# Study 000B Abstract

## Title

Adaptive Efficiency And Internal Cost Under Specialization: A Flagship Companion Study Following Study 000A

## Abstract

This flagship companion study was conducted after `Study 000A` to determine whether later running specialization in the high-resolution window coincided with adaptive efficiency, persistent unexplained HR burden, or both. Using bundled QC-pass running rows and the unified daily timeline, run-level efficiency metrics, next-day recovery measures, and a simple descriptive heart-rate residual model were evaluated.

Across the first and last 30 QC-pass runs, running share of 28-day activity increased from `15.26%` to `56.40%`. Speed-per-heart-rate efficiency improved by `13.41%`, while power-per-heart-rate efficiency improved by only `2.82%`. Next-day resting heart rate and next-day sleep score moved in a favorable direction. However, the simple speed-plus-power HR model showed that mean residual burden shifted upward rather than disappearing, from `-1.60` bpm to `3.09` bpm.

These results support a mixed interpretation. Specialization coincided with better adaptive efficiency and more favorable background recovery markers, but it did not eliminate session-level unexplained HR burden. As a result, `Study 000B` strengthens the broader program by showing that later adaptation in this system was not reducible either to pure hidden cost or to pure efficiency gain.

# Study 000B Methods

## Design

Primary flagship companion study conducted after `Study 000A` to examine whether later specialization coincided with adaptive efficiency, persistent unexplained HR burden, or both.

## Relationship to Study 000A

`Study 000A` established that the system adapted through selective flexibility and specialization.

`Study 000B` does not reopen that question. It stands alongside the flagship and asks a second primary program question:

- did external output become more efficient relative to cardiovascular cost?
- did some background recovery markers move in a favorable direction as specialization increased?
- did session-level internal burden disappear, or did part of it persist?

## Core question

As running specialization increased in the later high-resolution window, did the system show better efficiency, persistent unexplained HR burden, or both together?

## Packaged source tables

| table_name | relative_path | bytes | sha256 |
|---|---|---|---|
| v7_pillar_conserved_mechanics_runs_v1.csv | source_tables/v7_pillar_conserved_mechanics_runs_v1.csv | 204809 | baaba0ea64e74da234a19e8dd1eaac864ead0163ef5c52ea505e8bdf92c68f0c |
| v7_total_fitness_profile_timeline_v3.csv | source_tables/v7_total_fitness_profile_timeline_v3.csv | 618684 | e9a1c71bcf06f880c0b7fd1c011336ee3323687e4fd8d5cb857508e727c06028 |
| v7_food_pdf_garmin_overlap_v1.csv | source_tables/v7_food_pdf_garmin_overlap_v1.csv | 15436 | 82fc9280f4e7d36865086c1cd02b898b081ca618c4db37a7e39c8092a393965a |

## Analytic structure

1. QC-pass high-resolution runs were linked back to the unified daily timeline.
2. Run-level efficiency metrics were derived as `speed_per_hr` and `power_per_hr`.
3. Early and late 30-run windows were compared on output, cost, specialization, and next-day recovery. These windows were matched by run count rather than elapsed time, spanning `93` calendar days early and `43` calendar days late.
4. A simple descriptive HR model (`HR ~ speed + power`) was fit across QC-pass runs to estimate unexplained session HR burden after basic external-output adjustment.
5. Monthly summaries and specialization correlations were generated to characterize broader late-window trends.
6. The food overlap layer was retained only as partial exploratory late-window context.

## Interpretation boundary

This study is descriptive and within-subject. It does not prove physiology mechanism or clinical causation. It asks whether the data support a mixed pattern of better efficiency together with persistent unexplained HR burden.

