# 32-63 status split audit

Finite-sample descriptive exploration only. No mechanism, proof, causality, or global Collatz claim is made.

## Populations

- control 32-63 status rows: 47
- miss-depth-3 32-63 status rows: 120

## Main Read

- The split is visible in `stage_chain_status`: controls are `32-63:avoid_then_caught`, miss-depth-3 rows are `32-63:avoid`.
- But the local exit-event classification at 32-63 is not different: both groups are `avoid_then_caught` in `stage_event_classification`.
- This means the split is not simply a different local lower-5pct event label. It is a chain-status distinction: in miss-depth-3, 32-63 is counted as part of a longer consecutive avoidance run; in controls, 32-63 already terminates as `avoid_then_caught` before the max-depth run begins at 16-31.
- Local descriptors still differ in position and timing: controls have larger/longer 32-63 windows, while miss-depth-3 is closer to the 32-63 exit front.

## Confirmed Differences

- 32-63 chain status: controls `avoid_then_caught:47`; miss-depth-3 `avoid:120`.
- entry_R: controls `63:46; 61:1`; miss-depth-3 `46:30; 63:28; 41:10; 61:6; 58:6; 62:6; 49:5; 50:4`.
- exit_R: controls `29:44; 30:2; 31:1`; miss-depth-3 `31:72; 30:32; 29:8; 28:5; 27:3`.
- wait length inside 32-63: controls `22:36; 21:6; 19:2; 20:1; 17:1; 16:1`; miss-depth-3 `14:17; 5:16; 4:14; 6:13; 13:10; 16:8; 3:7; 15:6`.
- last event before 16-31: controls `R=32->29|k=3|res=0->29:44; R=32->30|k=2|res=0->30:2; R=33->31|k=2|res=1->31:1`; miss-depth-3 `R=35->31|k=4|res=3->31:38; R=36->31|k=5|res=4->31:23; R=35->30|k=5|res=3->30:20; R=36->30|k=6|res=4->30:12; R=37->31|k=6|res=5->31:9; R=36->29|k=7|res=4->29:3; R=35->27|k=8|res=3->27:3; R=36->28|k=8|res=4->28:2`.

## Confirmed Similarities

- local event classification: controls `avoid_then_caught:47`; miss-depth-3 `avoid_then_caught:120`.
- next 16-31 stage class: controls `avoid_in_max_depth_run:47`; miss-depth-3 `avoid_in_max_depth_run:120`.
- first event in 16-31 overlaps strongly: controls `R=29|k=1|res=29->28:44; R=30|k=1|res=30->29:2; R=31|k=2|res=31->29:1`; miss-depth-3 `R=31|k=1|res=31->30:40; R=31|k=3|res=31->28:25; R=30|k=1|res=30->29:14; R=30|k=2|res=30->28:13; R=30|k=3|res=30->27:5; R=28|k=1|res=28->27:5; R=31|k=2|res=31->29:4; R=29|k=2|res=29->27:4`.

## Minimal Selector Audit

- one-coordinate perfect selectors found: 7
- two-coordinate perfect selectors found: 126

