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567
+ },
568
+ {
569
+ "k": 2048,
570
+ "preserved_rate": 1.0,
571
+ "mean_retention": 0.8723438769261905
572
+ },
573
+ {
574
+ "k": 4096,
575
+ "preserved_rate": 1.0,
576
+ "mean_retention": 0.7166338284234478
577
+ }
578
+ ],
579
+ "basin_width_80": 4096,
580
+ "basin_width_50": 4096
581
+ }
582
+ },
583
+ "D": {
584
+ "condition_name": "D) anchored_tail + tau_gated",
585
+ "routing_mode": "tau_gated",
586
+ "readout_mode": "tau_weighted",
587
+ "interference_mode": "gaussian",
588
+ "analysis": {
589
+ "preservation_curve": [
590
+ {
591
+ "k": 0,
592
+ "preserved_rate": 1.0,
593
+ "mean_retention": 1.0
594
+ },
595
+ {
596
+ "k": 64,
597
+ "preserved_rate": 1.0,
598
+ "mean_retention": 0.9968489111315394
599
+ },
600
+ {
601
+ "k": 128,
602
+ "preserved_rate": 1.0,
603
+ "mean_retention": 0.99349330439582
604
+ },
605
+ {
606
+ "k": 256,
607
+ "preserved_rate": 1.0,
608
+ "mean_retention": 0.9879556069927743
609
+ },
610
+ {
611
+ "k": 512,
612
+ "preserved_rate": 1.0,
613
+ "mean_retention": 0.9729722198202259
614
+ },
615
+ {
616
+ "k": 1024,
617
+ "preserved_rate": 1.0,
618
+ "mean_retention": 0.9402356788396578
619
+ },
620
+ {
621
+ "k": 2048,
622
+ "preserved_rate": 1.0,
623
+ "mean_retention": 0.8815645792706723
624
+ },
625
+ {
626
+ "k": 4096,
627
+ "preserved_rate": 1.0,
628
+ "mean_retention": 0.7318858903611966
629
+ }
630
+ ],
631
+ "basin_width_80": 4096,
632
+ "basin_width_50": 4096
633
+ }
634
+ }
635
+ }
636
+ },
637
+ "verdict": "ROUTING_GENUINE",
638
+ "explanation": "C/D dominate B even under UNIFORM readout:\n B (uniform readout): 2048\n C (uniform readout): 4096\n D (uniform readout): 4096\n\u2192 Routing genuinely improves global retention, not just aligned readout."
639
+ },
640
+ "part_b": {
641
+ "results": {
642
+ "gaussian": {
643
+ "B": {
644
+ "condition_name": "B) anchored + uniform",
645
+ "routing_mode": "uniform",
646
+ "readout_mode": "uniform",
647
+ "interference_mode": "gaussian",
648
+ "analysis": {
649
+ "preservation_curve": [
650
+ {
651
+ "k": 0,
652
+ "preserved_rate": 1.0,
653
+ "mean_retention": 1.0
654
+ },
655
+ {
656
+ "k": 64,
657
+ "preserved_rate": 1.0,
658
+ "mean_retention": 0.9806563798674307
659
+ },
660
+ {
661
+ "k": 128,
662
+ "preserved_rate": 1.0,
663
+ "mean_retention": 0.9441072143665781
664
+ },
665
+ {
666
+ "k": 256,
667
+ "preserved_rate": 1.0,
668
+ "mean_retention": 0.8769405591968306
669
+ },
670
+ {
671
+ "k": 512,
672
+ "preserved_rate": 1.0,
673
+ "mean_retention": 0.73121750615748
674
+ },
675
+ {
676
+ "k": 1024,
677
+ "preserved_rate": 0.5833333333333334,
678
+ "mean_retention": 0.5670807509053054
679
+ },
680
+ {
681
+ "k": 2048,
682
+ "preserved_rate": 0.5,
683
+ "mean_retention": 0.48906202248967795
684
+ },
685
+ {
686
+ "k": 4096,
687
+ "preserved_rate": 0.2916666666666667,
688
+ "mean_retention": 0.3330496741627256
689
+ }
690
+ ],
691
+ "basin_width_80": 512,
692
+ "basin_width_50": 2048
693
+ }
694
+ },
695
+ "C": {
696
+ "condition_name": "C) anchored + tau_weighted",
697
+ "routing_mode": "tau_weighted",
698
