cascade-heat11-var4-tsar-stationary-sd

Heat11 is Heat10 plus exactly one mathematical correction: the AR(1) innovations in trend_seasonal_ar are scaled so that the configured sigma is the stationary residual standard deviation. This is explicitly distinct from the keyupdate.md / Heat9 empirical-Bayes integrated-SV correction. Heat10's family and curriculum weights, Heat9 correction, Numba kernels, batching, throughput optimizations, requirements, and all unrelated code are preserved.

Mathematical correction

For

x_t = phi*x_{t-1} + eps_t,

Var(x) = sigma_eps^2 / (1 - phi^2).

Set

sigma_eps = sigma_target*sqrt(1 - phi^2),

so Var(x) = sigma_target^2. The family samples phi ~ U(0, 0.85). Previously, the maximum stationary-SD inflation was 1/sqrt(1 - .85^2) = 1.898; its average over the uniform distribution was asin(.85)/.85 ~= 1.20. The correction preserves autocorrelation rho(k) = phi^k; it only removes the unintended coupling between persistence and residual scale.

The directly affected family mass is 10% at final weights and 12% at curriculum start. Expected throughput impact is negligible.

Evaluation rationale and limits

Heat8 all-snapshot absolute MASE remains high on daily (2.0646) and sales (2.8579), and the 07-25 remaining issue is MASE (0.9971) more than MWSQL (0.08485). Trend + seasonal + AR structure is semantically relevant to daily and sales series, but these observations do not prove causal improvement.

The Berkeley AR notes give the stationary-variance result. ForecastPFN provides evidence that synthetic noise design and scale materially affect learnability. ForecastPFN uses a different model and noise-removal setup, so it supports the importance of noise calibration, not this exact correction.

Input arcsinh causal standardization may reduce the effect. A paired Heat10 / Heat11 A/B with identical training and evaluation conditions is required; no improvement is guaranteed.

Validate

From the repository root:

python3 - <<'PY'
import json
from pathlib import Path

root = Path("generators/07-26")
a = json.loads((root / "cascade-heat10/config.json").read_text())
b = json.loads((root / "cascade-heat11/config.json").read_text())
for key in ("name", "description"):
    a.pop(key)
    b.pop(key)
assert a == b
print("config metadata-only diff: OK")
PY

diff -u generators/07-26/cascade-heat10/generator.py \
  generators/07-26/cascade-heat11/generator.py
cmp generators/07-26/cascade-heat10/requirements.txt \
  generators/07-26/cascade-heat11/requirements.txt
python3 -m py_compile generators/07-26/cascade-heat11/generator.py
uv run ruff check generators/07-26/cascade-heat11
docker run --rm \
  --entrypoint /root/cascade/.venv/bin/cascade \
  -v "$PWD/chain.toml:/workspace/chain.toml:ro" \
  -v "$PWD/generators/07-26/cascade-heat11:/workspace/candidate:ro" \
  ghcr.io/tensorlink-ai/cascade-worker@sha256:f73c77276b80942c61e7c5570bbbafbd69c8fd15e79cffbbcf75c8855715c9a0 \
  verify /workspace/candidate --chain-toml /workspace/chain.toml

The generator diff must contain only the innovation scaling block and its comment. Validation must not start training.