# Band-general boundary-front geometry audit

Finite-sample descriptive geometry only. This audit does not require miss events to exist in a band and does not claim mechanism, causality, proof, counterexample, or global Collatz behavior.

## Definitions

- `lower_edge_front`: `last_before_exit_distance in {0,1}`
- `near_exit_front`: `last_before_exit_distance in {2,3,4,5,6,7,8}`
- `deeper_front`: `last_before_exit_distance > 8`
- `last_before_exit_distance` is a boundary-aligned coordinate: `last_before_R - band_lower`.
- `miss_supported_shape_rows` counts waiting-hall rows whose `(residue_pair_mod32, transition_k)` belongs to the observed miss-event shape support. This is a shape-support diagnostic, not a miss label.

## Compact Cross-Band Table

| band | rows | front_classes_present | dominant_front | dominant_chain_by_front | dominant_local_class_by_front | dominant_near_behavior_by_front | miss_rows | miss_supported_shape_rows | front_purity_for_chain_status | local_class_purity_for_chain_status | front_better_than_local_class | notes |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 4-7 | 2581 | lower_edge_front:2581 | lower_edge_front | lower_edge_front=>caught:1556; avoid_then_caught:1025 | lower_edge_front=>caught:1556; avoid_then_caught:1025 | lower_edge_front=>NA:2581 | 0 | 0 | 0.602867 | 1.0 | False | no observed miss events in this band; no miss-supported local shapes observed |
| 8-15 | 2744 | lower_edge_front:2583; near_exit_front:161 | lower_edge_front | lower_edge_front=>avoid:2527; avoid_then_caught:47; caught:9 \| near_exit_front=>avoid:161 | lower_edge_front=>avoid_then_caught:2574; caught:9 \| near_exit_front=>avoid_then_caught:161 | lower_edge_front=>NA:2583 \| near_exit_front=>NA:161 | 0 | 0 | 0.979592 | 0.982872 | False | no observed miss events in this band; no miss-supported local shapes observed; lower/near front structure present |
| 16-31 | 2744 | deeper_front:10; lower_edge_front:814; near_exit_front:1920 | near_exit_front | deeper_front=>avoid:10 \| lower_edge_front=>avoid:456; avoid_then_caught:356; caught:2 \| near_exit_front=>avoid:1920 | deeper_front=>avoid_then_caught:10 \| lower_edge_front=>avoid_then_caught:812; caught:2 \| near_exit_front=>avoid_then_caught:1920 | deeper_front=>NA:10 \| lower_edge_front=>NA:814 \| near_exit_front=>NA:1920 | 0 | 0 | 0.869534 | 0.870262 | False | no observed miss events in this band; no miss-supported local shapes observed; lower/near front structure present |
| 32-63 | 2489 | lower_edge_front:2204; near_exit_front:285 | lower_edge_front | lower_edge_front=>avoid_then_caught:2182; caught:22 \| near_exit_front=>avoid:285 | lower_edge_front=>avoid_then_caught:2182; caught:22 \| near_exit_front=>avoid_then_caught:285 | lower_edge_front=>drift:2166; exit:35; wait:3 \| near_exit_front=>wait:157; drift:120; exit:4 | 159 | 159 | 0.991161 | 0.885496 | True | miss-supported local shapes appear; lower/near front structure present |
| 64-127 | 1754 | lower_edge_front:1615; near_exit_front:139 | lower_edge_front | lower_edge_front=>avoid_then_caught:1549; caught:66 \| near_exit_front=>avoid_then_caught:102; avoid:28; caught:9 | lower_edge_front=>avoid_then_caught:1549; caught:66 \| near_exit_front=>avoid_then_caught:130; caught:9 | lower_edge_front=>drift:1506; exit:99; wait:10 \| near_exit_front=>drift:75; wait:56; exit:6 | 53 | 97 | 0.941277 | 0.984036 | False | miss-supported local shapes appear; lower/near front structure present |
| 128-255 | 241 | lower_edge_front:197; near_exit_front:44 | lower_edge_front | lower_edge_front=>avoid_then_caught:134; caught:63 \| near_exit_front=>avoid_then_caught:38; caught:6 | lower_edge_front=>avoid_then_caught:134; caught:63 \| near_exit_front=>avoid_then_caught:38; caught:6 | lower_edge_front=>drift:149; exit:37; wait:9 \| near_exit_front=>drift:25; wait:19 | 16 | 19 | 0.713693 | 1.0 | False | miss-supported local shapes appear; lower/near front structure present |
| 256-511 | 3 | lower_edge_front:3 | lower_edge_front | lower_edge_front=>caught:2; avoid_then_caught:1 | lower_edge_front=>caught:2; avoid_then_caught:1 | lower_edge_front=>NA:3 | 0 | 0 | 0.666667 | 1.0 | False | no observed miss events in this band; no miss-supported local shapes observed |
| 512-1023 | 0 | not_available | NA | NA | NA | NA | 0 | 0 | 0.0 | 0.0 | False | no lower_5pct exit-event rows for this band |