# Study 000B Results

## Summary

This flagship companion study supports a mixed answer rather than a simple one:

- later specialization coincided with better speed-per-heart-rate efficiency
- background recovery markers moved in a favorable direction as running became a larger share of recent activity
- session heart rate did not simply normalize away
- a small positive late-window unexplained HR burden remained even after simple speed-plus-power adjustment

## Early-to-late adaptive efficiency window

| window_label | run_count | start_date | end_date | speed_mps_mean | pace_min_per_mile_mean | avg_hr_bpm_mean | avg_power_w_mean | cadence_spm_mean | stride_length_m_mean | speed_per_hr_mean | power_per_hr_mean | hr_residual_bpm_mean | running_hours_28d_mean | total_activity_hours_28d_mean | running_share_28d_activity_pct_mean | next_day_resting_hr_mean | next_day_sleep_score_mean | next_day_hrv_mean |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| early_qc_window | 30 | 2025-04-16 | 2025-07-18 | 2.14820 | 13.13 | 137.10 | 262.67 | 141.53 | 0.91 | 0.01559 | 1.89463 | -1.59691 | 7.38 | 49.03 | 15.26 | 50.97 | 51.04 | None |
| late_qc_window | 30 | 2026-04-22 | 2026-06-04 | 2.92387 | 9.19 | 165.93 | 321.97 | 171.47 | 1.02 | 0.01768 | 1.94806 | 3.09257 | 14.36 | 25.47 | 56.40 | 41.20 | 54.37 | 74.67 |

The main pattern is visible immediately:

- speed increased
- heart rate also increased
- speed per heart-rate cost improved
- power per heart-rate cost improved only slightly
- running specialization rose sharply
- next-day resting heart rate improved and next-day sleep score improved

These two windows are matched by run count, not by elapsed time. The early window spans `93` calendar days, while the late window spans `43`, so specialization and rolling-load contrasts should be read as denser-late versus broader-early context rather than as perfectly matched periods.

## Early-to-late change table

| metric | early_value | late_value | change_value | change_units |
|---|---|---|---|---|
| speed_mps_mean | 2.14820 | 2.92387 | 36.11 | pct_change |
| pace_min_per_mile_mean | 13.13 | 9.19 | -29.99 | pct_change |
| avg_hr_bpm_mean | 137.10 | 165.93 | 21.03 | pct_change |
| avg_power_w_mean | 262.67 | 321.97 | 22.58 | pct_change |
| cadence_spm_mean | 141.53 | 171.47 | 21.15 | pct_change |
| stride_length_m_mean | 0.91 | 1.02 | 12.24 | pct_change |
| speed_per_hr_mean | 0.01559 | 0.01768 | 13.41 | pct_change |
| power_per_hr_mean | 1.89463 | 1.94806 | 2.82 | pct_change |
| hr_residual_bpm_mean | -1.59691 | 3.09257 | 4.69 | bpm_shift |
| running_share_28d_activity_pct_mean | 15.26 | 56.40 | 269.52 | pct_change |
| next_day_resting_hr_mean | 50.97 | 41.20 | -19.16 | pct_change |
| next_day_sleep_score_mean | 51.04 | 54.37 | 6.53 | pct_change |

This table shows why the study is not just a "higher HR" story:

- speed improved by more than heart rate did
- `speed_per_hr_mean` improved by double digits
- `power_per_hr_mean` improved only modestly
- `hr_residual_bpm_mean` shifted upward rather than disappearing

That is the core mixed signal: the system became more efficient in one sense, but not cost-free.

## Session HR residual model

| model_name | intercept | speed_coef | power_coef | early_mean_residual_bpm | late_mean_residual_bpm | early_residual_sd_bpm | late_residual_sd_bpm |
|---|---|---|---|---|---|---|---|
| hr_from_speed_power | 66.40 | 26.91 | 0.06 | -1.60 | 3.09 | 11.26 | 9.61 |

The HR model is intentionally simple and descriptive. It uses speed and power to estimate expected session HR. The unexplained HR pattern matters more than the coefficients themselves:

- early-window residual burden was slightly negative on average
- late-window residual burden was slightly positive on average

That means the late window does not look like a pure internal-burden reduction story even though output efficiency improved.

