# Method, written before the study was run

**Committed 2026-09-18, before a single run.** The whole point of this study is
that a method decided after seeing results is worthless, so this file is the
commitment and the git history is the proof of when it was made.

## The question

When someone looks through a health diary for "what came before my bad days",
and there is nothing there to find, how often does the method report a finding
anyway?

## Why it matters

Every symptom tracker, spreadsheet and general AI assistant will happily
return a pattern. Almost nobody reports how often those patterns are noise.
If the honest number is high, that is the most useful thing we can tell a
person who has been handed a "trigger" by an app.

## The data

Synthetic diaries only. No person's records, no scraped data, nothing real.
Each diary has:

- One outcome (a daily 0 to 10 "how I felt", higher is worse).
- Eight tracked measures (steps, sleep hours, a pain score, caffeine, stress,
  screen time, minutes outdoors, resting heart rate).
- **A weekly rhythm** in the outcome and in three of the measures, because
  real life has weekends.
- **Day-to-day drift**: AR(1) with phi 0.5, because yesterday's state carries
  into today in real records.
- **Ragged logging**: 15% of cells missing at random, because real diaries have
  gaps.
- **No true relationship of any kind** between any measure and the outcome, at
  any lag. That is the entire construction.

Lengths: 60, 90, 180 and 292 days. 100 diaries per length, seeded so anyone can
reproduce them (seed = 20260918 + index).

## The three methods compared

| Arm | What it does | What it stands for |
|---|---|---|
| **A. Naive** | Spearman correlation of every measure against the outcome at lags 0 to 3, report anything with p < 0.05 | A spreadsheet, or an assistant asked "find my triggers" |
| **B. Corrected** | Same grid, Benjamini-Yekutieli correction across all comparisons, report q < 0.06 | Someone who knows about multiple comparisons |
| **C. Full** | Arm B plus the weekday effect removed first and a permutation null | What Arkhelion's engine does |

## What gets measured

1. **False-alarm rate:** the share of diaries where the arm reports at least
   one finding. In diaries built with nothing in them, every finding is a
   false alarm.
2. **Findings per diary**, mean.
3. **A power check, so the answer is not just "be conservative":** the same
   grid on diaries with ONE real effect planted (a measure raising the outcome
   two days later, rho about 0.30). The share of those where each arm finds
   the planted effect.

## What would make this study wrong

- If the synthetic diaries are unrealistically smooth, every arm looks better
  than it is. The AR(1) drift, the weekly rhythm and the missingness are there
  for that reason, and the generator is published with the results.
- A single seed could be lucky. 100 diaries per cell, all seeds recorded.
- This measures **noise**, not usefulness. A method that reports nothing ever
  would score perfectly here and be worthless, which is why the power check is
  part of the study and not an appendix.

## Publication rules

- The generator, the runner and the raw results are committed, so the numbers
  can be checked.
- Arkhelion's own arm is reported with the same honesty as the others,
  including its false-alarm rate, whatever it is.
- No claim that any arm finds causes. The word is "pattern", never "trigger".
- If arm C is not better than arm A, that gets published too.