## Main Read

- The audit is now a boundary-front geometry audit, not a miss/control audit.
- Bands with no miss events are kept in the table and interpreted only through front class, chain status, local event classification, near behavior, trajectory behavior, and shape support.
- `front_purity_for_chain_status` and `local_class_purity_for_chain_status` are finite-table summaries of how well each coordinate groups the observed chain-status labels.

## Per-Band Front Distribution

| band | front_class | rows | stage_chain_status | stage_event_classification | near_behavior | trajectory_behavior_class | max_avoidance_depth | eventual_capture_band | miss_rows | miss_supported_shape_rows |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 4-7 | lower_edge_front | 2581 | caught:1556; avoid_then_caught:1025 | caught:1556; avoid_then_caught:1025 | NA:2581 | NA:2581 | 2:2108; 1:278; 3:195 | 4-7:2521; 16-31:52; 32-63:8 | 0 | 0 |
| 8-15 | lower_edge_front | 2583 | avoid:2527; avoid_then_caught:47; caught:9 | avoid_then_caught:2574; caught:9 | NA:2583 | NA:2583 | 2:2089; 1:271; 3:193; 0:30 | 4-7:2470; 16-31:53; NA:30; 8-15:22; 32-63:8 | 0 | 0 |
| 8-15 | near_exit_front | 161 | avoid:161 | avoid_then_caught:161 | NA:161 | NA:161 | 2:81; 1:75; 3:5 | NA:87; 4-7:47; 16-31:26; 32-63:1 | 0 | 0 |
| 16-31 | deeper_front | 10 | avoid:10 | avoid_then_caught:10 | NA:10 | NA:10 | 2:10 | 4-7:9; NA:1 | 0 | 0 |
| 16-31 | lower_edge_front | 814 | avoid:456; avoid_then_caught:356; caught:2 | avoid_then_caught:812; caught:2 | NA:814 | NA:814 | 2:401; 1:330; 3:51; 0:32 | 4-7:617; NA:105; 16-31:79; 32-63:9; 8-15:4 | 0 | 0 |
| 16-31 | near_exit_front | 1920 | avoid:1920 | avoid_then_caught:1920 | NA:1920 | NA:1920 | 2:1759; 3:147; 1:14 | 4-7:1889; 8-15:18; NA:13 | 0 | 0 |
| 32-63 | lower_edge_front | 2204 | avoid_then_caught:2182; caught:22 | avoid_then_caught:2182; caught:22 | drift:2166; exit:35; wait:3 | drift_down:2169; direct_to_exit:33; mid_band_wait_then_drop:2 | 2:1990; 1:195; 0:19 | 4-7:2124; NA:69; 32-63:9; 8-15:2 | 0 | 0 |
| 32-63 | near_exit_front | 285 | avoid:285 | avoid_then_caught:285 | wait:157; drift:120; exit:4; miss:4 | no_exit_layer_observed:159; drift_down:120; direct_to_exit:6 | 3:198; 1:79; 2:8 | 4-7:195; 16-31:79; 8-15:8; NA:3 | 159 | 159 |
| 64-127 | lower_edge_front | 1615 | avoid_then_caught:1549; caught:66 | avoid_then_caught:1549; caught:66 | drift:1506; exit:99; wait:10 | drift_down:1098; mid_band_wait_then_drop:427; direct_to_exit:90 | 2:1488; 1:78; 3:46; 0:3 | 4-7:1577; 16-31:24; NA:14 | 0 | 43 |
| 64-127 | near_exit_front | 139 | avoid_then_caught:102; avoid:28; caught:9 | avoid_then_caught:130; caught:9 | drift:75; wait:56; exit:6; miss:2 | drift_down:60; no_exit_layer_observed:53; mid_band_wait_then_drop:15; direct_to_exit:11 | 2:114; 1:16; 3:9 | 4-7:126; 32-63:9; 16-31:2; 8-15:1; NA:1 | 53 | 54 |
| 128-255 | lower_edge_front | 197 | avoid_then_caught:134; caught:63 | avoid_then_caught:134; caught:63 | drift:149; exit:37; wait:9; NA:2 | drift_down:108; direct_to_exit:46; mid_band_wait_then_drop:41; NA:2 | 2:180; 1:15; 3:2 | 4-7:188; 32-63:7; NA:1; 16-31:1 | 0 | 1 |
| 128-255 | near_exit_front | 44 | avoid_then_caught:38; caught:6 | avoid_then_caught:38; caught:6 | drift:25; wait:19 | drift_down:20; no_exit_layer_observed:16; mid_band_wait_then_drop:5; direct_to_exit:3 | 2:40; 1:4 | 4-7:42; 32-63:1; NA:1 | 16 | 18 |
| 256-511 | lower_edge_front | 3 | caught:2; avoid_then_caught:1 | caught:2; avoid_then_caught:1 | NA:3 | NA:3 | 2:3 | 4-7:3 | 0 | 0 |
| 512-1023 | not_available | 0 | NA | NA | NA | NA | NA | NA | 0 | 0 |