| selector | dimension | separates_groups | mixed_coordinate_cells | coordinate_cells | top_cells |
| --- | --- | --- | --- | --- | --- |
| stage_chain_status | 1 | True | 0 | 2 | avoid => miss_depth3_32_63_avoid:120 | avoid_then_caught => control_32_63_avoid_then_caught:47 |
| stage_avoided_exit_layer_in_window | 1 | True | 0 | 2 | 1 => miss_depth3_32_63_avoid:120 | 0 => control_32_63_avoid_then_caught:47 |
| last_before_exit_distance | 1 | True | 0 | 8 | 3 => miss_depth3_32_63_avoid:63 | 0 => control_32_63_avoid_then_caught:46 | 4 => miss_depth3_32_63_avoid:40 | 5 => miss_depth3_32_63_avoid:13 | 8 => miss_depth3_32_63_avoid:2 | 1 => control_32_63_avoid_then_caught:1 | 2 => miss_depth3_32_63_avoid:1 | 7 => miss_depth3_32_63_avoid:1 |
| exit_residue_pair_mod32 | 1 | True | 0 | 19 | 0->29 => control_32_63_avoid_then_caught:44 | 3->31 => miss_depth3_32_63_avoid:38 | 4->31 => miss_depth3_32_63_avoid:23 | 3->30 => miss_depth3_32_63_avoid:20 | 4->30 => miss_depth3_32_63_avoid:12 | 5->31 => miss_depth3_32_63_avoid:9 | 3->27 => miss_depth3_32_63_avoid:3 | 4->29 => miss_depth3_32_63_avoid:3 |
| last_before_residue_pair_mod32 | 1 | True | 0 | 19 | 0->29 => control_32_63_avoid_then_caught:44 | 3->31 => miss_depth3_32_63_avoid:38 | 4->31 => miss_depth3_32_63_avoid:23 | 3->30 => miss_depth3_32_63_avoid:20 | 4->30 => miss_depth3_32_63_avoid:12 | 5->31 => miss_depth3_32_63_avoid:9 | 3->27 => miss_depth3_32_63_avoid:3 | 4->29 => miss_depth3_32_63_avoid:3 |
| last_event_before_16_31 | 1 | True | 0 | 19 | R=32->29|k=3|res=0->29 => control_32_63_avoid_then_caught:44 | R=35->31|k=4|res=3->31 => miss_depth3_32_63_avoid:38 | R=36->31|k=5|res=4->31 => miss_depth3_32_63_avoid:23 | R=35->30|k=5|res=3->30 => miss_depth3_32_63_avoid:20 | R=36->30|k=6|res=4->30 => miss_depth3_32_63_avoid:12 | R=37->31|k=6|res=5->31 => miss_depth3_32_63_avoid:9 | R=35->27|k=8|res=3->27 => miss_depth3_32_63_avoid:3 | R=36->29|k=7|res=4->29 => miss_depth3_32_63_avoid:3 |
| last_k_window_5_before_16_31 | 1 | True | 0 | 86 | 1,2,1,1,1 => control_32_63_avoid_then_caught:36 | 1,1,3,1,5 => miss_depth3_32_63_avoid:7 | 1,3,1,2,4 => miss_depth3_32_63_avoid:7 | 2,1,1,1,1 => control_32_63_avoid_then_caught:6 | 1,2,1,1,5 => miss_depth3_32_63_avoid:5 | 1,6,3,3,5 => miss_depth3_32_63_avoid:5 | 2,2,1,1,4 => miss_depth3_32_63_avoid:3 | 3,1,2,1,5 => miss_depth3_32_63_avoid:3 |
| stage_chain_status + stage_event_classification | 2 | True | 0 | 2 | avoid,avoid_then_caught => miss_depth3_32_63_avoid:120 | avoid_then_caught,avoid_then_caught => control_32_63_avoid_then_caught:47 |
| stage_chain_status + stage_avoided_exit_layer_in_window | 2 | True | 0 | 2 | avoid,1 => miss_depth3_32_63_avoid:120 | avoid_then_caught,0 => control_32_63_avoid_then_caught:47 |
| stage_event_classification + stage_avoided_exit_layer_in_window | 2 | True | 0 | 2 | avoid_then_caught,1 => miss_depth3_32_63_avoid:120 | avoid_then_caught,0 => control_32_63_avoid_then_caught:47 |
| stage_chain_status + exit_R | 2 | True | 0 | 8 | avoid,31 => miss_depth3_32_63_avoid:72 | avoid_then_caught,29 => control_32_63_avoid_then_caught:44 | avoid,30 => miss_depth3_32_63_avoid:32 | avoid,29 => miss_depth3_32_63_avoid:8 | avoid,28 => miss_depth3_32_63_avoid:5 | avoid,27 => miss_depth3_32_63_avoid:3 | avoid_then_caught,30 => control_32_63_avoid_then_caught:2 | avoid_then_caught,31 => control_32_63_avoid_then_caught:1 |
| stage_chain_status + last_before_exit_distance | 2 | True | 0 | 8 | avoid,3 => miss_depth3_32_63_avoid:63 | avoid_then_caught,0 => control_32_63_avoid_then_caught:46 | avoid,4 => miss_depth3_32_63_avoid:40 | avoid,5 => miss_depth3_32_63_avoid:13 | avoid,8 => miss_depth3_32_63_avoid:2 | avoid,2 => miss_depth3_32_63_avoid:1 | avoid,7 => miss_depth3_32_63_avoid:1 | avoid_then_caught,1 => control_32_63_avoid_then_caught:1 |
