Beam search non-convergence/syndrome-failure spike on Gross [[144,12,12]] at p=0.05

[aleverrier]

Hi BeamSearchDecoder authors,

We found a reproducible stability issue in beam decoding on the Gross [[144,12,12]] BB code at bit-flip prior p=0.05.

Symptom:

• many syndrome-invalid outputs at p=0.05
• nearby priors (0.049, 0.051) do not show this

Patch summary (decoder/src_cpp/beam_search.hpp):

1. strict sign ties: <=0 -> <0
2. deterministic tiny per-bit/per-shot LLR jitter to break exact ties
3. reset decoding state per shot

After patch, the p=0.05 syndrome-failure spike disappears and beam becomes comparable to BP+OSD/MILP on this test.

I can provide full reproduction details if useful.