Composable models and A/B tests of the 2024 ideas; add powerlaw.

Models are now a Composite of drift, volatility and (optional) shape
components, so an experiment can swap one part against a fixed control.

btcmodel/experiments.py holds seven experiments built from the ideas in the
old branches (catalogued in docs/2024-ideas.md), each with its hypothesis
and source, and a verdict rule fixed before anything ran. `just ab` runs
them on development data. Results:

- Shrinking the cycle drift, and a power-law trend (plain or reverting),
  beat their controls. The power law beats the random walk by 53-63% at
  3-4 years with unbiased outcomes, so it is promoted to MODELS.
- Every alternative volatility estimate (EWMA blends, other windows,
  reversion to a level or trend) is worse than the trailing 365-day window.
  Cycle-dependent volatility, heavy tails and stretched cycle phase show no
  reliable effect.

README.md

@@ -59,20 +59,45 @@ the same way:
 - `cycle`: the 2024 model's one real idea. Expected return depends on the day of
   the halving cycle, estimated from past cycles, with recent cycles weighted
   more.
+- `powerlaw`: log price grows linearly in log time since genesis, so growth
+  keeps slowing. Fitted walk-forward; the exponent has stayed between 5.4 and
+  6.0 in every fit since 2014.
 
 ### Findings so far (development data)
 
-- Nothing beats the random walk with any confidence at any horizon. At 2-4
-  years there are only 3-5 independent outcomes in the whole history.
-- `drift_rw` leads at 2-4 years (+13-18% skill, but the intervals span zero).
-- `cycle` loses to both at every horizon, and so does every setting tried
-  (recency half-life 0.25-2 cycles, smoothing bandwidth 15-60 days). The cycle
-  *shape* costs accuracy. The level is the problem: each cycle has grown less
-  than the last (log return 4.0, 2.6, 2.0, i.e. roughly ×55, ×13, ×7), so any
-  average of past cycles overshoots.
+- `cycle` loses to the random walk at every horizon, and so does every setting
+  tried (recency half-life 0.25-2 cycles, smoothing bandwidth 15-60 days).
+  The level is the problem: each cycle has grown less than the last (log
+  return 4.0, 2.6, 2.0, i.e. roughly ×55, ×13, ×7), so any average of past
+  cycles overshoots.
+- `powerlaw` models exactly that, and it is the first model to beat the random
+  walk with some confidence: +53% and +63% skill at 3 and 4 years, with
+  unbiased outcomes (mean PIT 0.51). Only 3-4 independent windows back that
+  up, the functional form is famous *because* it fits Bitcoin's history, and
+  the holdout hasn't been run yet.
+- Its intervals are too wide at long horizons (the 80% interval held every
+  3-year outcome), because it treats deviations from the trend as permanent.
 
-That points at diminishing returns as the structure worth modelling, e.g. a
-power-law trend, which is next.
+### A/B tests of the 2024 ideas
+
+`just ab` runs the experiments in `btcmodel/experiments.py`: ideas salvaged
+from the old branches (catalogued in [docs/2024-ideas.md](docs/2024-ideas.md)),
+each a control plus variants that change one component. Hypotheses and the
+verdict rule were written down before anything ran. With ~100 comparisons,
+expect a few flukes either way.
+
+| Experiment | Idea | Verdict |
+|---|---|---|
+| shrink-cycle | scale the cycle drift by 0.25/0.5/0.75 | better, all three: it fixes the level crudely |
+| diminishing-returns | power-law trend, optionally reverting to it, or the cycle shape rescaled to it | better (both power-law variants); cycle shape on the power law inconclusive |
+| vol-window | EWMA blends, shorter or longer windows | worse: the plain 365-day window wins |
+| vol-reversion | volatility reverting to a long-run level or falling trend | worse |
+| cycle-vol | volatility by cycle position | inconclusive (no effect) |
+| tails | Student-t, or empirical horizon-level shape | Student-t worse; empirical +5% at 1 month only |
+| cycle-phase | align cycles by fraction elapsed, not days | inconclusive |
+
+Next: a power law whose deviations revert with bounded variance, and a
+registered test of whether the cycle's timing adds anything on top of it.
 
 ## Usage
 
@@ -83,6 +108,7 @@ nix develop
 just update     # fetch new daily prices from Coinbase
 just backtest   # score models on development data -> output/backtest/
 just forecast   # forecast from the latest price -> output/forecast/
+just ab         # run A/B experiments -> output/ab/
 just test
 just holdout    # score on held-out outcomes; sparingly
 ```
@@ -98,7 +124,8 @@ btcmodel/
   halving.py    halving calendar, position in cycle
   forecast.py   Forecast (quantiles of log price), CRPS, PIT
   evaluate.py   walk-forward backtest and summary
-  models/       one file per model family; register new ones in __init__.py
+  experiments.py  A/B tests: hypothesis, control, variants, verdict rule
+  models/       drift, volatility and shape components; register models in __init__.py
   plots.py      fan chart, skill and calibration charts
 ```