# 32-63 boundary-transition audit

Finite-sample descriptive exploration only. Local event classification, chain status, and boundary-front position are kept separate.

## Main Read

- The simple boundary-front selector separates the two groups in this finite table.
- Selector result: `True`.
- Controls leave 32-63 from the lower edge: mostly `R=32->29`, k=3, residue `0->29`.
- Miss-depth-3 leaves 32-63 from the miss-front: mostly `R=35/36/37 -> 31/30`, k=4/5/6.
- This is not a local event-classification split: both groups remain `stage_event_classification = avoid_then_caught` at 32-63.
- Downstream does not immediately become identical. The first 16-31 event has overlap, but group-specific modes remain visible for several prefix summaries.

## Exact Boundary Transition Frequencies

- controls boundary events: `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 boundary events: `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`

## Simple Selector Audit

| group | rows | lower_edge_0_1 | miss_front_2_8_observed | other | selector_distribution |
| --- | --- | --- | --- | --- | --- |
| control_32_63_avoid_then_caught | 47 | 47 | 0 | 0 | lower_edge_0_1:47 |
| miss_depth3_32_63_avoid | 120 | 0 | 120 | 0 | miss_front_2_8_observed:120 |

Selector tested:

- controls: `last_before_exit_distance in {0,1}`
- miss-depth-3: `last_before_exit_distance in {2,3,4,5,7,8}`

## Downstream Reconvergence

| feature | control_unique | miss_unique | shared_unique | control_top | miss_top | shared_values_preview |
| --- | --- | --- | --- | --- | --- | --- |
| first_16_31 | 3 | 14 | 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 | 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=29|k=1|res=29->28; R=30|k=1|res=30->29; R=31|k=2|res=31->29 |
| 16-31_k_prefix_3 | 3 | 27 | 2 | 1,1,1:45; 1,1,7:1; 2,1,1:1 | 1,1,1:30; 3,1,1:13; 1,2,1:12; 3,1,5:11; 2,1,2:10 | 1,1,1; 2,1,1 |
| 16-31_k_prefix_5 | 4 | 33 | 1 | 1,1,1,4,2:44; 1,1,7,2,1:1; 1,1,1,1,4:1; 2,1,1,1,6:1 | 1,1,1,2,1:16; 3,1,1,6,1:13; 1,2,1,3,1:12; 3,1,5,1,2:11; 2,1,2,3,1:10 | 2,1,1,1,6 |
| 16-31_classification | 1 | 1 | 1 | avoid_then_caught:47 | avoid_then_caught:120 | avoid_then_caught |
| 16-31_eventually_caught_band | 1 | 2 | 1 | 4-7:47 | 4-7:119; NA:1 | 4-7 |
| 8-15_k_prefix_3 | 3 | 9 | 3 | 3,1,1:45; 1,3,1:1; 4,1,1:1 | 1,3,1:57; 4,1,1:53; 1,1,2:2; 5,1,5:2; 3,1,1:2 | 1,3,1; 3,1,1; 4,1,1 |
| 8-15_k_prefix_5 | 3 | 9 | 3 | 3,1,1,5:45; 1,3,1,2:1; 4,1,1,2:1 | 1,3,1,2:57; 4,1,1,2:53; 1,1,2:2; 5,1,5:2; 3,1,1,5:2 | 1,3,1,2; 3,1,1,5; 4,1,1,2 |
| 8-15_classification | 1 | 1 | 1 | avoid_then_caught:47 | avoid_then_caught:120 | avoid_then_caught |
| 4-7_k_prefix_3 | 2 | 3 | 2 | 4:45; 3,4:2 | 3,4:115; 4:4; NA:1 | 3,4; 4 |
| 4-7_classification | 2 | 3 | 2 | caught:45; avoid_then_caught:2 | avoid_then_caught:115; caught:4; NA:1 | avoid_then_caught; caught |
| downstream_signature_16_8_4 | 4 | 34 | 1 | 16:1,1,1,4,2|8:3,1,1,5|4:4:44; 16:1,1,7,2,1|8:1,3,1,2|4:3,4:1; 16:1,1,1,1,4|8:3,1,1,5|4:4:1; 16:2,1,1,1,6|8:4,1,1,2|4:3,4:1 | 16:1,1,1,2,1|8:4,1,1,2|4:3,4:16; 16:3,1,1,6,1|8:4,1,1,2|4:3,4:13; 16:1,2,1,3,1|8:1,3,1,2|4:3,4:12; 16:3,1,5,1,2|8:1,3,1,2|4:3,4:11; 16:2,1,2,3,1|8:1,3,1,2|4:3,4:10 | 16:2,1,1,1,6|8:4,1,1,2|4:3,4 |