## Monthly efficiency and specialization summary

| year_month | qc_run_count | speed_mps_norm | avg_hr_bpm | avg_power_w | speed_per_hr | power_per_hr | hr_residual_bpm | running_share_28d_activity_pct | next_day_resting_hr | next_day_sleep_score | next_day_hrv |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2025-04 | 4 | 1.82925 | 127.00 | 198.75 | 0.01466 | 1.58664 | 0.41080 | 21.39 | 53.25 | 54.25 | None |
| 2025-05 | 4 | 2.00500 | 136.25 | 220.00 | 0.01452 | 1.57730 | 3.75943 | 9.17 | 57.50 | 41.67 | None |
| 2025-06 | 11 | 2.10982 | 132.45 | 257.00 | 0.01584 | 1.91874 | -4.89700 | 10.52 | 49.64 | 57.10 | None |
| 2025-07 | 14 | 2.40314 | 146.50 | 316.21 | 0.01633 | 2.15027 | -2.01035 | 20.80 | 48.86 | 49.14 | None |
| 2025-08 | 13 | 2.33777 | 148.77 | 307.23 | 0.01567 | 2.04775 | 2.51351 | 19.61 | 46.62 | 62.15 | None |
| 2025-10 | 6 | 2.45600 | 157.83 | 320.50 | 0.01561 | 2.03600 | 7.66422 | 7.02 | 47.67 | 60.33 | 61.50 |
| 2025-11 | 7 | 2.43714 | 144.57 | 294.86 | 0.01686 | 2.03840 | -3.67625 | 15.76 | 49.00 | 65.50 | 57.17 |
| 2025-12 | 9 | 2.53411 | 149.33 | 327.22 | 0.01698 | 2.19238 | -3.30850 | 20.14 | 47.33 | 62.25 | 61.12 |
| 2026-01 | 25 | 2.43808 | 150.56 | 315.80 | 0.01624 | 2.10112 | 1.13230 | 42.49 | 40.88 | 68.30 | 72.87 |
| 2026-02 | 22 | 2.39555 | 150.09 | 290.95 | 0.01605 | 1.93804 | 3.17786 | 72.57 | 40.77 | 67.76 | 71.38 |
| 2026-03 | 25 | 2.65948 | 148.92 | 324.92 | 0.01799 | 2.20210 | -6.96869 | 65.59 | 40.84 | 64.05 | 75.82 |
| 2026-04 | 24 | 2.86079 | 163.46 | 317.83 | 0.01755 | 1.95039 | 2.54290 | 75.74 | 40.46 | 60.87 | 72.91 |
| 2026-05 | 19 | 2.91453 | 166.32 | 320.05 | 0.01755 | 1.92725 | 3.83193 | 55.73 | 41.26 | 49.95 | 75.32 |
| 2026-06 | 3 | 2.91900 | 154.67 | 326.00 | 0.01924 | 2.15454 | -8.26553 | 51.59 | 40.67 | 78.00 | 79.67 |

At the monthly level:

- running share of recent activity rose markedly into 2026
- speed-per-HR improved into the later months
- HR residual burden remained mixed rather than collapsing monotonically

This supports a specialization-with-mixed-cost reading better than a simple fitness-improvement reading.

## Specialization correlations

| relationship | correlation_r | n_points |
|---|---|---|
| running_share_vs_speed_per_hr | 0.31 | 187 |
| running_share_vs_power_per_hr | 0.02 | 187 |
| running_share_vs_hr_residual | -0.02 | 187 |
| running_share_vs_nextday_resting_hr | -0.81 | 187 |
| running_share_vs_nextday_sleep_score | 0.16 | 176 |
| running_share_vs_nextday_hrv | 0.42 | 131 |

These correlations are descriptive and likely time-confounded, but they still help position the system:

- higher running share tracked better speed-per-HR efficiency
- higher running share tracked lower next-day resting HR
- higher running share tracked higher available HRV in the late window
- specialization did not meaningfully reduce the simple run-level unexplained HR burden by itself

## Partial late-window food context

| subset | n_days | mean_food_calories | mean_net_carbs_g | mean_sleep_score | mean_hrv | mean_running_hours_7d |
|---|---|---|---|---|---|---|
| all_overlap_days | 109 | 437.05 | 4.90 | 61.79 | 75.13 | 3.77 |
| food_item_days_only | 30 | 1587.93 | 17.80 | 63.72 | 75.90 | 4.32 |

| relationship | correlation_r | n_points |
|---|---|---|
| food_calories_vs_running_hours_7d | 0.31 | 109 |
| net_carbs_vs_sleep_score | 0.16 | 100 |
| food_calories_vs_hrv | 0.02 | 100 |

The food layer remains partial and late-window only. It is useful as confound context, but not strong enough to anchor the central claim of this study.