| stage_event_classification + last_before_exit_distance | 2 | True | 0 | 8 | avoid_then_caught,3 => miss_depth3_32_63_avoid:63 | avoid_then_caught,0 => control_32_63_avoid_then_caught:46 | avoid_then_caught,4 => miss_depth3_32_63_avoid:40 | avoid_then_caught,5 => miss_depth3_32_63_avoid:13 | avoid_then_caught,8 => miss_depth3_32_63_avoid:2 | avoid_then_caught,1 => control_32_63_avoid_then_caught:1 | avoid_then_caught,2 => miss_depth3_32_63_avoid:1 | avoid_then_caught,7 => miss_depth3_32_63_avoid:1 |
| stage_avoided_exit_layer_in_window + exit_R | 2 | True | 0 | 8 | 1,31 => miss_depth3_32_63_avoid:72 | 0,29 => control_32_63_avoid_then_caught:44 | 1,30 => miss_depth3_32_63_avoid:32 | 1,29 => miss_depth3_32_63_avoid:8 | 1,28 => miss_depth3_32_63_avoid:5 | 1,27 => miss_depth3_32_63_avoid:3 | 0,30 => control_32_63_avoid_then_caught:2 | 0,31 => control_32_63_avoid_then_caught:1 |
| stage_avoided_exit_layer_in_window + last_before_exit_distance | 2 | True | 0 | 8 | 1,3 => miss_depth3_32_63_avoid:63 | 0,0 => control_32_63_avoid_then_caught:46 | 1,4 => miss_depth3_32_63_avoid:40 | 1,5 => miss_depth3_32_63_avoid:13 | 1,8 => miss_depth3_32_63_avoid:2 | 0,1 => control_32_63_avoid_then_caught:1 | 1,2 => miss_depth3_32_63_avoid:1 | 1,7 => miss_depth3_32_63_avoid:1 |
| stage_chain_status + exit_k | 2 | True | 0 | 11 | avoid_then_caught,3 => control_32_63_avoid_then_caught:44 | avoid,5 => miss_depth3_32_63_avoid:43 | avoid,4 => miss_depth3_32_63_avoid:38 | avoid,6 => miss_depth3_32_63_avoid:22 | avoid,8 => miss_depth3_32_63_avoid:7 | avoid,7 => miss_depth3_32_63_avoid:4 | avoid,9 => miss_depth3_32_63_avoid:3 | avoid_then_caught,2 => control_32_63_avoid_then_caught:3 |
| stage_avoided_exit_layer_in_window + exit_k | 2 | True | 0 | 11 | 0,3 => control_32_63_avoid_then_caught:44 | 1,5 => miss_depth3_32_63_avoid:43 | 1,4 => miss_depth3_32_63_avoid:38 | 1,6 => miss_depth3_32_63_avoid:22 | 1,8 => miss_depth3_32_63_avoid:7 | 1,7 => miss_depth3_32_63_avoid:4 | 0,2 => control_32_63_avoid_then_caught:3 | 1,9 => miss_depth3_32_63_avoid:3 |
| stage_chain_status + entry_k | 2 | True | 0 | 12 | avoid,1 => miss_depth3_32_63_avoid:68 | avoid_then_caught,2 => control_32_63_avoid_then_caught:36 | avoid,2 => miss_depth3_32_63_avoid:24 | avoid,3 => miss_depth3_32_63_avoid:19 | avoid_then_caught,4 => control_32_63_avoid_then_caught:6 | avoid,4 => miss_depth3_32_63_avoid:4 | avoid,5 => miss_depth3_32_63_avoid:3 | avoid_then_caught,1 => control_32_63_avoid_then_caught:3 |
| stage_avoided_exit_layer_in_window + entry_k | 2 | True | 0 | 12 | 1,1 => miss_depth3_32_63_avoid:68 | 0,2 => control_32_63_avoid_then_caught:36 | 1,2 => miss_depth3_32_63_avoid:24 | 1,3 => miss_depth3_32_63_avoid:19 | 0,4 => control_32_63_avoid_then_caught:6 | 1,4 => miss_depth3_32_63_avoid:4 | 1,5 => miss_depth3_32_63_avoid:3 | 0,1 => control_32_63_avoid_then_caught:3 |
| stage_chain_status + first_event_in_16_31 | 2 | True | 0 | 17 | avoid_then_caught,R=29|k=1|res=29->28 => control_32_63_avoid_then_caught:44 | avoid,R=31|k=1|res=31->30 => miss_depth3_32_63_avoid:40 | avoid,R=31|k=3|res=31->28 => miss_depth3_32_63_avoid:25 | avoid,R=30|k=1|res=30->29 => miss_depth3_32_63_avoid:14 | avoid,R=30|k=2|res=30->28 => miss_depth3_32_63_avoid:13 | avoid,R=30|k=3|res=30->27 => miss_depth3_32_63_avoid:5 | avoid,R=28|k=1|res=28->27 => miss_depth3_32_63_avoid:5 | avoid,R=31|k=2|res=31->29 => miss_depth3_32_63_avoid:4 |

