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.

==============================================================================

C6 relation-surface screen for c2_design_smallq  target=128 bits
q=7 N=513 block_size=3 blocks=171 n_c=512 m_c=4096 eta_c=6.103515625e-05
C4 entries=9747  C2 entries=58482  C4/C2=0.166667
C4 public CLPN rows=39923712
Row-difference samples=81743800320  eta2=0.000122066
Raw weight-3 relations=545832  rows=2235727872  eta3=0.000183092
Rank-capped relation dimension=9234  rows=37822464
Minimum finite screen bits=27.011271140999146
Verdict=reject-for-current-security-claim

LPN screens:
  - C6_expansion_key_sparse_LPN_rows: n=512 samples=263169 eta=1.52587890625e-05 min_bits=27.011271140999146 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 is sample-limited on this fixed public surface
  - C6_C4_CLPN_row_differences: n=512 samples=81743800320 eta=0.00012206596632794283 min_bits=27.0901707332135 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 is sample-limited on this fixed public surface
  - C6_C4_weight3_relations_rank_capped: n=512 samples=37822464 eta=0.00018309243054329523 min_bits=27.13525541178229 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 is sample-limited on this fixed public surface
  - C6_C4_weight3_relations_raw_upper_bound: n=512 samples=2235727872 eta=0.00018309243054329523 min_bits=27.13525541178229 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 is sample-limited on this fixed public surface

Blockers / required follow-up:
  - C6_expansion_key_sparse_LPN_rows below target: 27.01 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 is sample-limited on this fixed public surface
  - C6_C4_CLPN_row_differences below target: 27.09 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 is sample-limited on this fixed public surface
  - C6_C4_weight3_relations_rank_capped below target: 27.14 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: very large public sample-to-dimension ratio; multi-sample LPN attacks require specialist review
  - C6_C4_weight3_relations_rank_capped: q-ary block-BKW screen is sample-limited on this fixed public surface
  - C6_C4_weight3_relations_raw_upper_bound below target: 27.14 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 is sample-limited on this fixed public surface
  - 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.

==============================================================================

C6 relation-surface screen for prototype_medium  target=128 bits
q=65537 N=513 block_size=2 blocks=257 n_c=256 m_c=1024 eta_c=9.5367431640625e-07
C4 entries=16777729  C2 entries=1099545247744  C4/C2=1.52588e-05
C4 public CLPN rows=17180394496
Row-difference samples=8787771784704  eta2=1.90735e-06
Raw weight-3 relations=12010148767727616  rows=12298392338153078784  eta3=2.86102e-06
Rank-capped relation dimension=16777216  rows=17179869184
Minimum finite screen bits=24.00070444127384
Verdict=reject-for-current-security-claim

LPN screens:
  - C6_expansion_key_sparse_LPN_rows: n=512 samples=263169 eta=9.5367431640625e-07 min_bits=27.00070444127384 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 is sample-limited on this fixed public surface
  - C6_C4_CLPN_row_differences: n=256 samples=8787771784704 eta=1.9073477233316758e-06 min_bits=24.00070444127384 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 is sample-limited on this fixed public surface
  - C6_C4_weight3_relations_rank_capped: n=256 samples=17179869184 eta=2.8610202206652566e-06 min_bits=24.001056661910717 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 is sample-limited on this fixed public surface
  - C6_C4_weight3_relations_raw_upper_bound: n=256 samples=12298392338153078784 eta=2.8610202206652566e-06 min_bits=24.001056661910717 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 is sample-limited on this fixed public surface

Blockers / required follow-up:
  - C6_expansion_key_sparse_LPN_rows below target: 27.00 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 is sample-limited on this fixed public surface
  - C6_C4_CLPN_row_differences below target: 24.00 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 is sample-limited on this fixed public surface
  - C6_C4_weight3_relations_rank_capped below target: 24.00 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: very large public sample-to-dimension ratio; multi-sample LPN attacks require specialist review
  - C6_C4_weight3_relations_rank_capped: q-ary block-BKW screen is sample-limited on this fixed public surface
  - C6_C4_weight3_relations_raw_upper_bound below target: 24.00 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 is sample-limited on this fixed public surface
  - 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.

==============================================================================