## Count Table

| band | boundary_front_class | stage_chain_status | stage_event_classification | dominant_near_behavior | dominant_trajectory_behavior_class | max_avoidance_depth | eventual_capture_band | rows |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 128-255 | lower_edge_front | avoid_then_caught | avoid_then_caught | drift | drift_down | 2 | 4-7 | 81 |
| 128-255 | lower_edge_front | avoid_then_caught | avoid_then_caught | drift | mid_band_wait_then_drop | 2 | 4-7 | 40 |
| 128-255 | lower_edge_front | caught | caught | exit | direct_to_exit | 2 | 4-7 | 35 |
| 128-255 | lower_edge_front | caught | caught | drift | drift_down | 2 | 4-7 | 13 |
| 128-255 | lower_edge_front | caught | caught | wait | direct_to_exit | 2 | 4-7 | 8 |
| 128-255 | lower_edge_front | avoid_then_caught | avoid_then_caught | drift | drift_down | 1 | 32-63 | 7 |
| 128-255 | lower_edge_front | avoid_then_caught | avoid_then_caught | drift | drift_down | 1 | 4-7 | 3 |
| 128-255 | lower_edge_front | caught | caught | exit | direct_to_exit | 1 | 4-7 | 2 |
| 128-255 | lower_edge_front | caught | caught | nan | nan | 2 | 4-7 | 2 |
| 128-255 | lower_edge_front | avoid_then_caught | avoid_then_caught | drift | drift_down | 2 | nan | 1 |
| 128-255 | lower_edge_front | avoid_then_caught | avoid_then_caught | drift | drift_down | 3 | 4-7 | 1 |
| 128-255 | lower_edge_front | avoid_then_caught | avoid_then_caught | drift | mid_band_wait_then_drop | 1 | 4-7 | 1 |
| 128-255 | lower_edge_front | caught | caught | drift | drift_down | 1 | 16-31 | 1 |
| 128-255 | lower_edge_front | caught | caught | drift | drift_down | 3 | 4-7 | 1 |
| 128-255 | lower_edge_front | caught | caught | wait | direct_to_exit | 1 | 4-7 | 1 |
| 128-255 | near_exit_front | avoid_then_caught | avoid_then_caught | drift | drift_down | 2 | 4-7 | 17 |
| 128-255 | near_exit_front | avoid_then_caught | avoid_then_caught | wait | no_exit_layer_observed | 2 | 4-7 | 11 |
| 128-255 | near_exit_front | avoid_then_caught | avoid_then_caught | drift | mid_band_wait_then_drop | 2 | 4-7 | 5 |
| 128-255 | near_exit_front | caught | caught | wait | direct_to_exit | 2 | 4-7 | 3 |
| 128-255 | near_exit_front | caught | caught | wait | no_exit_layer_observed | 2 | 4-7 | 3 |
| 128-255 | near_exit_front | avoid_then_caught | avoid_then_caught | wait | no_exit_layer_observed | 1 | 4-7 | 2 |
| 128-255 | near_exit_front | avoid_then_caught | avoid_then_caught | drift | drift_down | 1 | 32-63 | 1 |
| 128-255 | near_exit_front | avoid_then_caught | avoid_then_caught | drift | drift_down | 1 | 4-7 | 1 |
| 128-255 | near_exit_front | avoid_then_caught | avoid_then_caught | drift | drift_down | 2 | nan | 1 |
| 16-31 | deeper_front | avoid | avoid_then_caught | nan | nan | 2 | 4-7 | 9 |
| 16-31 | deeper_front | avoid | avoid_then_caught | nan | nan | 2 | nan | 1 |
| 16-31 | lower_edge_front | avoid | avoid_then_caught | nan | nan | 2 | 4-7 | 360 |
| 16-31 | lower_edge_front | avoid_then_caught | avoid_then_caught | nan | nan | 1 | 4-7 | 207 |
| 16-31 | lower_edge_front | avoid_then_caught | avoid_then_caught | nan | nan | 1 | 16-31 | 79 |
| 16-31 | lower_edge_front | avoid | avoid_then_caught | nan | nan | 3 | 4-7 | 49 |
| 16-31 | lower_edge_front | avoid | avoid_then_caught | nan | nan | 2 | nan | 41 |