## Numeric Summary

| group | feature | n | min | median | mean | max | unique |
| --- | --- | --- | --- | --- | --- | --- | --- |
| control_32_63_avoid_then_caught | entry_R | 47 | 61.0 | 63.0 | 62.957447 | 63.0 | 2 |
| control_32_63_avoid_then_caught | exit_R | 47 | 29.0 | 29.0 | 29.085106 | 31.0 | 3 |
| control_32_63_avoid_then_caught | entry_k | 47 | 1.0 | 2.0 | 2.340426 | 8.0 | 5 |
| control_32_63_avoid_then_caught | exit_k | 47 | 2.0 | 3.0 | 2.93617 | 3.0 | 2 |
| control_32_63_avoid_then_caught | entry_exit_distance | 47 | 29.0 | 31.0 | 30.957447 | 31.0 | 2 |
| control_32_63_avoid_then_caught | last_before_R | 47 | 32.0 | 32.0 | 32.021277 | 33.0 | 2 |
| control_32_63_avoid_then_caught | last_after_R | 47 | 29.0 | 29.0 | 29.085106 | 31.0 | 3 |
| control_32_63_avoid_then_caught | last_before_k | 47 | 2.0 | 3.0 | 2.93617 | 3.0 | 2 |
| control_32_63_avoid_then_caught | last_before_exit_distance | 47 | 0.0 | 0.0 | 0.021277 | 1.0 | 2 |
| control_32_63_avoid_then_caught | wait_length_inside_32_63 | 47 | 16.0 | 22.0 | 21.468085 | 22.0 | 6 |
| control_32_63_avoid_then_caught | stage_R_drop_entry_to_exit | 47 | 32.0 | 34.0 | 33.87234 | 34.0 | 3 |
| control_32_63_avoid_then_caught | events_inside_32_63_waiting_rows | 47 | 17.0 | 20.0 | 19.893617 | 20.0 | 3 |
| control_32_63_avoid_then_caught | events_in_32_63_exit_event_sequence | 47 | 17.0 | 23.0 | 22.468085 | 23.0 | 6 |
| control_32_63_avoid_then_caught | max_R_in_band | 47 | 61.0 | 63.0 | 62.957447 | 63.0 | 2 |
| control_32_63_avoid_then_caught | min_R_in_band | 47 | 32.0 | 32.0 | 32.021277 | 33.0 | 2 |
| miss_depth3_32_63_avoid | entry_R | 120 | 35.0 | 50.0 | 52.458333 | 63.0 | 22 |
| miss_depth3_32_63_avoid | exit_R | 120 | 27.0 | 31.0 | 30.375 | 31.0 | 5 |
| miss_depth3_32_63_avoid | entry_k | 120 | 1.0 | 1.0 | 1.858333 | 11.0 | 7 |
| miss_depth3_32_63_avoid | exit_k | 120 | 3.0 | 5.0 | 5.283333 | 11.0 | 9 |
| miss_depth3_32_63_avoid | entry_exit_distance | 120 | 3.0 | 18.0 | 20.458333 | 31.0 | 22 |
| miss_depth3_32_63_avoid | last_before_R | 120 | 34.0 | 35.0 | 35.658333 | 40.0 | 6 |
| miss_depth3_32_63_avoid | last_after_R | 120 | 27.0 | 31.0 | 30.375 | 31.0 | 5 |
| miss_depth3_32_63_avoid | last_before_k | 120 | 3.0 | 5.0 | 5.283333 | 11.0 | 9 |
| miss_depth3_32_63_avoid | last_before_exit_distance | 120 | 2.0 | 3.0 | 3.658333 | 8.0 | 6 |
| miss_depth3_32_63_avoid | wait_length_inside_32_63 | 120 | 0.0 | 8.0 | 9.066667 | 18.0 | 19 |
| miss_depth3_32_63_avoid | stage_R_drop_entry_to_exit | 120 | 7.0 | 20.0 | 22.083333 | 35.0 | 26 |
| miss_depth3_32_63_avoid | events_inside_32_63_waiting_rows | 120 | 1.0 | 9.0 | 10.066667 | 19.0 | 19 |
| miss_depth3_32_63_avoid | events_in_32_63_exit_event_sequence | 120 | 1.0 | 9.0 | 10.066667 | 19.0 | 19 |
| miss_depth3_32_63_avoid | max_R_in_band | 120 | 35.0 | 50.0 | 52.458333 | 63.0 | 22 |
| miss_depth3_32_63_avoid | min_R_in_band | 120 | 34.0 | 35.0 | 35.658333 | 40.0 | 6 |

