Structured key family as the main configuration

Unconstrained key training converged to disjoint sparse supports: 99
percent of each users key energy sat on three or four of the sixteen
entries, with pairwise disjoint supports and one numerically dead
codebook column. That is an orthogonal slot allocation, so the
superposition collapsed into OMA and the key space was far smaller than
the dense direction the brute-force study assumes.

The main configuration is now the structured Walsh-Hadamard family,
which is dense, exactly orthogonal, unit modulus, and already the best
family in the key-family table. base_keys generalizes to any key length
by truncating the next power-of-two Sylvester order, and the key-length
sweep keeps only lengths where the truncated rows stay exactly
orthogonal, verified numerically.

Also fixes the M-PAM energy normalization in oma_ser_keylen, which used
sqrt(6g/(M^2-1)) where unit average symbol energy gives A^2=3/(M^2-1);
the closed form was 3 dB optimistic and now reproduces a direct Monte
Carlo to 1e-5.

Results move accordingly: the proposal now stays below OMA at every SNR
and reaches 1.52x at key length 64, while the jamming margin falls to
5.5-6.3 dB and the brute-force curve to 0.59 at a million guesses.

code/exp_refresh.py

@@ -45,7 +45,8 @@ import numpy as np
 import torch
 
 from sse_lib import DATA, DEVICE, SSE, write_csv, eval_ser_sse
-from exp_full import hadamard, get_model, eval_ser_eve, eve_wrong_mask
+from exp_full import (hadamard, get_model, base_keys, eval_ser_eve,
+                      eve_wrong_mask)
 from exp_kpa import collect_known_plaintext, solve_keys
 
 SEED = 5150
@@ -53,13 +54,6 @@ BLOCKS = 24
 FRAMES = 300_000
 
 
-def base_keys(U: int, Lp: int) -> torch.Tensor:
-    """The fixed orthogonal key set the codebook is trained around. Row 0
-    of the Sylvester construction is the all-ones vector, which any
-    adversary can write down, so the users take rows 1 to U."""
-    return torch.tensor(hadamard(Lp)[1:U + 1], dtype=torch.float32)
-
-
 def kdf_invariant(seed: int, block: int, U: int, Lp: int):
     """Derive one block's key material from the invariance group."""
     rng = np.random.default_rng([seed, block])