lock_end
plain-language theorem explainer
The declaration assigns the constant 3 in the Fin 8 type to mark the terminal phase of the LOCK segment in the hypothesized 8-beat cycle. Modelers of discretized recognition traces or LNAL bytecode segmentation would cite this boundary when partitioning observed folding dynamics into structure formation and equilibration intervals. The definition is a direct constant assignment with no lemmas or reductions required.
Claim. In the 8-tick discretization hypothesis, the terminal index of the LOCK interval (phases 0 through 3) is the element $3$ of the finite type of phases modulo 8.
background
The module states the 8-tick hypothesis as an explicit claim on observed traces: phases 0-3 constitute the LOCK stage of structure formation while phases 4-7 form the BALANCE stage of equilibration. Phase is introduced as the abbreviation Fin 8, supplying the discrete phase space for one cycle. This setting draws directly from the upstream Phase abbreviation in ChurchTuringPhysicsStructure, which likewise defines the 8-tick phase space, and from PhysicsComplexityStructure, which records that each tick updates at most 8 local neighbors under J-cost minimization.
proof idea
The definition is a direct constant assignment of the integer 3 inside the Phase type (Fin 8). No lemmas from the depends_on list are invoked; the declaration functions as a named boundary marker for the LOCK segment.
why it matters
This supplies the explicit endpoint separating LOCK from BALANCE within the 8-tick discretization hypothesis, enabling precise segmentation of recognition traces. It implements part of the testing interface for LNAL bytecode described in the module documentation and aligns with the eight-tick octave (T7) landmark in the Recognition Science forcing chain. With zero recorded downstream uses, its integration into larger proofs remains an open implementation step.
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