## Invariants And Near-Invariants

| group | feature | unique_values | top_value | top_count | exceptions | distribution |
| --- | --- | --- | --- | --- | --- | --- |
| control_32_63_avoid_then_caught | lower5_capture_band | 1 | 4-7 | 47 | 0 | 4-7:47 |
| control_32_63_avoid_then_caught | next_16_31_stage_class | 1 | avoid_in_max_depth_run | 47 | 0 | avoid_in_max_depth_run:47 |
| control_32_63_avoid_then_caught | stage_avoided_exit_layer_in_window | 1 | 0 | 47 | 0 | 0:47 |
| control_32_63_avoid_then_caught | stage_chain_status | 1 | avoid_then_caught | 47 | 0 | avoid_then_caught:47 |
| control_32_63_avoid_then_caught | stage_class | 1 | avoid_then_caught | 47 | 0 | avoid_then_caught:47 |
| control_32_63_avoid_then_caught | stage_event_classification | 1 | avoid_then_caught | 47 | 0 | avoid_then_caught:47 |
| control_32_63_avoid_then_caught | stage_eventually_caught_band | 1 | 32-63 | 47 | 0 | 32-63:47 |
| control_32_63_avoid_then_caught | entry_R | 2 | 63 | 46 | 1 | 63:46; 61:1 |
| control_32_63_avoid_then_caught | entry_exit_distance | 2 | 31 | 46 | 1 | 31:46; 29:1 |
| control_32_63_avoid_then_caught | last_before_exit_distance | 2 | 0 | 46 | 1 | 0:46; 1:1 |
| control_32_63_avoid_then_caught | lower5_final_status | 2 | eventually_reentered_exit_layer:caught | 45 | 2 | eventually_reentered_exit_layer:caught:45; eventually_reentered_exit_layer:avoid_then_caught:2 |
| control_32_63_avoid_then_caught | events_inside_32_63_waiting_rows | 3 | 20 | 45 | 2 | 20:45; 18:1; 17:1 |
| control_32_63_avoid_then_caught | exit_k | 2 | 3 | 44 | 3 | 3:44; 2:3 |
| control_32_63_avoid_then_caught | exit_R | 3 | 29 | 44 | 3 | 29:44; 30:2; 31:1 |
| control_32_63_avoid_then_caught | exit_residue_pair_mod32 | 3 | 0->29 | 44 | 3 | 0->29:44; 0->30:2; 1->31:1 |
| control_32_63_avoid_then_caught | first_event_in_16_31 | 3 | R=29|k=1|res=29->28 | 44 | 3 | R=29|k=1|res=29->28:44; R=30|k=1|res=30->29:2; R=31|k=2|res=31->29:1 |
| control_32_63_avoid_then_caught | last_before_residue_pair_mod32 | 3 | 0->29 | 44 | 3 | 0->29:44; 0->30:2; 1->31:1 |
| control_32_63_avoid_then_caught | last_event_before_16_31 | 3 | R=32->29|k=3|res=0->29 | 44 | 3 | R=32->29|k=3|res=0->29:44; R=32->30|k=2|res=0->30:2; R=33->31|k=2|res=1->31:1 |
| control_32_63_avoid_then_caught | entry_k | 5 | 2 | 36 | 11 | 2:36; 4:6; 1:3; 3:1; 8:1 |
| control_32_63_avoid_then_caught | entry_residue_pair_mod32 | 5 | 31->29 | 36 | 11 | 31->29:36; 31->27:6; 31->30:3; 29->26:1; 31->23:1 |
| control_32_63_avoid_then_caught | events_in_32_63_exit_event_sequence | 6 | 23 | 36 | 11 | 23:36; 22:6; 20:2; 21:1; 18:1; 17:1 |
| control_32_63_avoid_then_caught | wait_length_inside_32_63 | 6 | 22 | 36 | 11 | 22:36; 21:6; 19:2; 20:1; 17:1; 16:1 |
| control_32_63_avoid_then_caught | entry_k_window_5 | 7 | 2,2,1,2,1 | 36 | 11 | 2,2,1,2,1:36; 4,1,2,1,1:6; 1,1,3,1,1:1; 3,2,1,1,2:1; 1,1,1,3,1:1; 1,2,3,1,1:1; 8,3,1,1,1:1 |
| control_32_63_avoid_then_caught | last_k_window_5_before_16_31 | 7 | 1,2,1,1,1 | 36 | 11 | 1,2,1,1,1:36; 2,1,1,1,1:6; 1,1,2,5,2:1; 1,1,1,1,1:1; 3,1,1,1,2:1; 1,2,1,2,2:1; 1,1,1,1,3:1 |
| miss_depth3_32_63_avoid | next_16_31_stage_class | 1 | avoid_in_max_depth_run | 120 | 0 | avoid_in_max_depth_run:120 |
| miss_depth3_32_63_avoid | stage_avoided_exit_layer_in_window | 1 | 1 | 120 | 0 | 1:120 |
