Foundation Pair Kernel Scale Breaking Source Residual

/-- Source-action duality alone admits both banked source magnitudes. Candidate
A pairs unit source with unit action; Candidate B pairs reciprocal native
source with native action. The physical action normalization is therefore a
separate scale-breaking statement. -/
theorem sourceActionDuality_alone_admits_distinct_banked_magnitudes :
    PostingSourceIsActionDual3
        (@unitPostingActionCountermodel3 3 inferInstance)
        (@unitSourceMagnitudeCountermodel3 3 inferInstance) ∧
      PostingSourceIsActionDual3
        (@nativePostingActionCandidate3 3 inferInstance)
        (@nativeDualSourceMagnitudeCandidate3 3 inferInstance) ∧
      ∃ event : PostingPair3 3,
        event ∈ realizedPrimitivePostingPairs3 3 ∧
          unitSourceMagnitudeCountermodel3 event =
            candidateA_sourceMagnitudeExpr.eval ∧
          nativeDualSourceMagnitudeCandidate3 event =
            candidateB_sourceMagnitudeExpr.eval ∧
          unitSourceMagnitudeCountermodel3 event ≠
            nativeDualSourceMagnitudeCandidate3 event := by
  refine
    ⟨unitAssignments_satisfy_sourceActionDuality,
      nativeCandidates_source_is_actionDual, ?_⟩
  obtain ⟨event, hevent, _hcert⟩ :=
    canonicalGeneratorSource_consumer_exists
      (N := 3) (by norm_num) (Equiv.refl (Fin 3))
  have hA :
      unitSourceMagnitudeCountermodel3 event =
        candidateA_sourceMagnitudeExpr.eval := by
    change (1 : ℝ) = candidateA_sourceMagnitudeExpr.eval
    exact candidateA_sourceMagnitude_eq_one.symm
  have hB :
      nativeDualSourceMagnitudeCandidate3 event =
        candidateB_sourceMagnitudeExpr.eval := by
    rfl
  refine ⟨event, hevent, hA, hB, ?_⟩
  intro heq
  exact candidates_select_distinct_magnitudes
    (hA.symm.trans (heq.trans hB))

/-- HYPOTHESIS: one physical posting has native action and its positive source
coordinate is the multiplicative dual measured in the Euler-J action unit.
The statement is target-blind and contains no continuum readout. -/
def NativeActionDualSourceLaw (sourceMagnitude : ℝ) : Prop :=
  0 < sourceMagnitude ∧
    sourceMagnitude * Constants.hbar = eulerJActionUnit

/-- The proposed native-action dual law selects exactly Candidate B. This is
a sufficiency theorem for the named physical law, not a derivation of the law
from the current source premises. -/
theorem nativeActionDualSourceLaw_iff_candidateB
    (sourceMagnitude : ℝ) :
    NativeActionDualSourceLaw sourceMagnitude ↔
      sourceMagnitude = candidateB_sourceMagnitudeExpr.eval := by
  change
    (0 < sourceMagnitude ∧
      sourceMagnitude * Constants.hbar = eulerJActionUnit) ↔
        sourceMagnitude = nativeActionQuantumInv
  rw [← nativeActionQuantum_eq_constants_hbar,
    eulerJActionUnit_eq_one]
  exact nativeQuantumSourceLaw_iff_inv sourceMagnitude

theorem candidateB_satisfies_nativeActionDualSourceLaw :
    NativeActionDualSourceLaw
      candidateB_sourceMagnitudeExpr.eval :=
  (nativeActionDualSourceLaw_iff_candidateB _).2 rfl

/-- Independent discrimination: the native-action dual law rejects the
one-act source candidate because the two banked magnitudes are distinct. -/
theorem nativeActionDualSourceLaw_rejects_candidateA :
    ¬ NativeActionDualSourceLaw
      candidateA_sourceMagnitudeExpr.eval := by
  intro hA
  exact candidates_select_distinct_magnitudes
    ((nativeActionDualSourceLaw_iff_candidateB _).1 hA)

/-- The new law is not hidden in the old package: Candidate A satisfies every
current premise and fails the native-action dual law. -/
theorem currentPremises_do_not_force_nativeActionDualSourceLaw :
    ¬ (∀ sourceMagnitude : ℝ,
      CurrentRecognitionSourcePremises sourceMagnitude →
        NativeActionDualSourceLaw sourceMagnitude) := by
  intro hforce
  exact nativeActionDualSourceLaw_rejects_candidateA
    (hforce _
      candidateA_satisfies_currentRecognitionSourcePremises)

/-- If the two missing physical statements are supplied on a realized event,
the source magnitude is Candidate B and its pair-kernel source equation uses
the independently fixed Green scale `q / 2`. -/
theorem physicalAttachment_attaches_candidateB_at_actionNormalizedScale
    {N : ℕ} [NeZero N]
    {postingAction sourceMagnitude : PostingPair3 N → ℝ}
    (hphysical :
      PhysicalPostingMagnitudeAttachment3
        postingAction sourceMagnitude)
    {event : PostingPair3 N}
    (hevent : event ∈ realizedPrimitivePostingPairs3 N)
    {n : ℕ}
    (w : Fin n → Fin n → ℝ)
    (e : Fin n → ℝ)
    (a b : Fin n)
    (hsymm : ∀ i j, w i j = w j i)
    (haction :
      PostingMagnitudeActionLaw
        (sourceMagnitude event) w e a b) :
    sourceMagnitude event =
        candidateB_sourceMagnitudeExpr.eval ∧
      ScaledSourceEquation w (dipole a b)
        (realGreenScaleFromPostingMagnitude
          candidateB_sourceMagnitudeExpr.eval) e := by
  have hsource :
      sourceMagnitude event =
        candidateB_sourceMagnitudeExpr.eval := by
    change sourceMagnitude event = nativeActionQuantumInv
    exact
      physicalPostingAttachment_forces_nativeActionQuantumInv
        hphysical hevent
  refine ⟨hsource, ?_⟩
  rw [← hsource]
  exact
    (postingMagnitudeActionLaw_iff_scaledSourceEquation
      (sourceMagnitude event) w e a b hsymm).1 haction