summary
plain-language theorem explainer
This definition enumerates five statements on supersymmetry breaking in Recognition Science, attributing the effect to J-cost differences that arise when bosons and fermions occupy even versus odd slots in the eight-tick phase cycle. A physicist modeling spontaneous breaking or comparing RS to conventional SUSY mechanisms would reference these points when discussing why superpartners remain unobserved below the TeV scale. The definition is a direct enumeration that draws its content from the upstream phase and cost functions without further le
Claim. The summary consists of the statements: bosons occupy even phases $k=0,2,4,6$ in the cycle of period $2^3$ ticks while fermions occupy odd phases $k=1,3,5,7$; the resulting J-cost asymmetry spontaneously breaks supersymmetry; this accounts for the absence of superpartners at low energies; and the Recognition Science framework functions independently of exact supersymmetry.
background
The eight-tick phase function assigns values $kπ/4$ for $k=0..7$ to recognition events, with the base time unit being one tick. J-cost is the non-negative scalar returned by the cost function on a recognition event or on the comparator of a multiplicative recognizer. The module sets the local context by noting that supersymmetry would equate boson and fermion masses, yet the phase distinction forces unequal J-costs and therefore spontaneous breaking at a scale above 1 TeV.
proof idea
The definition constructs the list of strings directly from the phase distinction supplied by EightTick.phase together with the cost definitions in MultiplicativeRecognizerL4 and ObserverForcing. No lemmas or tactics are invoked; the body is a literal enumeration of the five statements listed in the module documentation.
why it matters
The definition records the central claim of the SM-010 module that J-cost asymmetry arising from the eight-tick octave supplies the mechanism for supersymmetry breaking. It aligns with the T7 landmark of the forcing chain and shows that Recognition Science remains consistent whether or not supersymmetry is imposed. Because the used-by list is empty, the entry functions as a self-contained explanatory anchor rather than a lemma feeding a larger theorem.
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