a specified falsifier, and status label.
background
The Gap-45 Recognition Barrier module formalizes the mathematical consequences of gcd(8,45)=1. The BarrierCert structure packages the core facts: coprimality of 8 and 45, that 37 is prime, that gcd(37,360)=1, that no proper divisor w<360 divides both 8 and 45, that 360 is a common multiple, and that the aliasing ratio 37/45 is less than 1. This sets the local theoretical setting where proved theorems cover the barrier itself while the connection to consciousness remains a hypothesis. Upstream, the tick is defined as the fundamental time quantum of 1 in RS-native units, and related results from PhiForcingDerived supply the phi-ladder.
proof idea
The declaration is a structure definition that directly specifies the four fields: the barrier certificate, the claim string, the falsifier string, and the status string. It performs no computation or lemma application and serves as pure packaging of the hypothesis data.
why it matters
This structure earns its place by providing the explicit hypothesis interface that connects the proved Gap-45 barrier to phenomenology, as stated in the module documentation. It is instantiated in the downstream consciousness_hypothesis definition. Within the Recognition Science framework it references the eight-tick octave and raises the open question of whether the barrier forces experiential navigation.
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