| 16-31 | lower_edge_front | avoid_then_caught | avoid_then_caught | nan | nan | 0 | nan | 32 |
| 16-31 | lower_edge_front | avoid_then_caught | avoid_then_caught | nan | nan | 1 | nan | 29 |
| 16-31 | lower_edge_front | avoid_then_caught | avoid_then_caught | nan | nan | 1 | 32-63 | 9 |
| 16-31 | lower_edge_front | avoid | avoid_then_caught | nan | nan | 1 | 8-15 | 4 |
| 16-31 | lower_edge_front | avoid | avoid_then_caught | nan | nan | 3 | nan | 2 |
| 16-31 | lower_edge_front | caught | caught | nan | nan | 1 | 4-7 | 1 |
| 16-31 | lower_edge_front | caught | caught | nan | nan | 1 | nan | 1 |
| 16-31 | near_exit_front | avoid | avoid_then_caught | nan | nan | 2 | 4-7 | 1739 |
| 16-31 | near_exit_front | avoid | avoid_then_caught | nan | nan | 3 | 4-7 | 146 |
| 16-31 | near_exit_front | avoid | avoid_then_caught | nan | nan | 2 | nan | 12 |
| 16-31 | near_exit_front | avoid | avoid_then_caught | nan | nan | 1 | 8-15 | 10 |
| 16-31 | near_exit_front | avoid | avoid_then_caught | nan | nan | 2 | 8-15 | 8 |
| 16-31 | near_exit_front | avoid | avoid_then_caught | nan | nan | 1 | 4-7 | 4 |
| 16-31 | near_exit_front | avoid | avoid_then_caught | nan | nan | 3 | nan | 1 |
| 256-511 | lower_edge_front | caught | caught | nan | nan | 2 | 4-7 | 2 |
| 256-511 | lower_edge_front | avoid_then_caught | avoid_then_caught | nan | nan | 2 | 4-7 | 1 |
| 32-63 | lower_edge_front | avoid_then_caught | avoid_then_caught | drift | drift_down | 2 | 4-7 | 1935 |
| 32-63 | lower_edge_front | avoid_then_caught | avoid_then_caught | drift | drift_down | 1 | 4-7 | 157 |
| 32-63 | lower_edge_front | avoid_then_caught | avoid_then_caught | drift | drift_down | 2 | nan | 27 |
| 32-63 | lower_edge_front | avoid_then_caught | avoid_then_caught | drift | drift_down | 1 | nan | 18 |
| 32-63 | lower_edge_front | avoid_then_caught | avoid_then_caught | drift | drift_down | 0 | nan | 16 |
| 32-63 | lower_edge_front | caught | caught | exit | direct_to_exit | 2 | 4-7 | 14 |
| 32-63 | lower_edge_front | avoid_then_caught | avoid_then_caught | drift | drift_down | 1 | 32-63 | 9 |
| 32-63 | lower_edge_front | caught | caught | exit | direct_to_exit | 1 | 4-7 | 6 |
| 32-63 | lower_edge_front | avoid_then_caught | avoid_then_caught | exit | direct_to_exit | 2 | 4-7 | 3 |
| 32-63 | lower_edge_front | avoid_then_caught | avoid_then_caught | exit | direct_to_exit | 2 | nan | 3 |
| 32-63 | lower_edge_front | avoid_then_caught | avoid_then_caught | exit | drift_down | 2 | 4-7 | 3 |
| 32-63 | lower_edge_front | avoid_then_caught | avoid_then_caught | drift | drift_down | 1 | 8-15 | 2 |
| 32-63 | lower_edge_front | avoid_then_caught | avoid_then_caught | wait | direct_to_exit | 2 | 4-7 | 2 |
| 32-63 | lower_edge_front | avoid_then_caught | avoid_then_caught | drift | mid_band_wait_then_drop | 1 | 4-7 | 1 |
| 32-63 | lower_edge_front | avoid_then_caught | avoid_then_caught | drift | mid_band_wait_then_drop | 2 | 4-7 | 1 |
| 32-63 | lower_edge_front | avoid_then_caught | avoid_then_caught | exit | direct_to_exit | 0 | nan | 1 |
| 32-63 | lower_edge_front | avoid_then_caught | avoid_then_caught | exit | direct_to_exit | 1 | 4-7 | 1 |
| 32-63 | lower_edge_front | avoid_then_caught | avoid_then_caught | exit | drift_down | 1 | 4-7 | 1 |