+ "readout_mode": "uniform",
699
+ "interference_mode": "gaussian",
700
+ "analysis": {
701
+ "preservation_curve": [
702
+ {
703
+ "k": 0,
704
+ "preserved_rate": 1.0,
705
+ "mean_retention": 1.0
706
+ },
707
+ {
708
+ "k": 64,
709
+ "preserved_rate": 1.0,
710
+ "mean_retention": 0.9928310975888586
711
+ },
712
+ {
713
+ "k": 128,
714
+ "preserved_rate": 1.0,
715
+ "mean_retention": 0.9865045945822777
716
+ },
717
+ {
718
+ "k": 256,
719
+ "preserved_rate": 1.0,
720
+ "mean_retention": 0.9780594443431792
721
+ },
722
+ {
723
+ "k": 512,
724
+ "preserved_rate": 1.0,
725
+ "mean_retention": 0.9585847756236353
726
+ },
727
+ {
728
+ "k": 1024,
729
+ "preserved_rate": 1.0,
730
+ "mean_retention": 0.9208216503894681
731
+ },
732
+ {
733
+ "k": 2048,
734
+ "preserved_rate": 1.0,
735
+ "mean_retention": 0.8695088781684711
736
+ },
737
+ {
738
+ "k": 4096,
739
+ "preserved_rate": 0.875,
740
+ "mean_retention": 0.6985904947285809
741
+ }
742
+ ],
743
+ "basin_width_80": 4096,
744
+ "basin_width_50": 4096
745
+ }
746
+ }
747
+ },
748
+ "low_rank": {
749
+ "B": {
750
+ "condition_name": "B) anchored + uniform",
751
+ "routing_mode": "uniform",
752
+ "readout_mode": "uniform",
753
+ "interference_mode": "low_rank",
754
+ "analysis": {
755
+ "preservation_curve": [
756
+ {
757
+ "k": 0,
758
+ "preserved_rate": 1.0,
759
+ "mean_retention": 1.0
760
+ },
761
+ {
762
+ "k": 64,
763
+ "preserved_rate": 1.0,
764
+ "mean_retention": 0.787501807669793
765
+ },
766
+ {
767
+ "k": 128,
768
+ "preserved_rate": 1.0,
769
+ "mean_retention": 0.7102322970611293
770
+ },
771
+ {
772
+ "k": 256,
773
+ "preserved_rate": 0.875,
774
+ "mean_retention": 0.6547879566460884
775
+ },
776
+ {
777
+ "k": 512,
778
+ "preserved_rate": 0.7083333333333334,
779
+ "mean_retention": 0.559923442306188
780
+ },
781
+ {
782
+ "k": 1024,
783
+ "preserved_rate": 0.2916666666666667,
784
+ "mean_retention": 0.35890126107549075
785
+ },
786
+ {
787
+ "k": 2048,
788
+ "preserved_rate": 0.25,
789
+ "mean_retention": 0.3148174479310639
790
+ },
791
+ {
792
+ "k": 4096,
793
+ "preserved_rate": 0.125,
794
+ "mean_retention": 0.275989487197799
795
+ }
796
+ ],
797
+ "basin_width_80": 256,
798
+ "basin_width_50": 512
799
+ }
800
+ },
801
+ "C": {
802
+ "condition_name": "C) anchored + tau_weighted",
803
+ "routing_mode": "tau_weighted",
804
+ "readout_mode": "uniform",
805
+ "interference_mode": "low_rank",
806
+ "analysis": {
807
+ "preservation_curve": [
808
+ {
809
+ "k": 0,
810
+ "preserved_rate": 1.0,
811
+ "mean_retention": 1.0
812
+ },
813
+ {
814
+ "k": 64,
815
+ "preserved_rate": 1.0,
816
+ "mean_retention": 0.907354342170715
817
+ },
818
+ {
819
+ "k": 128,
820
+ "preserved_rate": 1.0,
821
+ "mean_retention": 0.8725564278121754
822
+ },
823
+ {
824
+ "k": 256,
825
+ "preserved_rate": 1.0,
826
+ "mean_retention": 0.8525946440633777
827
+ },
828
+ {
829
+ "k": 512,
830
+ "preserved_rate": 1.0,
831
+ "mean_retention": 0.7963329794113297
832
+ },
833
+ {
834
+ "k": 1024,
835
+ "preserved_rate": 0.7083333333333334,
836
+ "mean_retention": 0.6089381740233489
837
+ },
838
+ {
839
+ "k": 2048,
840
+ "preserved_rate": 0.4166666666666667,
