physical_sensor_charge_zero

formal source

 944In RS language: the Law of Existence (T1) forces every physical recognition
 945event to have zero topological charge.  Nonzero charge requires divergent
 946cost, which T1 forbids for physically realizable ledger entries. -/
 947theorem physical_sensor_charge_zero (ps : PhysicalSensor) :
 948    ps.val.charge = 0 :=
 949  (ontological_dichotomy ps.val).mpr ps.property
 950
 951/-- **RH from the ontological dichotomy.**  If every sensor physically exists,
 952then every sensor has charge `0`. -/
 953theorem rh_from_ontological_dichotomy
 954    (h : ∀ sensor : DefectSensor, PhysicallyExists sensor) :
 955    ∀ (sensor : DefectSensor), sensor.charge ≠ 0 → False := by
 956  intro sensor hm
 957  exact hm ((ontological_dichotomy sensor).mpr (h sensor))
 958
 959/-- The converse: RH implies all sensors physically exist (vacuously —
 960charge `0` sensors are T1-bounded). -/
 961theorem all_physicallyExist_of_rh
 962    (hrh : ∀ sensor : DefectSensor, sensor.charge ≠ 0 → False) :
 963    ∀ sensor : DefectSensor, PhysicallyExists sensor := by
 964  intro sensor
 965  exact (ontological_dichotomy sensor).mp (by
 966    by_contra hm
 967    exact hrh sensor hm)
 968
 969/-- **RH ↔ all sensors physically exist.**  Machine-verified equivalence
 970between the number-theoretic statement and the RS physical principle. -/
 971theorem rh_iff_all_physical :
 972    (∀ sensor : DefectSensor, sensor.charge ≠ 0 → False) ↔
 973      (∀ sensor : DefectSensor, PhysicallyExists sensor) :=
 974  ⟨all_physicallyExist_of_rh, rh_from_ontological_dichotomy⟩
 975
 976end UnifiedRH
 977end Unification