| 32-63 | lower_edge_front | avoid_then_caught | avoid_then_caught | exit | drift_down | 2 | nan | 1 |
| 32-63 | lower_edge_front | avoid_then_caught | avoid_then_caught | wait | direct_to_exit | 0 | nan | 1 |
| 32-63 | lower_edge_front | caught | caught | exit | direct_to_exit | 0 | nan | 1 |
| 32-63 | lower_edge_front | caught | caught | exit | direct_to_exit | 2 | nan | 1 |
| 32-63 | near_exit_front | avoid | avoid_then_caught | wait | no_exit_layer_observed | 3 | 4-7 | 116 |
| 32-63 | near_exit_front | avoid | avoid_then_caught | drift | drift_down | 3 | 4-7 | 75 |
| 32-63 | near_exit_front | avoid | avoid_then_caught | drift | drift_down | 1 | 16-31 | 37 |
| 32-63 | near_exit_front | avoid | avoid_then_caught | wait | no_exit_layer_observed | 1 | 16-31 | 37 |
| 32-63 | near_exit_front | avoid | avoid_then_caught | drift | drift_down | 2 | 8-15 | 6 |
| 32-63 | near_exit_front | avoid | avoid_then_caught | drift | drift_down | 3 | nan | 2 |
| 32-63 | near_exit_front | avoid | avoid_then_caught | exit | direct_to_exit | 1 | 16-31 | 2 |
| 32-63 | near_exit_front | avoid | avoid_then_caught | miss | no_exit_layer_observed | 1 | 16-31 | 2 |
| 32-63 | near_exit_front | avoid | avoid_then_caught | miss | no_exit_layer_observed | 3 | 4-7 | 2 |
| 32-63 | near_exit_front | avoid | avoid_then_caught | exit | direct_to_exit | 2 | 8-15 | 1 |
| 32-63 | near_exit_front | avoid | avoid_then_caught | exit | direct_to_exit | 3 | 4-7 | 1 |
| 32-63 | near_exit_front | avoid | avoid_then_caught | wait | direct_to_exit | 1 | 16-31 | 1 |
| 32-63 | near_exit_front | avoid | avoid_then_caught | wait | direct_to_exit | 3 | 4-7 | 1 |
| 32-63 | near_exit_front | avoid | avoid_then_caught | wait | no_exit_layer_observed | 2 | 8-15 | 1 |
| 32-63 | near_exit_front | avoid | avoid_then_caught | wait | no_exit_layer_observed | 3 | nan | 1 |
| 4-7 | lower_edge_front | caught | caught | nan | nan | 2 | 4-7 | 1496 |
| 4-7 | lower_edge_front | avoid_then_caught | avoid_then_caught | nan | nan | 2 | 4-7 | 612 |
| 4-7 | lower_edge_front | avoid_then_caught | avoid_then_caught | nan | nan | 3 | 4-7 | 186 |
| 4-7 | lower_edge_front | avoid_then_caught | avoid_then_caught | nan | nan | 1 | 4-7 | 170 |
| 4-7 | lower_edge_front | avoid_then_caught | avoid_then_caught | nan | nan | 1 | 16-31 | 49 |
| 4-7 | lower_edge_front | caught | caught | nan | nan | 1 | 4-7 | 48 |
| 4-7 | lower_edge_front | caught | caught | nan | nan | 3 | 4-7 | 9 |
| 4-7 | lower_edge_front | avoid_then_caught | avoid_then_caught | nan | nan | 1 | 32-63 | 8 |
| 4-7 | lower_edge_front | caught | caught | nan | nan | 1 | 16-31 | 3 |
| 64-127 | lower_edge_front | avoid_then_caught | avoid_then_caught | drift | drift_down | 2 | 4-7 | 995 |
| 64-127 | lower_edge_front | avoid_then_caught | avoid_then_caught | drift | mid_band_wait_then_drop | 2 | 4-7 | 414 |
| 64-127 | lower_edge_front | avoid_then_caught | avoid_then_caught | drift | drift_down | 3 | 4-7 | 32 |
| 64-127 | lower_edge_front | caught | caught | exit | direct_to_exit | 2 | 4-7 | 29 |
| 64-127 | lower_edge_front | avoid_then_caught | avoid_then_caught | drift | drift_down | 1 | 4-7 | 22 |
| 64-127 | lower_edge_front | caught | caught | exit | direct_to_exit | 1 | 4-7 | 20 |
| 64-127 | lower_edge_front | avoid_then_caught | avoid_then_caught | drift | drift_down | 1 | 16-31 | 19 |