## Paired Examples

| example | group | sample_id | trajectory_id | boundary_event | boundary_exit_distance | wait_length_inside_32_63 | first_16_31 | 16_31_k_prefix_5 | 8_15_k_prefix_5 | 4_7_k_prefix_5 | lower5_final_status |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| typical_control_32_to_29 | control_32_63_avoid_then_caught | Sample_A_baseline | 4551 | R=32->29|k=3|res=0->29 | 0 | 22 | R=29|k=1|res=29->28 | 1,1,1,4,2 | 3,1,1,5 | 4 | eventually_reentered_exit_layer:caught |
| rare_control_32_to_30 | control_32_63_avoid_then_caught | Sample_C_higher_range_550 | 50331 | R=32->30|k=2|res=0->30 | 0 | 19 | R=30|k=1|res=30->29 | 1,1,7,2,1 | 1,3,1,2 | 3,4 | eventually_reentered_exit_layer:avoid_then_caught |
| rare_control_33_to_31 | control_32_63_avoid_then_caught | Sample_E_stratified_550 | 618657 | R=33->31|k=2|res=1->31 | 1 | 17 | R=31|k=2|res=31->29 | 2,1,1,1,6 | 4,1,1,2 | 3,4 | eventually_reentered_exit_layer:avoid_then_caught |
| typical_miss_35_to_31 | miss_depth3_32_63_avoid | Sample_B_next_range_550 | 4636 | R=35->31|k=4|res=3->31 | 3 | 4 | R=31|k=1|res=31->30 | 1,1,1,2,1 | 4,1,1,2 | 3,4 | eventually_reentered_exit_layer:avoid_then_caught |
| typical_miss_36_to_31 | miss_depth3_32_63_avoid | Sample_B_next_range_550 | 4647 | R=36->31|k=5|res=4->31 | 4 | 4 | R=31|k=1|res=31->30 | 1,1,1,3,5 | 4,1,1,2 | 3,4 | eventually_reentered_exit_layer:avoid_then_caught |
| miss_35_to_30 | miss_depth3_32_63_avoid | Sample_B_next_range_550 | 4674 | R=35->30|k=5|res=3->30 | 3 | 4 | R=30|k=2|res=30->28 | 2,1,2,3,1 | 1,3,1,2 | 3,4 | eventually_reentered_exit_layer:avoid_then_caught |
| rare_miss_34_to_31 | miss_depth3_32_63_avoid | Sample_E_stratified_550 | 560062 | R=34->31|k=3|res=2->31 | 2 | 16 | R=31|k=1|res=31->30 | 1,3,2,3,1 | 1,3,1,2 | 3,4 | eventually_reentered_exit_layer:avoid_then_caught |
| rare_miss_40_to_31 | miss_depth3_32_63_avoid | Sample_C_higher_range_550 | 50027 | R=40->31|k=9|res=8->31 | 8 | 4 | R=31|k=1|res=31->30 | 1,3,2,3,1 | 1,3,1,2 | 3,4 | eventually_reentered_exit_layer:avoid_then_caught |

## Failed Hypotheses

- `transition_k alone is the split`: too narrow; k differs strongly at the boundary, but it is coupled to boundary-front position and residue.
- `residue alone is the whole story`: too narrow; residue separates in this finite table, but it is the residue of the boundary-front event and tracks position.
- `the two groups reconverge immediately after entering 16-31`: not fully supported; some first 16-31 shapes overlap, but prefix distributions remain visibly different.
- `local event classification explains the split`: false; both groups have the same 32-63 local event classification.

## Wording Recommendation

A cautious manuscript sentence:

> In the finite event table, the 32-63 split is best described as a boundary-front split rather than as a different local event-classification label: control trajectories leave 32-63 from the lower edge, usually `32->29`, whereas miss-depth-3 trajectories leave from the miss-front, most often `35/36/37 -> 31/30`, and remain in the consecutive avoidance run.

Keep the following distinction explicit:

- local event classification: both groups are `avoid_then_caught` at 32-63
- chain status: controls are `avoid_then_caught`; miss-depth-3 rows are `avoid`
- boundary-front coordinate: controls are `{0,1}` from the lower edge; miss-depth-3 rows are `{2,3,4,5,7,8}`

## Output Files

- `boundary_transition_detail.csv`
- `boundary_transition_frequency_table.csv`
- `simple_boundary_front_selector_audit.csv`
- `downstream_reconvergence_table.csv`
- `boundary_transition_paired_examples.csv`