8787 "FUNCTION_TO_GLYPH" ,
8888 "GLYPH_TO_FUNCTION" ,
8989 "STRUCTURAL_FREQUENCIES" ,
90+ "DUAL_FREQUENCY_OPERATORS" ,
9091 "FREQUENCY_TRANSITIONS" ,
9192 "glyph_function_name" ,
9293 "function_name_to_glyph" ,
@@ -661,6 +662,62 @@ def _has_recent_destabilizer(self, current_index: int) -> bool:
661662 for _ , dest_index in self ._bifurcation_context
662663 )
663664
665+ def _validate_reception_context (self , reception_index : int ) -> bool :
666+ """Validate that RECEPTION has sufficient prior coherence for destabilization.
667+
668+ RECEPTION (EN) as a weak destabilizer requires context: it must operate on
669+ a node with existing structural base to generate sufficient ΔNFR for transformers.
670+
671+ Parameters
672+ ----------
673+ reception_index : int
674+ Index of the RECEPTION operator in the sequence
675+
676+ Returns
677+ -------
678+ bool
679+ True if RECEPTION has adequate prior structural coherence
680+
681+ Notes
682+ -----
683+ Valid patterns include:
684+ - AL → EN → IL → EN (emission provides base, first EN consolidated, second can destabilize)
685+ - EN → IL → EN (first EN consolidated, second can destabilize)
686+ - OZ → IL → EN (dissonance resolved provides base)
687+
688+ Invalid patterns include:
689+ - EN as first operator (no prior base)
690+ - EN immediately after SHA (silence removes base)
691+
692+ Theoretical justification:
693+ From nodal equation ∂EPI/∂t = νf · ΔNFR, RECEPTION has medium νf.
694+ For EN → ZHIR to be valid, EN must generate high ΔNFR. This is only possible
695+ when EN captures external coherence into a structurally prepared node,
696+ creating reorganization pressure from the integration.
697+ """
698+ # RECEPTION at position 0 cannot have prior coherence
699+ if reception_index == 0 :
700+ return False
701+
702+ # Look for stabilizer (IL or THOL) before RECEPTION
703+ # This indicates the node has structural base for destabilization
704+ for i in range (reception_index ):
705+ op = self ._canonical [i ]
706+ if op in {COHERENCE , SELF_ORGANIZATION }:
707+ # Found stabilizer - check it's not too far back
708+ # For context, we require stabilizer within 3 operators before EN
709+ if reception_index - i <= 3 :
710+ # Additionally, ensure no SILENCE between stabilizer and EN
711+ # (SILENCE would remove the coherent base)
712+ has_silence = any (
713+ self ._canonical [j ] == SILENCE
714+ for j in range (i + 1 , reception_index )
715+ )
716+ if not has_silence :
717+ return True
718+
719+ return False
720+
664721 def _has_graduated_destabilizer (self , current_index : int ) -> bool :
665722 """Check if any level of destabilizer satisfies its window requirement.
666723
@@ -680,9 +737,16 @@ def _has_graduated_destabilizer(self, current_index: int) -> bool:
680737 - Strong destabilizers (OZ): window of 4 operators
681738 - Moderate destabilizers (NAV, VAL): window of 2 operators
682739 - Weak destabilizers (EN): must be immediate predecessor (window of 1)
740+ AND have sufficient prior coherence context
683741
684742 The method checks each level in order of window size (largest first)
685743 to provide the most permissive validation.
744+
745+ RECEPTION (EN) Context Validation:
746+ EN as weak destabilizer requires validation of structural context.
747+ According to DUAL_FREQUENCY_OPERATORS, EN has medium base frequency
748+ but can generate ΔNFR when capturing external coherence into a prepared
749+ node. This validation ensures EN → ZHIR transitions are structurally sound.
686750 """
687751 # Check strong destabilizers (longest window = 4)
688752 if self ._destabilizer_context ["strong" ]:
@@ -697,10 +761,14 @@ def _has_graduated_destabilizer(self, current_index: int) -> bool:
697761 return True
698762
699763 # Check weak destabilizers (window = 1, must be immediate)
764+ # RECEPTION requires additional context validation for dual-role coherence
700765 if self ._destabilizer_context ["weak" ]:
701766 last_weak = self ._destabilizer_context ["weak" ][- 1 ]
702767 if current_index - last_weak == 1 :
703- return True
768+ # Validate that RECEPTION has sufficient context for destabilization
769+ # This implements the "requires_prior_coherence" condition from
770+ # DUAL_FREQUENCY_OPERATORS
771+ return self ._validate_reception_context (last_weak )
704772
705773 return False
706774
@@ -983,7 +1051,7 @@ class StructuralPattern(Enum):
9831051# - zero: Operators that suspend reorganization while preserving form
9841052STRUCTURAL_FREQUENCIES : dict [str , str ] = {
9851053 EMISSION : "high" , # AL: initiation/reorganization
986- RECEPTION : "medium" , # EN: structural capture
1054+ RECEPTION : "medium" , # EN: structural capture (base frequency)
9871055 COHERENCE : "medium" , # IL: stabilization
9881056 DISSONANCE : "high" , # OZ: tension
9891057 COUPLING : "medium" , # UM: coupling
@@ -997,6 +1065,37 @@ class StructuralPattern(Enum):
9971065 RECURSIVITY : "medium" , # REMESH: fractal echo
9981066}
9991067
1068+ # Dual-role operators: operators with context-dependent destabilization capacity
1069+ # Resolves the structural inconsistency between base frequency (νf) and ΔNFR generation.
1070+ #
1071+ # RECEPTION (EN) is the canonical dual-role operator:
1072+ # - Base frequency: "medium" (νf for structural capture)
1073+ # - Destabilization capacity: "weak" (can generate ΔNFR when integrating external coherence)
1074+ # - Condition: Requires prior coherence base for effective destabilization
1075+ #
1076+ # Theoretical foundation (nodal equation):
1077+ # ∂EPI/∂t = νf · ΔNFR
1078+ #
1079+ # RECEPTION has medium νf (moderate reorganization rate) but can act as weak
1080+ # destabilizer in graduated bifurcation (R4) when capturing external coherence
1081+ # into a node with existing structural base. The external input can generate
1082+ # sufficient ΔNFR to enable transformers (ZHIR/THOL) despite medium base frequency.
1083+ #
1084+ # Context requirement: EN → ZHIR valid only when EN operates on coherent base
1085+ # (e.g., AL → EN → IL → EN → ZHIR). Direct EN → ZHIR without context violates
1086+ # structural coherence as medium νf alone cannot sustain high ΔNFR for mutation.
1087+ DUAL_FREQUENCY_OPERATORS : dict [str , dict [str , str ]] = {
1088+ RECEPTION : {
1089+ "base_freq" : "medium" ,
1090+ "destabilization_capacity" : "weak" ,
1091+ "conditions" : "requires_prior_coherence" ,
1092+ "rationale" : (
1093+ "Captures external coherence which can generate ΔNFR when "
1094+ "integrated into structurally prepared node"
1095+ ),
1096+ }
1097+ }
1098+
10001099# Frequency compatibility: operators with harmonic frequencies can transition
10011100# Valid transitions preserve structural coherence:
10021101# - high ↔ medium: High energy can stabilize or stabilized can amplify
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