susyViability
Recognition Science defines SUSY viability as constrained but not excluded, with spontaneous breaking arising from J-cost asymmetry between boson and fermion sectors. Model builders evaluating split or stealth SUSY against LHC data would cite this when checking consistency with the eight-tick phase structure. The definition is a direct string assignment that records the outcome of the J-cost comparison.
claimSupersymmetry remains viable in Recognition Science when the breaking scale exceeds 1 TeV, with spontaneous breaking induced by the distinct J-costs of bosons and fermions that follow from their differing 8-tick phases.
background
The module SM-010 sets the target of deriving supersymmetry breaking from J-cost. Supersymmetry pairs each boson with a fermionic partner, yet exact SUSY would force equal masses and immediate detection, which is ruled out. Recognition Science supplies the asymmetry through the 8-tick phases defined by phase(k) = k π /4 for k = 0 to 7, so that boson and fermion sectors acquire different J-costs. Upstream, PhiForcingDerived.of supplies the structure of J-cost while EightTick.phase supplies the periodic phases with period 2π.
proof idea
This is a one-line definition that directly assigns the string value summarizing the viability conclusion.
why it matters in Recognition Science
The definition records the conclusion of the SM-010 target in the StandardModel module. It invokes the eight-tick octave (T7) to explain why SUSY, if present, must break spontaneously without fine-tuning. No downstream theorems currently depend on it, leaving open the quantitative extraction of LSP masses or breaking scales from the phi-ladder.
scope and limits
- Does not derive a numerical breaking scale from the phi-ladder.
- Does not prove or disprove the existence of superpartners.
- Does not compute cross sections for LHC searches.
- Does not address gauge unification predictions under RS.
formal statement (Lean)
177def susyViability : String :=
proof body
Definition body.
178 "Constrained but not excluded; RS explains breaking regardless"
179
180/-! ## The LSP and Dark Matter -/
181
182/-- If SUSY exists, the Lightest Superpartner (LSP) is stable:
183
184 R-parity conservation → LSP can't decay
185 LSP is a dark matter candidate!
186
187 Candidates:
188 - Neutralino (mix of photino, zino, higgsino)
189 - Gravitino (superpartner of graviton)
190 - Sneutrino (ruled out by direct detection)
191
192 In RS: LSP would be in the dark (odd-phase) sector. -/