C6 relation-surface screen for c4_projective_toy_noisy  target=128 bits
q=7 N=17 block_size=2 blocks=9 n_c=24 m_c=97 eta_c=0.0005
C4 entries=65  C2 entries=390  C4/C2=0.166667
C4 public CLPN rows=6305
Row-difference samples=302640  eta2=0.000999708
Raw weight-3 relations=448  rows=43456  eta3=0.00149913
Rank-capped relation dimension=48  rows=4656
Minimum finite screen bits=8.78463484555752
Verdict=reject-for-current-security-claim

LPN screens:
  - C6_expansion_key_sparse_LPN_rows: n=16 samples=289 eta=0.0005 min_bits=8.78463484555752 passes=False
      warning: public/evaluation key exposes at least as many samples as the secret dimension
      warning: very small sparse row weight; use only for tests unless justified by a proof/estimator
      warning: q-ary block-BKW screen below 128 bits
  - C6_C4_CLPN_row_differences: n=24 samples=302640 eta=0.000999708333333452 min_bits=11.422064766172813 passes=False
      warning: public/evaluation key exposes at least as many samples as the secret dimension
      warning: very large public sample-to-dimension ratio; multi-sample LPN attacks require specialist review
      warning: q-ary block-BKW screen below 128 bits
  - C6_C4_weight3_relations_rank_capped: n=24 samples=4656 eta=0.001499125170138996 min_bits=11.591989767615125 passes=False
      warning: public/evaluation key exposes at least as many samples as the secret dimension
      warning: q-ary block-BKW screen below 128 bits
  - C6_C4_weight3_relations_raw_upper_bound: n=24 samples=43456 eta=0.001499125170138996 min_bits=11.422064766172813 passes=False
      warning: public/evaluation key exposes at least as many samples as the secret dimension
      warning: very large public sample-to-dimension ratio; multi-sample LPN attacks require specialist review
      warning: q-ary block-BKW screen below 128 bits

Blockers / required follow-up:
  - C6_expansion_key_sparse_LPN_rows below target: 8.78 bits
  - C6_expansion_key_sparse_LPN_rows: public/evaluation key exposes at least as many samples as the secret dimension
  - C6_expansion_key_sparse_LPN_rows: q-ary block-BKW screen below 128 bits
  - C6_C4_CLPN_row_differences below target: 11.42 bits
  - C6_C4_CLPN_row_differences: public/evaluation key exposes at least as many samples as the secret dimension
  - C6_C4_CLPN_row_differences: very large public sample-to-dimension ratio; multi-sample LPN attacks require specialist review
  - C6_C4_CLPN_row_differences: q-ary block-BKW screen below 128 bits
  - C6_C4_weight3_relations_rank_capped below target: 11.59 bits
  - C6_C4_weight3_relations_rank_capped: public/evaluation key exposes at least as many samples as the secret dimension
  - C6_C4_weight3_relations_rank_capped: q-ary block-BKW screen below 128 bits
  - C6_C4_weight3_relations_raw_upper_bound below target: 11.42 bits
  - C6_C4_weight3_relations_raw_upper_bound: public/evaluation key exposes at least as many samples as the secret dimension
  - C6_C4_weight3_relations_raw_upper_bound: very large public sample-to-dimension ratio; multi-sample LPN attacks require specialist review
  - C6_C4_weight3_relations_raw_upper_bound: q-ary block-BKW screen below 128 bits
  - C4 projective blocks of width >= 2 expose weight-3 zero-message relation combinations; this must be addressed before security claims.

C6 is a diagnostic screening layer, not a certified cryptanalysis result. It corrects the C5 relation-weight heuristic by counting weight-3 projective-line relations in C4. A security-grade design should avoid full projective block dictionaries of width >= 2 or prove that the resulting relation-derived samples do not help known LPN attacks.