## Boundary Transition Frequency Preview

| band | boundary_front_class | feature | value | count |
| --- | --- | --- | --- | --- |
| 128-255 | lower_edge_front | boundary_k | 2 | 68 |
| 128-255 | lower_edge_front | boundary_k | 1 | 67 |
| 128-255 | lower_edge_front | boundary_k | 3 | 40 |
| 128-255 | lower_edge_front | boundary_k | 4 | 11 |
| 128-255 | lower_edge_front | boundary_k | 5 | 9 |
| 128-255 | lower_edge_front | boundary_k | 6 | 2 |
| 128-255 | lower_edge_front | boundary_residue_pair_mod32 | 0->31 | 67 |
| 128-255 | lower_edge_front | boundary_residue_pair_mod32 | 0->30 | 35 |
| 128-255 | lower_edge_front | boundary_residue_pair_mod32 | 1->31 | 33 |
| 128-255 | lower_edge_front | boundary_residue_pair_mod32 | 1->30 | 22 |
| 128-255 | lower_edge_front | boundary_residue_pair_mod32 | 0->29 | 18 |
| 128-255 | lower_edge_front | boundary_residue_pair_mod32 | 1->29 | 8 |
| 128-255 | lower_edge_front | boundary_residue_pair_mod32 | 1->28 | 5 |
| 128-255 | lower_edge_front | boundary_residue_pair_mod32 | 0->27 | 4 |
| 128-255 | lower_edge_front | boundary_residue_pair_mod32 | 0->28 | 3 |
| 128-255 | lower_edge_front | boundary_residue_pair_mod32 | 0->26 | 2 |
| 128-255 | lower_edge_front | boundary_transition | 128->127 | 67 |
| 128-255 | lower_edge_front | boundary_transition | 128->126 | 35 |
| 128-255 | lower_edge_front | boundary_transition | 129->127 | 33 |
| 128-255 | lower_edge_front | boundary_transition | 129->126 | 22 |
| 128-255 | lower_edge_front | boundary_transition | 128->125 | 18 |
| 128-255 | lower_edge_front | boundary_transition | 129->125 | 8 |
| 128-255 | lower_edge_front | boundary_transition | 129->124 | 5 |
| 128-255 | lower_edge_front | boundary_transition | 128->123 | 4 |
| 128-255 | lower_edge_front | boundary_transition | 128->124 | 3 |
| 128-255 | lower_edge_front | boundary_transition | 128->122 | 2 |
| 128-255 | lower_edge_front | dominant_near_behavior | drift | 149 |
| 128-255 | lower_edge_front | dominant_near_behavior | exit | 37 |
| 128-255 | lower_edge_front | dominant_near_behavior | wait | 9 |
| 128-255 | lower_edge_front | dominant_near_behavior | nan | 2 |
| 128-255 | lower_edge_front | last_before_exit_distance | 0 | 129 |
| 128-255 | lower_edge_front | last_before_exit_distance | 1 | 68 |
| 128-255 | lower_edge_front | stage_chain_status | avoid_then_caught | 134 |
| 128-255 | lower_edge_front | stage_chain_status | caught | 63 |
| 128-255 | lower_edge_front | stage_event_classification | avoid_then_caught | 134 |
| 128-255 | lower_edge_front | stage_event_classification | caught | 63 |
| 128-255 | near_exit_front | boundary_k | 3 | 24 |
| 128-255 | near_exit_front | boundary_k | 6 | 8 |
| 128-255 | near_exit_front | boundary_k | 4 | 6 |
| 128-255 | near_exit_front | boundary_k | 5 | 6 |
| 128-255 | near_exit_front | boundary_residue_pair_mod32 | 2->31 | 24 |
| 128-255 | near_exit_front | boundary_residue_pair_mod32 | 3->30 | 5 |
| 128-255 | near_exit_front | boundary_residue_pair_mod32 | 3->31 | 5 |
| 128-255 | near_exit_front | boundary_residue_pair_mod32 | 5->31 | 3 |