| miss_depth3_32_63_avoid | stage_chain_status | 1 | avoid | 120 | 0 | avoid:120 |
| miss_depth3_32_63_avoid | stage_class | 1 | avoid_in_max_depth_run | 120 | 0 | avoid_in_max_depth_run:120 |
| miss_depth3_32_63_avoid | stage_event_classification | 1 | avoid_then_caught | 120 | 0 | avoid_then_caught:120 |
| miss_depth3_32_63_avoid | lower5_capture_band | 2 | 4-7 | 119 | 1 | 4-7:119; NA:1 |
| miss_depth3_32_63_avoid | stage_eventually_caught_band | 2 | 4-7 | 119 | 1 | 4-7:119; NA:1 |
| miss_depth3_32_63_avoid | lower5_final_status | 3 | eventually_reentered_exit_layer:avoid_then_caught | 115 | 5 | eventually_reentered_exit_layer:avoid_then_caught:115; eventually_reentered_exit_layer:caught:4; ended_without_later_exit_layer_reentry_observed:1 |
| miss_depth3_32_63_avoid | exit_R | 5 | 31 | 72 | 48 | 31:72; 30:32; 29:8; 28:5; 27:3 |
| miss_depth3_32_63_avoid | entry_k | 7 | 1 | 68 | 52 | 1:68; 2:24; 3:19; 4:4; 5:3; 8:1; 11:1 |
| miss_depth3_32_63_avoid | last_before_exit_distance | 6 | 3 | 63 | 57 | 3:63; 4:40; 5:13; 8:2; 7:1; 2:1 |
| miss_depth3_32_63_avoid | exit_k | 9 | 5 | 43 | 77 | 5:43; 4:38; 6:22; 8:7; 7:4; 9:3; 11:1; 10:1; 3:1 |
| miss_depth3_32_63_avoid | first_event_in_16_31 | 14 | R=31|k=1|res=31->30 | 40 | 80 | R=31|k=1|res=31->30:40; R=31|k=3|res=31->28:25; R=30|k=1|res=30->29:14; R=30|k=2|res=30->28:13; R=30|k=3|res=30->27:5; R=28|k=1|res=28->27:5; R=31|k=2|res=31->29:4; R=29|k=2|res=29->27:4; R=29|k=1|res=29->28:3; R=31|k=4|res=31->27:2; R=27|k=4|res=27->23:2; R=31|k=9|res=31->22:1; R=29|k=3|res=29->26:1; R=27|k=3|res=27->24:1 |
| miss_depth3_32_63_avoid | exit_residue_pair_mod32 | 16 | 3->31 | 38 | 82 | 3->31:38; 4->31:23; 3->30:20; 4->30:12; 5->31:9; 4->29:3; 3->27:3; 4->28:2; 5->29:2; 5->28:2; 8->31:1; 8->29:1; 3->29:1; 3->28:1; 7->29:1; 2->31:1 |
| miss_depth3_32_63_avoid | last_before_residue_pair_mod32 | 16 | 3->31 | 38 | 82 | 3->31:38; 4->31:23; 3->30:20; 4->30:12; 5->31:9; 4->29:3; 3->27:3; 4->28:2; 5->29:2; 5->28:2; 8->31:1; 8->29:1; 3->29:1; 3->28:1; 7->29:1; 2->31:1 |
| miss_depth3_32_63_avoid | last_event_before_16_31 | 16 | R=35->31|k=4|res=3->31 | 38 | 82 | R=35->31|k=4|res=3->31:38; R=36->31|k=5|res=4->31:23; R=35->30|k=5|res=3->30:20; R=36->30|k=6|res=4->30:12; R=37->31|k=6|res=5->31:9; R=36->29|k=7|res=4->29:3; R=35->27|k=8|res=3->27:3; R=36->28|k=8|res=4->28:2; R=37->29|k=8|res=5->29:2; R=37->28|k=9|res=5->28:2; R=40->31|k=9|res=8->31:1; R=40->29|k=11|res=8->29:1; R=35->29|k=6|res=3->29:1; R=35->28|k=7|res=3->28:1; R=39->29|k=10|res=7->29:1; R=34->31|k=3|res=2->31:1 |
| miss_depth3_32_63_avoid | entry_R | 22 | 46 | 30 | 90 | 46:30; 63:28; 41:10; 61:6; 58:6; 62:6; 49:5; 50:4; 57:3; 38:3; 42:3; 60:3; 54:2; 40:2; 44:2; 59:1; 43:1; 35:1; 55:1; 47:1; 51:1; 53:1 |
| miss_depth3_32_63_avoid | entry_exit_distance | 22 | 14 | 30 | 90 | 14:30; 31:28; 9:10; 29:6; 26:6; 30:6; 17:5; 18:4; 25:3; 6:3; 10:3; 28:3; 22:2; 8:2; 12:2; 27:1; 11:1; 3:1; 23:1; 15:1; 19:1; 21:1 |
| miss_depth3_32_63_avoid | events_in_32_63_exit_event_sequence | 19 | 15 | 17 | 103 | 15:17; 6:16; 5:14; 7:13; 14:10; 17:8; 4:7; 16:6; 9:5; 13:5; 10:4; 18:3; 12:3; 3:2; 8:2; 1:2; 11:1; 2:1; 19:1 |
