# Experiment 3: RT550 Odd-Accelerated remaining_K Overlay

## Purpose

This experiment maps the Rozier-Terracol Appendix C benchmark set into our odd-accelerated-to-1 remaining_K coordinate. It is an overlay, not the Rozier-Terracol definition itself and not the sampled-universe trace_escape window.

## Inputs

- RT pure baseline: `rt_pure_reproduction_report.md`.
- Overlay source set: the same `593` RT Appendix C occurrences collapsed to `550` distinct starting integers.
- Recomputed overlay audit: `rt550_coordinate_reaudit_summary.csv`.

## Coordinate

- `odd_core` mode: strip the initial power of two from `n`, then iterate the odd-accelerated Collatz map until 1.
- `original_n_strict` mode: prepend the initial `v2(n)` to the odd-accelerated tail.
- remaining_K is computed on that generated k-word: `remaining_K_before(pos) = sum(word) - sum(word[:pos])`.
- This coordinate does not use RT's `(j,q)` finite interval as its window, and it does not use our sampled-universe `trace_escape(n, 1 << power)` window.

## Reproduction Check

- Recomputed odd-core overlay mismatching rows against existing `rozier_overlay_signature_hits.csv`: `0`.

## Main Metrics

### odd_core

| metric | hits | total | share |
|---|---:|---:|---:|
| `hits_64_95_to_32_63` | `536` | `550` | `0.974545` |
| `hits_start_in_layer_64_95` | `443` | `550` | `0.805455` |
| `hits_transition_k1_64_95` | `516` | `550` | `0.938182` |
| `hits_pre111_64_95` | `468` | `550` | `0.850909` |
| `hits_full_A_signature` | `377` | `550` | `0.685455` |
| `hits_32_63_signature` | `0` | `550` | `0.000000` |
| `first_hit_strict_64_to_32` | `7` | `550` | `0.012727` |
| `A_events_over_focus_events` | `377` | `18882` | `0.019966` |
| `entered_32_63` | `545` | `550` | `0.990909` |
| `first_32_63_exit_R32` | `545` | `545` | `1.000000` |

### original_n_strict

| metric | hits | total | share |
|---|---:|---:|---:|
| `hits_64_95_to_32_63` | `538` | `550` | `0.978182` |
| `hits_start_in_layer_64_95` | `431` | `550` | `0.783636` |
| `hits_transition_k1_64_95` | `517` | `550` | `0.940000` |
| `hits_pre111_64_95` | `469` | `550` | `0.852727` |
| `hits_full_A_signature` | `365` | `550` | `0.663636` |
| `hits_32_63_signature` | `0` | `550` | `0.000000` |
| `first_hit_strict_64_to_32` | `5` | `550` | `0.009091` |
| `A_events_over_focus_events` | `365` | `19137` | `0.019073` |
| `entered_32_63` | `545` | `550` | `0.990909` |
| `first_32_63_exit_R32` | `545` | `545` | `1.000000` |

## Reading

- In `odd_core` mode, integer-level any-event A-like overlap is `377/550` = `0.685455`.
- In `original_n_strict` mode, the same A-like overlap is `365/550` = `0.663636`.
- First-hit strict `64-95 -> 32-63` is much smaller in `odd_core` mode: `7/550` = `0.012727`.
- Occurrence-level A-event share among focus events is also small: `377/18882` = `0.019966`.
- Among rows that enter `32-63`, the first `32-63 -> 16-31` exit occurs at R=32 in `545/545` = `1.000000`.

So the overlay supports a narrow statement: RT550 is strongly enriched for having some A-like `64-95 -> 32-63` event somewhere in the odd-accelerated-to-1 remaining_K path. It does not support the stronger statement that the first `64-95` event is usually A-like, nor that RT's own `(j,q)` interval is the same as this remaining_K window.

## Limits

- This is an overlay from RT occurrences into our coordinate, not an RT-native remaining_K calculation.
- The appropriate claim depends on counting mode: integer-level any-event, first-hit strict, or occurrence-level.
- This should be kept separate from Experiment 2-A, the sampled-universe `trace_escape` analysis.

## Related Outputs

- `rt550_coordinate_reaudit.md`
- `rt550_coordinate_reaudit_summary.csv`
- `rt550_coordinate_reaudit_mismatches.csv`
- `rt_pure_reproduction_report.md`