| 128-255 | near_exit_front | boundary_residue_pair_mod32 | 2->28 | 2 |
| 128-255 | near_exit_front | boundary_residue_pair_mod32 | 4->30 | 2 |
| 128-255 | near_exit_front | boundary_residue_pair_mod32 | 2->29 | 1 |
| 128-255 | near_exit_front | boundary_residue_pair_mod32 | 2->30 | 1 |
| 128-255 | near_exit_front | boundary_residue_pair_mod32 | 3->29 | 1 |
| 128-255 | near_exit_front | boundary_transition | 130->127 | 24 |
| 128-255 | near_exit_front | boundary_transition | 131->126 | 5 |
| 128-255 | near_exit_front | boundary_transition | 131->127 | 5 |
| 128-255 | near_exit_front | boundary_transition | 133->127 | 3 |
| 128-255 | near_exit_front | boundary_transition | 130->124 | 2 |
| 128-255 | near_exit_front | boundary_transition | 132->126 | 2 |
| 128-255 | near_exit_front | boundary_transition | 130->125 | 1 |
| 128-255 | near_exit_front | boundary_transition | 130->126 | 1 |
| 128-255 | near_exit_front | boundary_transition | 131->125 | 1 |
| 128-255 | near_exit_front | dominant_near_behavior | drift | 25 |
| 128-255 | near_exit_front | dominant_near_behavior | wait | 19 |
| 128-255 | near_exit_front | last_before_exit_distance | 2 | 28 |
| 128-255 | near_exit_front | last_before_exit_distance | 3 | 11 |
| 128-255 | near_exit_front | last_before_exit_distance | 5 | 3 |
| 128-255 | near_exit_front | last_before_exit_distance | 4 | 2 |
| 128-255 | near_exit_front | stage_chain_status | avoid_then_caught | 38 |
| 128-255 | near_exit_front | stage_chain_status | caught | 6 |
| 128-255 | near_exit_front | stage_event_classification | avoid_then_caught | 38 |
| 128-255 | near_exit_front | stage_event_classification | caught | 6 |
| 16-31 | deeper_front | boundary_k | 15 | 5 |
| 16-31 | deeper_front | boundary_k | 10 | 2 |
| 16-31 | deeper_front | boundary_k | 12 | 1 |
| 16-31 | deeper_front | boundary_k | 13 | 1 |
| 16-31 | deeper_front | boundary_k | 16 | 1 |
| 16-31 | deeper_front | boundary_residue_pair_mod32 | 25->10 | 5 |
| 16-31 | deeper_front | boundary_residue_pair_mod32 | 25->15 | 2 |
| 16-31 | deeper_front | boundary_residue_pair_mod32 | 27->14 | 1 |
| 16-31 | deeper_front | boundary_residue_pair_mod32 | 27->15 | 1 |
| 16-31 | deeper_front | boundary_residue_pair_mod32 | 29->13 | 1 |
| 16-31 | deeper_front | boundary_transition | 25->10 | 5 |
| 16-31 | deeper_front | boundary_transition | 25->15 | 2 |
| 16-31 | deeper_front | boundary_transition | 27->14 | 1 |
| 16-31 | deeper_front | boundary_transition | 27->15 | 1 |
| 16-31 | deeper_front | boundary_transition | 29->13 | 1 |
| 16-31 | deeper_front | dominant_near_behavior | nan | 10 |
| 16-31 | deeper_front | last_before_exit_distance | 9 | 7 |
| 16-31 | deeper_front | last_before_exit_distance | 11 | 2 |
| 16-31 | deeper_front | last_before_exit_distance | 13 | 1 |
| 16-31 | deeper_front | stage_chain_status | avoid | 10 |
| 16-31 | deeper_front | stage_event_classification | avoid_then_caught | 10 |
| 16-31 | lower_edge_front | boundary_k | 2 | 438 |
| 16-31 | lower_edge_front | boundary_k | 3 | 128 |
| 16-31 | lower_edge_front | boundary_k | 4 | 68 |
| 16-31 | lower_edge_front | boundary_k | 7 | 49 |
