P3: normalization fit (1.2.0 and 1.1.2), apply, polar, simurg normalize

- signal/normalization/numerics.py: vendor percentile, trimmean, MAD sigma
  (old/new), bisquare robust fits, float32/float64 typing and sequential
  sums reproduced exactly (ported from gtc2vcf, MIT)
- signal/normalization/fit.py: outlier removal, offset, rotation, shear,
  scale, nn12/rr12, single-channel model for small Infinium I bins,
  exact and binned nearest-neighbour sweeps; vendor quirks marked QUIRK
- signal/normalization/apply.py: affine transform and theta/R
- pipeline/normalize.py + CLI `simurg normalize`
- oracle GTCs rebuilt with -ffp-contract=off (aarch64 gcc fuses a*b+c by
  default, shifting the last bits); the old FMA oracle differed by <=4 ULP

Result: transforms bit-identical to the oracle for all 36 GSA samples x
48 bins, for both normalization versions (3456/3456 bins, 0 ULP).

Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01814GKVzZVL3FuF3DeiZXhv

src/simurg/core/schemas.py

@@ -20,6 +20,8 @@ from simurg.formats.bpm import Manifest
 LOCI_SCHEMA_ID = "simurg.loci/1"
 INTENSITY_SCHEMA_ID = "simurg.sample_intensity/1"
 CONTROLS_SCHEMA_ID = "simurg.sample_controls/1"
+NORMALIZED_SCHEMA_ID = "simurg.sample_normalized/1"
+TRANSFORMS_SCHEMA_ID = "simurg.sample_transforms/1"
 
 LOCI_SCHEMA = pa.schema(
     [
@@ -56,6 +58,33 @@ CONTROLS_SCHEMA = pa.schema(
     metadata={"simurg.schema": CONTROLS_SCHEMA_ID},
 )
 
+NORMALIZED_SCHEMA = pa.schema(
+    [("norm_x", pa.float32()), ("norm_y", pa.float32()), ("theta", pa.float32()), ("r", pa.float32())],
+    metadata={"simurg.schema": NORMALIZED_SCHEMA_ID},
+)
+
+TRANSFORMS_SCHEMA = pa.schema(
+    [
+        ("bin_index", pa.int32()),
+        ("norm_bin_id", pa.uint8()),
+        ("n_loci", pa.int32()),
+        ("version", pa.int32()),
+        ("offset_x", pa.float32()),
+        ("offset_y", pa.float32()),
+        ("scale_x", pa.float32()),
+        ("scale_y", pa.float32()),
+        ("shear", pa.float32()),
+        ("theta", pa.float32()),
+        ("cvx", pa.float32()),
+        ("cvy", pa.float32()),
+        ("nn12", pa.float32()),
+        ("rr12", pa.float32()),
+        ("taa", pa.float32()),
+        ("tbb", pa.float32()),
+    ],
+    metadata={"simurg.schema": TRANSFORMS_SCHEMA_ID},
+)
+
 _WRITE_OPTS: dict[str, Any] = {"compression": "zstd", "use_dictionary": True, "write_statistics": True}
 
 
@@ -122,6 +151,26 @@ def controls_table(addresses: np.ndarray, red: np.ndarray, green: np.ndarray, me
     return with_metadata(t, meta)
 
 
+def normalized_table(
+    nx: np.ndarray, ny: np.ndarray, theta: np.ndarray, r: np.ndarray, meta: dict[str, Any]
+) -> pa.Table:
+    t = pa.table(
+        {
+            "norm_x": pa.array(nx, pa.float32()),
+            "norm_y": pa.array(ny, pa.float32()),
+            "theta": pa.array(theta, pa.float32()),
+            "r": pa.array(r, pa.float32()),
+        },
+        schema=NORMALIZED_SCHEMA,
+    )
+    return with_metadata(t, meta)
+
+
+def transforms_table(rows: list[dict[str, Any]], meta: dict[str, Any]) -> pa.Table:
+    t = pa.Table.from_pylist(rows, schema=TRANSFORMS_SCHEMA)
+    return with_metadata(t, meta)
+
+
 def write_parquet(table: pa.Table, path: Path) -> None:
     """Atomic, deterministic Parquet write."""
     with atomic_open(Path(path), "wb") as fh: