implement foundational Kinematic Sieve Operator and the halting mechanisms for logical jamming

Author: ryanncode

TensorSieve/Kinematics.lean

@@ -1,5 +1,5 @@
-import Mathlib.NumberTheory.Padics.PadicValuation
-import Mathlib.CategoryTheory.Quiver.Basic
+import Mathlib.NumberTheory.Padics.PadicVal.Basic
+import Mathlib.Combinatorics.Quiver.Basic
 
 namespace KinematicSieve
 
@@ -10,13 +10,62 @@ namespace KinematicSieve
 inductive SemanticAddress : Type
   | root : SemanticAddress
   | step : (p : Nat) → (val : Nat) → SemanticAddress → SemanticAddress
+  deriving DecidableEq
 
 /--
   The Quiver instance defining the incidence relation.
   An edge exists from `a` to `b` exclusively if `b` is generated
   by exactly one prime multiplication operation from `a`.
 -/
+structure Edge (a b : SemanticAddress) : Type where
+  p : Nat
+  h : b = SemanticAddress.step p 1 a
+
 instance : Quiver SemanticAddress where
-  Hom a b := ∃ (p : Nat), b = SemanticAddress.step p 1 a
+  Hom a b := Edge a b
+
+/--
+  Local Adjacency Function (K)
+  Evaluates arithmetic divergence purely combinatorially.
+  K(x, y) = 1 if they differ by exactly one prime multiplication or division.
+-/
+def adjacency (x y : SemanticAddress) : Int :=
+  sorry
+
+/--
+  Local Degree Function (D)
+  Restricted locally to the active computational domain.
+-/
+def degree (x : SemanticAddress) : Int :=
+  sorry
+
+/--
+  Discrete Combinatorial Laplacian (L_c = D - K)
+  Evaluates pointwise.
+-/
+def laplacian (x y : SemanticAddress) : Int :=
+  if x = y then degree x
+  else if adjacency x y == 1 then -1
+  else 0
+
+/--
+  Discrete shift operator step function navigating topological distance
+  exclusively via divisibility gating.
+-/
+def shift_operator (x : SemanticAddress) (target_p : Nat) : Int :=
+  sorry
+
+/--
+  Unique prime factorization constraints as Decidable propositions.
+-/
+def satisfies_constraint (x : SemanticAddress) (target_p : Nat) : Bool :=
+  sorry
+
+/--
+  Algorithmic halting condition ("logical jamming").
+  Terminates the recursive traversal path upon constraint violation.
+-/
+def logical_jamming (x : SemanticAddress) (target_p : Nat) : Int :=
+  if satisfies_constraint x target_p then shift_operator x target_p else 0
 
 end KinematicSieve