841
+ "mean_retention": 0.46924366642499016
842
+ },
843
+ {
844
+ "k": 4096,
845
+ "preserved_rate": 0.16666666666666666,
846
+ "mean_retention": 0.3836127429293949
847
+ }
848
+ ],
849
+ "basin_width_80": 512,
850
+ "basin_width_50": 1024
851
+ }
852
+ }
853
+ },
854
+ "repeating": {
855
+ "B": {
856
+ "condition_name": "B) anchored + uniform",
857
+ "routing_mode": "uniform",
858
+ "readout_mode": "uniform",
859
+ "interference_mode": "repeating",
860
+ "analysis": {
861
+ "preservation_curve": [
862
+ {
863
+ "k": 0,
864
+ "preserved_rate": 1.0,
865
+ "mean_retention": 1.0
866
+ },
867
+ {
868
+ "k": 64,
869
+ "preserved_rate": 1.0,
870
+ "mean_retention": 0.9593609230016776
871
+ },
872
+ {
873
+ "k": 128,
874
+ "preserved_rate": 1.0,
875
+ "mean_retention": 0.8366475714482472
876
+ },
877
+ {
878
+ "k": 256,
879
+ "preserved_rate": 0.75,
880
+ "mean_retention": 0.5898593505475229
881
+ },
882
+ {
883
+ "k": 512,
884
+ "preserved_rate": 0.2916666666666667,
885
+ "mean_retention": 0.3806044065737439
886
+ },
887
+ {
888
+ "k": 1024,
889
+ "preserved_rate": 0.08333333333333333,
890
+ "mean_retention": 0.2803877439136357
891
+ },
892
+ {
893
+ "k": 2048,
894
+ "preserved_rate": 0.08333333333333333,
895
+ "mean_retention": 0.237637136333383
896
+ },
897
+ {
898
+ "k": 4096,
899
+ "preserved_rate": 0.08333333333333333,
900
+ "mean_retention": 0.21880460650076006
901
+ }
902
+ ],
903
+ "basin_width_80": 128,
904
+ "basin_width_50": 256
905
+ }
906
+ },
907
+ "C": {
908
+ "condition_name": "C) anchored + tau_weighted",
909
+ "routing_mode": "tau_weighted",
910
+ "readout_mode": "uniform",
911
+ "interference_mode": "repeating",
912
+ "analysis": {
913
+ "preservation_curve": [
914
+ {
915
+ "k": 0,
916
+ "preserved_rate": 1.0,
917
+ "mean_retention": 1.0
918
+ },
919
+ {
920
+ "k": 64,
921
+ "preserved_rate": 1.0,
922
+ "mean_retention": 0.9865270430884303
923
+ },
924
+ {
925
+ "k": 128,
926
+ "preserved_rate": 1.0,
927
+ "mean_retention": 0.955483915357199
928
+ },
929
+ {
930
+ "k": 256,
931
+ "preserved_rate": 1.0,
932
+ "mean_retention": 0.8675320069736152
933
+ },
934
+ {
935
+ "k": 512,
936
+ "preserved_rate": 0.9583333333333334,
937
+ "mean_retention": 0.6845707634724798
938
+ },
939
+ {
940
+ "k": 1024,
941
+ "preserved_rate": 0.4166666666666667,
942
+ "mean_retention": 0.4735716391824138
943
+ },
944
+ {
945
+ "k": 2048,
946
+ "preserved_rate": 0.20833333333333334,
947
+ "mean_retention": 0.33137773675602217
948
+ },
949
+ {
950
+ "k": 4096,
951
+ "preserved_rate": 0.08333333333333333,
952
+ "mean_retention": 0.2560143288938028
953
+ }
954
+ ],
955
+ "basin_width_80": 512,
956
+ "basin_width_50": 512
957
+ }
958
+ }
959
+ }
960
+ },
961
+ "verdict": "ROUTING_ROBUST",
962
+ "explanation": "Routing advantage holds across ALL interference types."
963
+ },
964
+ "overall": {
965
+ "verdict": "ROUTING_CONFIRMED",
966
+ "explanation": "Routing is GENUINE and ROBUST:\n - Holds under uniform readout (not alignment artifact)\n - Holds under structured interference (not noise-specific)\n\u2192 Ready to integrate into FDRA training."
967
+ }
968
+ }