## What this study can and cannot answer

| category | question | answer |
|---|---|---|
| answered | Did adaptive efficiency improve as specialization increased in the later running window? | Yes, at least at the speed-per-heart-rate level. The late window shows better external speed per unit heart-rate cost than the early window. |
| answered | Did background recovery markers move in a favorable direction as specialization increased? | Yes, descriptively for next-day resting heart rate and next-day sleep score. HRV is late-window only and should be treated as contextual rather than symmetric early-late evidence. |
| supported_not_proven | Did unexplained session HR burden disappear as adaptation advanced? | No. Session heart rate remained high, and a simple speed-plus-power HR model shows slightly positive late-window unexplained HR burden rather than a full disappearance of burden. |
| not_answered | Can this study prove causal physiology or exact fatigue mechanism? | No. The study characterizes a mixed pattern of improved efficiency and persistent session-level burden, but it does not prove mechanism. |

# Study 000B Discussion

## What this flagship companion study adds to Study 000A

`Study 000A` established that later adaptation occurred through selective flexibility under increasing specialization. `Study 000B` asks what that specialization coincided with in terms of internal burden.

The answer is not "cost disappeared" and not "everything got worse." The answer is mixed.

## Best-supported interpretation

The clearest result is that adaptive efficiency improved.

Across the first and last 30 QC-pass runs:

- speed-per-heart-rate efficiency improved by `13.41%`
- power-per-heart-rate efficiency improved by only `2.82%`
- running share of 28-day activity rose from `15.26%` to `56.40%`

That makes it hard to say the later system was merely working harder in a crude sense. It was producing more speed per unit heart-rate cost.

## Why the study still finds persistent burden

The mixed part of the picture is equally important.

The simple speed-plus-power HR model shows that average unexplained HR burden shifted from `-1.60` bpm to `3.09` bpm, an upward shift of `4.69` bpm. In plain language, late sessions still carried slightly more HR than the simple external-output model would predict.

So the late system looks more efficient, but not frictionless.

## Recovery moved in a more favorable direction

Some background recovery markers moved in a favorable direction alongside specialization:

- next-day resting heart rate changed `-19.16%`
- next-day sleep score changed `6.53%`
- late-window HRV became available, but early-window missingness prevents a symmetric early-late comparison

That means the later system may have been better supported in the background even while harder sessions still carried real acute burden.

## Specialization appears relevant, but not sufficient by itself

Specialization tracked better speed efficiency (`r = 0.3103`) and lower next-day resting HR (`r = -0.8127`), but it did not by itself erase the simple run-level unexplained HR burden.

That is the most honest synthesis of the study:

`specialization coincided with better adaptive efficiency and more favorable background recovery markers, while leaving a persistent session-level unexplained HR burden`

## Why this matters for the broader program

This is valuable because it keeps the research program from collapsing into a false choice.

The system did not simply become more costly.
The system did not simply become more efficient.

It appears to have become more efficient in output terms while still carrying some unexplained burden in session terms.

That mixed pattern is likely one of the most important things this dataset can currently say.

# Study 000B Limitations

1. This is a single-subject within-system study and does not support population inference.
2. The HR residual model is intentionally simple and descriptive, not a validated physiology model.
3. The early and late comparison windows are matched by run count rather than elapsed time, spanning `93` versus `43` calendar days.
4. High-resolution running mechanics and session HR are concentrated in the later device-supported window.
5. Specialization correlations are descriptive and likely partly time-confounded.
6. HRV is available only late, which limits symmetric early-late comparison.
7. Sleep availability is slightly uneven across windows, and recovery markers are not equally mature in both periods.
8. The food layer is partial and late-window only, so it can only provide confound context rather than causal adjudication.
9. The study cannot prove exact physiological mechanism for the unexplained HR burden signal.