| miss_depth3_32_63_avoid | events_inside_32_63_waiting_rows | 19 | 15 | 17 | 103 | 15:17; 6:16; 5:14; 7:13; 14:10; 17:8; 4:7; 16:6; 9:5; 13:5; 10:4; 18:3; 12:3; 3:2; 8:2; 1:2; 11:1; 2:1; 19:1 |
| miss_depth3_32_63_avoid | wait_length_inside_32_63 | 19 | 14 | 17 | 103 | 14:17; 5:16; 4:14; 6:13; 13:10; 16:8; 3:7; 15:6; 8:5; 12:5; 9:4; 17:3; 11:3; 2:2; 7:2; 0:2; 10:1; 1:1; 18:1 |
| miss_depth3_32_63_avoid | entry_residue_pair_mod32 | 44 | 14->13 | 17 | 103 | 14->13:17; 31->30:11; 31->28:10; 9->8:7; 14->12:6; 29->28:6; 17->16:5; 31->29:5; 26->25:4; 25->24:3; 14->11:3; 30->29:3; 9->7:2; 14->9:2; 14->10:2; 22->21:2; 28->27:2; 18->17:2; 30->28:2; 10->9:2; 9->6:1; 6->4:1; 6->3:1; 6->5:1; 27->25:1; 10->8:1; 26->24:1; 11->8:1; 3->27:1; 8->29:1; 31->26:1; 8->6:1; 18->14:1; 31->27:1; 30->27:1; 26->23:1; 28->26:1; 23->22:1; 12->9:1; 15->14:1; 18->16:1; 12->10:1; 19->17:1; 21->20:1 |
| miss_depth3_32_63_avoid | last_k_window_5_before_16_31 | 79 | 1,1,3,1,5 | 7 | 113 | 1,1,3,1,5:7; 1,3,1,2,4:7; 1,6,3,3,5:5; 1,2,1,1,5:5; 2,2,1,1,4:3; 5,1,2,1,5:3; 3,1,2,1,5:3; 4,2,1,1,4:3; 1,1,2,1,6:2; 3,1,4,2,5:2; 2,3,3,1,4:2; 1,1,1,3,6:2; 3,1,1,3,6:2; 5,2,1,2,4:2; 1,1,3,2,4:2; 3,1,3,2,4:2; 6,3,1,1,6:2; 6,1,1,2,4:2; 1,1,1,7,5:2; 3,1,1,2,8:2; 2,2,1,1,9:2; 2,1,1,2,4:1; 3,1,2,4:1; 1,1,1,1,6:1; 1,1,2,1,5:1; 1,2,2,1,5:1; 1,4,1,5:1; 1,1,3,6:1; 1,2,1,2,4:1; 2,1,4:1; 3,4:1; 1,1,5:1; 1,2,2,1,9:1; 3,2,2,2,5:1; 1,1,4,2,5:1; 2,1,2,2,6:1; 3,4,1,1,4:1; 1,5,3,1,4:1; 1,4,1,1,5:1; 2,1,2,1,6:1; 3,1,2,1,6:1; 5,1,2,1,6:1; 2,5,2,1,6:1; 5,1,1,3,6:1; 3,2,1,2,4:1; 2,2,3,1,6:1; 2,2,2,2,7:1; 1,4,2,2,7:1; 1,1,1,2,4:1; 2,1,1,1,6:1; 3,3,1,2,4:1; 1,2,3,4,7:1; 4,5,4,2,5:1; 3,2,1,6:1; 8:1; 11:1; 3,1,1,3,5:1; 1,3,4,1,5:1; 2,1,1,5:1; 5,1,2,5,5:1; 5,4,1,1,4:1; 3,3,5,3,5:1; 2,3,2,2,8:1; 1,4,1,3,5:1; 2,7,1,2,4:1; 2,1,5,1,8:1; 3,1,3,2,5:1; 1,6,2,1,5:1; 1,2,2,4,4:1; 2,5,1,8:1; 1,1,2,2,6:1; 3,1,7,1,6:1; 3,1,2,3,7:1; 2,1,5,1,4:1; 1,1,1,10:1; 1,1,1,6,4:1; 2,2,1,1,8:1; 1,7,2,1,6:1; 4,1,3,1,3:1 |
| miss_depth3_32_63_avoid | entry_k_window_5 | 101 | 3,1,1,1,2 | 5 | 115 | 3,1,1,1,2:5; 1,2,1,1,1:4; 1,1,1,2,1:3; 1,1,1,3,1:3; 1,1,1,1,1:3; 3,1,1,2,1:2; 1,3,1,2,1:2; 1,1,1,1,2:2; 1,1,4,2,2:2; 1,1,1,1,4:2; 1,1,1,2,2:2; 2,1,1,2,4:1; 3,1,2,4:1; 1,1,1,1,6:1; 1,1,2,1,5:1; 1,2,2,1,5:1; 1,4,1,5:1; 2,2,1,1,4:1; 1,1,2,1,6:1; 1,1,3,6:1; 1,2,1,2,4:1; 1,2,1,1,2:1; 2,1,4:1; 3,4:1; 1,1,5:1; 1,2,2,1,9:1; 2,3,2,2,2:1; 1,2,1,1,4:1; 1,3,1,4,2:1; 1,1,2,1,2:1; 3,2,2,2,1:1; 1,4,2,2,1:1; 2,1,4,2,1:1; 3,4,2,1,1:1; 2,3,4,1,1:1; 1,1,2,3,3:1; 1,1,5,3,1:1; 1,2,1,4,1:1; 5,1,1,2,1:1; 3,3,1,2,1:1; 1,5,1,2,1:1; 4,1,1,1,3:1; 2,5,2,1,6:1; 2,3,1,1,3:1; 5,1,1,3,6:1; 1,2,3,2,1:1; 1,5,2,1,2:1; 2,2,1,1,3:1; 4,1,1,3,2:1; 1,1,3,1,3:1; 1,2,2,3,1:1; 1,1,2,2,2:1; 1,1,2,1,1:1; 2,4,1,2,1:1; 2,1,2,2,2:1; 2,1,1,1,6:1; 2,3,1,1,1:1; 3,1,1,4,3:1; 1,1,1,4,1:1; 1,2,3,4,7:1; 3,2,1,6:1; 8:1; 11:1; 1,4,2,3,1:1; 1,2,6,4,1:1; 5,2,1,5,2:1; 2,1,1,5:1; 1,1,4,2,1:1; 3,2,2,1,5:1; 2,1,3,1,1:1; 4,1,1,1,1:1; 4,1,2,2,1:1; 3,4,3,1,2:1; 1,3,3,5,3:1; 3,3,4,1,3:1; 3,1,1,3,3:1; 2,2,2,1,1:1; 1,4,1,2,2:1; 1,2,1,3,2:1; 2,3,4,1,2:1; 3,1,1,3,6:1; 2,1,1,1,1:1; 2,3,3,1,4:1; 1,2,5,1,1:1; 1,3,1,1,1:1; 2,5,1,8:1; 1,1,2,2,1:1; 1,3,3,3,2:1; 2,3,5,1,1:1; 2,3,1,7,1:1; 1,2,3,1,1:1; 1,2,1,1,3:1; 1,1,1,3,3:1; 2,1,1,1,2:1; 1,3,1,2,4:1; 1,2,2,1,2:1; 1,1,1,10:1; 1,2,2,6,1:1; 2,1,2,1,3:1; 1,3,1,4,1:1; 1,3,4,3,1:1 |

