fix(alignment): correct gauss_model midpoint anchor (GH #34)

[sipemu]

Fixes #34.

Problem

gauss_model (and joint_gauss_model) produced samples whose mean was offset by a constant (~+1.0) from the data mean, and whose curves left the data range.

Root cause

build_augmented_srsfs (elastic_fpca.rs:717) encodes the curve level at the domain midpoint m/2:

let id = m / 2;
q_aug[(i, m)] = fid.signum() * fid.abs().sqrt();   // level at the MIDPOINT

But the generative reconstruction recovered that value and passed it to srsf_inverse as f0, which srsf_inverse treats as f(argvals[0]) — the start. So each reconstructed curve was pinned at its start to the midpoint level, shifting the whole curve by a constant (≈ the midpoint value, ~1.0 for the reporter's peak‑1 bumps).

Fix

Reconstruct from a zero start and shift so the midpoint matches the recovered level (generative.rs, both gauss_model and joint_gauss_model):

let f_mid = aug_val.signum() * aug_val * aug_val;
let mut f_new = srsf_inverse(&q_new[..m], argvals, 0.0);
let shift = f_mid - f_new[m / 2];
for val in f_new.iter_mut() { *val += shift; }

Tests

New regression gauss_model_sample_mean_no_constant_offset asserts the average sample‑mean offset from the data mean stays < 0.3 (it was ~+1.0). Full alignment (244) + elastic_fpca (15) + R‑validation (173) suites pass; clippy clean.

Note (not changed here)

The same midpoint‑vs‑start anchor mismatch also exists in the elastic_fpca.rs eigenfunctions_f reconstruction (two sites). Those feed a display output (the generative samples use eigenfunctions_q, not _f) and are R‑validated, so I've left them for a separate, carefully‑validated change rather than bundle them here.

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 89.02%. Comparing base (fca0a0e) to head (71ef10c).
⚠️ Report is 3 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main      #35   +/-   ##
=======================================
  Coverage   89.01%   89.02%           
=======================================
  Files         200      200           
  Lines       44099    44131   +32     
=======================================
+ Hits        39255    39287   +32     
  Misses       4844     4844           

Flag	Coverage Δ
rust	89.02% <100.00%> (+<0.01%)	⬆️

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Files with missing lines	Coverage Δ
fdars-core/src/alignment/generative.rs	87.03% <100.00%> (+1.59%)	⬆️

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