| 16-31 | lower_edge_front | boundary_k | 1 | 43 |
| 16-31 | lower_edge_front | boundary_k | 6 | 39 |
| 16-31 | lower_edge_front | boundary_k | 5 | 38 |
| 16-31 | lower_edge_front | boundary_k | 8 | 9 |
| 16-31 | lower_edge_front | boundary_k | 16 | 2 |
| 16-31 | lower_edge_front | boundary_residue_pair_mod32 | 17->15 | 334 |
| 16-31 | lower_edge_front | boundary_residue_pair_mod32 | 16->14 | 104 |
| 16-31 | lower_edge_front | boundary_residue_pair_mod32 | 16->13 | 95 |
| 16-31 | lower_edge_front | boundary_residue_pair_mod32 | 16->12 | 52 |
| 16-31 | lower_edge_front | boundary_residue_pair_mod32 | 16->15 | 43 |
| 16-31 | lower_edge_front | boundary_residue_pair_mod32 | 17->11 | 39 |
| 16-31 | lower_edge_front | boundary_residue_pair_mod32 | 16->11 | 37 |
| 16-31 | lower_edge_front | boundary_residue_pair_mod32 | 17->10 | 33 |
| 16-31 | lower_edge_front | boundary_residue_pair_mod32 | 17->14 | 33 |
| 16-31 | lower_edge_front | boundary_residue_pair_mod32 | 16->9 | 16 |
| 16-31 | lower_edge_front | boundary_residue_pair_mod32 | 17->13 | 16 |
| 16-31 | lower_edge_front | boundary_residue_pair_mod32 | 16->8 | 9 |
| 16-31 | lower_edge_front | boundary_residue_pair_mod32 | 16->0 | 2 |
| 16-31 | lower_edge_front | boundary_residue_pair_mod32 | 17->12 | 1 |
| 16-31 | lower_edge_front | boundary_transition | 17->15 | 334 |
| 16-31 | lower_edge_front | boundary_transition | 16->14 | 104 |
| 16-31 | lower_edge_front | boundary_transition | 16->13 | 95 |
| 16-31 | lower_edge_front | boundary_transition | 16->12 | 52 |
| 16-31 | lower_edge_front | boundary_transition | 16->15 | 43 |
| 16-31 | lower_edge_front | boundary_transition | 17->11 | 39 |
| 16-31 | lower_edge_front | boundary_transition | 16->11 | 37 |
| 16-31 | lower_edge_front | boundary_transition | 17->10 | 33 |

## Notes On Bands With No Miss Events

- `4-7`: no observed miss events in this band; no miss-supported local shapes observed
- `8-15`: no observed miss events in this band; no miss-supported local shapes observed; lower/near front structure present
- `16-31`: no observed miss events in this band; no miss-supported local shapes observed; lower/near front structure present
- `256-511`: no observed miss events in this band; no miss-supported local shapes observed
- `512-1023`: no lower_5pct exit-event rows for this band

## Wording Recommendation

> The cross-band audit should be phrased as a boundary-front geometry check, not as a miss/control replication test. Higher bands may contain no observed miss events; nevertheless, their lower-edge, near-exit, and deeper-front rows can be compared descriptively against chain status, local event classification, near behavior, and miss-supported local shape support. In this sense the question is whether the geometry of leaving a dyadic band is scale-stable, not whether miss events themselves recur at every scale.

## Output Files

- `band_stage_boundary_detail.csv`
- `band_grouped_count_table.csv`
- `band_front_distribution.csv`
- `band_boundary_transition_frequencies.csv`
- `band_compact_cross_band_table.csv`