rsWithoutSusy
Recognition Science supplies alternatives to supersymmetry for the hierarchy problem and dark matter via its phi-ladder structure and ledger shadows. A physicist comparing RS to SUSY extensions would cite this summary list to note that SUSY remains compatible but unnecessary. The declaration is a direct definition that enumerates four fixed strings with no computation or lemmas.
claimThe Recognition Science view without supersymmetry is the list $L = [$``Hierarchy from $φ$-ladder (not SUSY)'', ``Dark matter from ledger shadows (not LSP)'', ``Gauge unification may still work'', ``SUSY is optional, not required''$]$.
background
Recognition Science builds all physics from the J-cost equation and the eight-tick octave (period $2^3$). Module SM-010 examines how J-cost differs between bosons and fermions because they occupy distinct phases in the eight-tick cycle, producing spontaneous SUSY breaking. Upstream results supply the fundamental tick $τ_0 = 1$ (Constants.tick) and the phi-tier structure for nuclear densities (NucleosynthesisTiers.of). The module states that exact SUSY would force equal boson-fermion masses, yet LHC limits already push any superpartners above 1 TeV.
proof idea
The declaration is a definition that directly constructs the four-element string list. No lemmas or tactics are invoked; the body is a literal enumeration of the summary points.
why it matters in Recognition Science
This definition shows that the Recognition Science framework solves the hierarchy problem and dark matter without SUSY, using the phi-ladder (T6) and ledger shadows instead. It aligns with the eight-tick octave (T7) and J-uniqueness (T5) from the forcing chain. The summary touches the open question of whether gauge unification survives without superpartners. No downstream theorems depend on the list.
scope and limits
- Does not derive the J-cost difference between bosons and fermions.
- Does not compute a numerical SUSY-breaking scale.
- Does not compare predictions against specific LHC exclusion limits.
- Does not prove gauge unification occurs in the absence of SUSY.
formal statement (Lean)
208def rsWithoutSusy : List String := [
proof body
Definition body.
209 "Hierarchy from φ-ladder (not SUSY)",
210 "Dark matter from ledger shadows (not LSP)",
211 "Gauge unification may still work",
212 "SUSY is optional, not required"
213]
214
215/-! ## Summary -/
216
217/-- RS perspective on supersymmetry breaking:
218
219 1. **8-tick phases**: Bosons and fermions have different phases
220 2. **J-cost asymmetry**: Different phases → different J-costs
221 3. **SUSY breaking**: J_boson ≠ J_fermion
222 4. **Scale**: From magnitude of J-cost difference
223 5. **LHC limits**: Push SUSY to >1 TeV
224 6. **RS flexibility**: Works with or without SUSY -/