## Paired Examples Preview

| control_sample_id | control_trajectory_id | control_stage_status | control_entry_R | control_exit_R | control_entry_shape | control_last_event_before_16_31 | control_entry_k_window_5 | control_last_k_window_5 | miss_sample_id | miss_trajectory_id | miss_stage_status | miss_entry_R | miss_exit_R | miss_entry_shape | miss_last_event_before_16_31 | miss_entry_k_window_5 | miss_last_k_window_5 | pair_score_32_63 | same_entry_shape | same_last_event_before_16_31 | same_entry_k_window_5 | same_last_k_window_5 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Sample_D_random_550 | 555169 | avoid_then_caught | 63 | 30 | 31->30|k=1 | R=32->30|k=2|res=0->30 | 1,1,1,3,1 | 3,1,1,1,2 | Sample_E_stratified_550 | 99182 | avoid | 47 | 30 | 15->14|k=1 | R=35->30|k=5|res=3->30 | 1,1,1,3,1 | 3,1,3,2,5 | 20.16 | False | False | True | False |
| Sample_E_stratified_550 | 618657 | avoid_then_caught | 63 | 31 | 31->30|k=1 | R=33->31|k=2|res=1->31 | 1,2,3,1,1 | 1,2,1,2,2 | Sample_E_stratified_550 | 594123 | avoid | 60 | 31 | 28->27|k=1 | R=35->31|k=4|res=3->31 | 1,2,3,1,1 | 4,2,1,1,4 | 24.03 | False | False | True | False |
| Sample_A_baseline | 4551 | avoid_then_caught | 63 | 29 | 31->29|k=2 | R=32->29|k=3|res=0->29 | 2,2,1,2,1 | 1,2,1,1,1 | Sample_D_random_550 | 216559 | avoid | 63 | 31 | 31->29|k=2 | R=35->31|k=4|res=3->31 | 2,1,2,2,2 | 6,1,1,2,4 | 29.0 | True | False | False | False |
| Sample_B_next_range_550 | 4862 | avoid_then_caught | 63 | 29 | 31->29|k=2 | R=32->29|k=3|res=0->29 | 2,2,1,2,1 | 1,2,1,1,1 | Sample_D_random_550 | 216559 | avoid | 63 | 31 | 31->29|k=2 | R=35->31|k=4|res=3->31 | 2,1,2,2,2 | 6,1,1,2,4 | 29.0 | True | False | False | False |
| Sample_C_higher_range_550 | 50015 | avoid_then_caught | 63 | 29 | 31->27|k=4 | R=32->29|k=3|res=0->29 | 4,1,2,1,1 | 2,1,1,1,1 | Sample_D_random_550 | 792274 | avoid | 63 | 31 | 31->27|k=4 | R=35->31|k=4|res=3->31 | 4,1,2,2,1 | 5,4,1,1,4 | 29.0 | True | False | False | False |
| Sample_C_higher_range_550 | 50033 | avoid_then_caught | 63 | 29 | 31->27|k=4 | R=32->29|k=3|res=0->29 | 4,1,2,1,1 | 2,1,1,1,1 | Sample_D_random_550 | 792274 | avoid | 63 | 31 | 31->27|k=4 | R=35->31|k=4|res=3->31 | 4,1,2,2,1 | 5,4,1,1,4 | 29.0 | True | False | False | False |
| Sample_C_higher_range_550 | 50121 | avoid_then_caught | 63 | 29 | 31->27|k=4 | R=32->29|k=3|res=0->29 | 4,1,2,1,1 | 2,1,1,1,1 | Sample_D_random_550 | 792274 | avoid | 63 | 31 | 31->27|k=4 | R=35->31|k=4|res=3->31 | 4,1,2,2,1 | 5,4,1,1,4 | 29.0 | True | False | False | False |
| Sample_C_higher_range_550 | 50206 | avoid_then_caught | 63 | 29 | 31->27|k=4 | R=32->29|k=3|res=0->29 | 4,1,2,1,1 | 2,1,1,1,1 | Sample_D_random_550 | 792274 | avoid | 63 | 31 | 31->27|k=4 | R=35->31|k=4|res=3->31 | 4,1,2,2,1 | 5,4,1,1,4 | 29.0 | True | False | False | False |
| Sample_C_higher_range_550 | 50268 | avoid_then_caught | 63 | 29 | 31->29|k=2 | R=32->29|k=3|res=0->29 | 2,2,1,2,1 | 1,2,1,1,1 | Sample_D_random_550 | 216559 | avoid | 63 | 31 | 31->29|k=2 | R=35->31|k=4|res=3->31 | 2,1,2,2,2 | 6,1,1,2,4 | 29.0 | True | False | False | False |
| Sample_C_higher_range_550 | 50269 | avoid_then_caught | 63 | 29 | 31->29|k=2 | R=32->29|k=3|res=0->29 | 2,2,1,2,1 | 1,2,1,1,1 | Sample_D_random_550 | 216559 | avoid | 63 | 31 | 31->29|k=2 | R=35->31|k=4|res=3->31 | 2,1,2,2,2 | 6,1,1,2,4 | 29.0 | True | False | False | False |
| Sample_C_higher_range_550 | 50331 | avoid_then_caught | 63 | 30 | 31->30|k=1 | R=32->30|k=2|res=0->30 | 1,1,3,1,1 | 1,1,2,5,2 | Sample_D_random_550 | 45028 | avoid | 63 | 31 | 31->30|k=1 | R=36->31|k=5|res=4->31 | 1,1,2,1,1 | 1,1,3,1,5 | 29.0 | True | False | False | False |
| Sample_C_higher_range_550 | 50503 | avoid_then_caught | 63 | 29 | 31->29|k=2 | R=32->29|k=3|res=0->29 | 2,2,1,2,1 | 1,2,1,1,1 | Sample_D_random_550 | 216559 | avoid | 63 | 31 | 31->29|k=2 | R=35->31|k=4|res=3->31 | 2,1,2,2,2 | 6,1,1,2,4 | 29.0 | True | False | False | False |

## Hypothesis Checks

- Mostly position? Supported descriptively. `entry_R`, `exit_R`, and wait length differ strongly.
- Mostly local shape? Weaker. Some local k/residue windows pair, but many local shape descriptors are not identical across groups.
- Mostly k-sequence? Mixed. The groups share some recurring suffix-window motifs, but k-window selectors also separate subsets.
- Mostly wait timing? Supported descriptively; controls show longer 32-63 windows.
- Chain-status definition artifact? Partly yes. The local `stage_event_classification` is `avoid_then_caught` for both groups, while `stage_chain_status` differs. The meaningful finite-table split is therefore at the chain-status layer plus associated 32-63 position/timing descriptors, not a different local event classification alone.

## Failed Hypotheses

- `32-63 local event classification separates the groups`: false; it is `avoid_then_caught` for both groups.
- `32-63 presence separates the groups`: false; both groups have the stage.
- `A pure transition_k selector explains the split`: not supported; k values overlap.
- `The split can be read as a mechanism`: not supported and not tested here.

## Suggested Next Exploration

- Pair the last 32-63 event before 16-31 with the first 16-31 event and inspect the boundary transition itself.
- Stratify controls by the two main 32-63 entry windows, then compare whether the downstream 16-31/8-15 suffix remains invariant.
- Keep the chain-status layer separate from the local event-classification layer in any manuscript wording.

## Output Files

- `stage_32_63_comparison_table.csv`
- `stage_32_63_numeric_summary.csv`
- `stage_32_63_distributions.csv`
- `stage_32_63_invariants.csv`
- `minimal_selector_audit.csv`
- `stage_32_63_paired_examples.csv`