eight_tick_cycle_exists
plain-language theorem explainer
Existence of a complete cover of 3-bit patterns with exact period 8 is asserted for D=3. Lattice modelers in Recognition Science cite the result when fixing the temporal stability window for discrete Navier-Stokes evolution. The proof is a direct term application of the period_exactly_8 lemma.
Claim. In three spatial dimensions there exists a complete cover $w$ of the 3-bit pattern space such that the period of $w$ equals 8.
background
The Eight-Tick Discrete-Time Dynamics module treats time as discrete, so that an 8-step window becomes the natural stability unit and certificates over one window propagate by iteration. CompleteCover 3 is the structure that ensures every 3-bit pattern appears inside the cycle. Upstream, SpectralEmergence.of forces D=3 together with 24 chiral fermions while PhysicsComplexityStructure.of shows that J-cost minimization produces local 8-tick neighbor updates.
proof idea
The proof is a one-line term wrapper that applies the period_exactly_8 lemma.
why it matters
The theorem realizes the eight-tick octave (T7) forced for D=3 (T8) inside the UnifiedForcingChain. It anchors the Navier-Stokes lattice program by supplying the minimal periodic cover whose certificates propagate. The result sits downstream of J-cost convexity in PhysicsComplexityStructure.of and supplies the temporal unit required by window_certificate_extends in the same module.
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